Treatment time reduction through parameter optimization in magnetic resonance guided high intensity focused ultrasound treatments

Magnetic Resonance guided High Intensity Focused Ultrasound (MRgHIFU) treatments are a promising modality for cancer treatments in which a focused beam of ultrasound energy is used to kill tumor tissue. However, obstacles still exist to its widespread clinical implementation, including long treatment times. This research demonstrates reductions in treatment times through intelligent selection of the usercontrollable parameters, including: the focal zone treatment path, focal zone size, focal zone spacing, and whether to treat one or several focal zone locations at any given time. Several treatments using various combinations of these parameters were simulated using a finite difference method to solve the Pennes bio-heat transfer equation for an ultrasonically heated tissue region with a wide range of acoustic, thermal, geometric, and tumor properties. The total treatment time was iteratively optimized using either a heuristic method or routines included in the Matlab software package, with constraints imposed for patient safety and treatment efficacy. The results demonstrate that large reductions in treatment time are possible through the intelligent selection of user-controllable treatment parameters. For the treatment path, treatment times are reduced by as much as an order of magnitude if the focal zones are arranged into stacks along the axial direction and a middle-front-back ordering is followed. For situations where normal tissue heating constraints are less stringent, these focal zones should have high levels of adjacency to further decrease treatment times; however, adjacency should be reduced in some cases where normal tissue constraints are more stringent. Also, the use of smaller, more concentrated focal zones produces shorter treatment times than larger, more diluted focal zones, a result verified in an agar phantom model. Further, focal zones should be packed using only a small amount of overlap in the axial direction and with a small gap in the transverse direction. These studies suggest that all treatment time reductions occur due to selection of parameters that advantageously use mechanisms of decreasing the focal zone size to concentrate the power density, increasing thermal superposition in the tumor, decreasing thermal superposition in the normal tissue, and advantageously using nonlinear rates of thermal dose deposition with increasing temperature.

TREATMENT TIME REDUCTION THROUGH PARAMETER OPTIMIZATION IN MAGNETIC RESONANCE GUIDED HIGH INTENSITY FOCUSED ULTRASOUND TREATMENTS by Joshua Coon A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Department of Physics and Astronomy The University of Utah December 2012 Copyright © Joshua Coon 2012 All Rights Reserved The Unive r si t y of Utah Graduat e School STATEMENT OF DISSERTATION APPROVAL The dissertation of Joshua Coon has been approved by the following supervisory committee members: Orest Symko Chair 06/19/2012 Date Approved Robert Roemer Member 06/14/2012 Date Approved Dennis Parker Member 06/18/2012 Date Approved Jordan Gerton Member 06/19/2012 Date Approved Stephan LeBohec Member 06/19/2012 Date Approved and by David Kieda Chair of the Department of ____________________ Physics and Astronomy and by Charles A. Wight, Dean of The Graduate School. ABSTRACT Magnetic Resonance guided High Intensity Focused Ultrasound (MRgHIFU) treatments are a promising modality for cancer treatments in which a focused beam of ultrasound energy is used to kill tumor tissue. However, obstacles still exist to its widespread clinical implementation, including long treatment times. This research demonstrates reductions in treatment times through intelligent selection of the user-controllable parameters, including: the focal zone treatment path, focal zone size, focal zone spacing, and whether to treat one or several focal zone locations at any given time. Several treatments using various combinations of these parameters were simulated using a finite difference method to solve the Pennes bio-heat transfer equation for an ultrasonically heated tissue region with a wide range of acoustic, thermal, geometric, and tumor properties. The total treatment time was iteratively optimized using either a heuristic method or routines included in the Matlab software package, with constraints imposed for patient safety and treatment efficacy. The results demonstrate that large reductions in treatment time are possible through the intelligent selection of user-controllable treatment parameters. For the treatment path, treatment times are reduced by as much as an order of magnitude if the focal zones are arranged into stacks along the axial direction and a middle-front-back ordering is followed. For situations where normal tissue heating constraints are less stringent, these focal zones should have high levels of adjacency to further decrease treatment times; however, adjacency should be reduced in some cases where normal tissue constraints are more stringent. Also, the use of smaller, more concentrated focal zones produces shorter treatment times than larger, more diluted focal zones, a result verified in an agar phantom model. Further, focal zones should be packed using only a small amount of overlap in the axial direction and with a small gap in the transverse direction. These studies suggest that all treatment time reductions occur due to selection of parameters that advantageously use mechanisms of decreasing the focal zone size to concentrate the power density, increasing thermal superposition in the tumor, decreasing thermal superposition in the normal tissue, and advantageously using nonlinear rates of thermal dose deposition with increasing temperature. iv TABLE OF CONTENTS ABSTRACT.......................................................................................................... iii LIST OF TABLES................................................................................................. vii ACKNOWLEDGEMENTS.................................................................................. viii Chapters 1. INTRODUCTION........................................................................................... 1 Background Theory................................................................................... 2 Ultrasound Physics.................................................................................... 2 Heating Due to Ultrasound Absorption...................................................... 4 Modeling Heat Diffusion and Loss in Biological Tissue............................ 5 Modeling Heat Damage in Biological Tissue............................................. 6 Optimizing Treatment Times..................................................................... 7 Outline of Dissertation.............................................................................. 10 References................................................................................................. 10 2. HIFU TREATMENT TIME REDUCTION IN SUPERFICIAL TUMORS THROUGH FOCAL ZONE PATH SELECTION....................................... 12 Abstract...................................................................................................... 13 Introduction............................................................................................... 13 Methods.................................................................................................... 14 Results...................................................................................................... 19 Discussion.................................................................................................. 24 Conclusion.................................................................................................. 27 Acknowledgement...................................................................................... 27 References.................................................................................................. 27 Appendix.................................................................................................... 28 3. HIFU TREATMENT TIME REDUCTION THROUGH HEATING APPROACH OPTIMIZATION.......................................................................................... 30 Abstract...................................................................................................... 31 Introduction............................................................................................... 31 Methods.................................................................................................... 33 Results...................................................................................................... 38 Discussion..................................................................................................... 44 Conclusion.................................................................................................. ...49 Acknowledgement...................................................................................... ...49 References.................................................................................................. ...50 4. PHANTOM AND SIMULATION TEMPERATURE MATCHING THROUGH LEAST SQUARES FIT OF DOSE LINES.......................................................53 References.................................................................................................. ...64 5. CONCLUSION............................................................................................... 65 Future Work............................................................................................. .... 66 Appendices A. GUIDE TO SIMULATION COMPUTER CODE.................................... .... 69 B. SIMULATION COMPUTER CODE............................................................ 80 v i LIST OF TABLES 2.1. Thermal and acoustic properties used in all simulations............................. 16 2.2 Simulation configurations.......................................................................... 17 2.3 Scanning patterns studied.......................................................................... 18 3.1 Tissue and acoustic properties held constant in all simulations except for the changing absorptivity study......................................................................... 37 4.1 Summary of parameters used in the phantom treatments............................. 55 A.1 Summary of purpose, input variables, and output variables for Matlab scripts and functions used for treatment simulations....................................................... 71 ACKNOWLEDGEMENTS I would first like to gratefully acknowledge the constant support of my mentor, Robert Roemer, with whom I credit more than any person except myself with the completion of my doctorate degree. Through countless hours of meetings, he patiently helped me to refine and expand my research, my scientific writing abilities, and my understanding of science. Over the years of working with him, I have developed a large and growing amount of respect for Bob, both on a personal and professional level. I hope to emulate in my own academic career many of the aspects of his career, including his many contributions to science and his indefatigable work ethic. I would also like to thank Dennis Parker for initially hiring me into the group, helping me to understand the physics and basic science behind HIFU, and providing sound observations about my research that helped make the research better. I also want to thank Douglas Christensen for his help in understanding the science behind ultrasound and for his input on my research. I thoroughly enjoyed Doug's ultrasound class, and I would highly recommend it to other students. I would also like to thank the other members of the HIFU group: Allison Payne, Nick Todd, Urvi Vyas, Yi Wang, Josh De Beaver, Mohamadou Diakite, Christopher Reed, Emily Minalga, Scott Almquist, Henrik Odeen, Robb Merrill, Nelly A. Volland, Tyler and Rock Hadley. Without your contributions, this work would have not been possible. I would also like to express my deep appreciation to my family for all their love and support throughout the years of graduate school. I especially want to thank my father, John D. Coon, my late mother Maridee Coon , and my siblings John, Sandra, Andrea, and Michelle. Finally, I would like to express my appreciation to several longtime friends: Ryan Gorely, Ethan Doetsch, Jeff Keyes (and his family), and Peter Carli. This work was partially supported by grants from NIH (R01-CA134599), Siemens Medical Solutions, the Focused Ultrasound Foundation, a University of Utah Synergy Grant, the Ben B. and Iris M. Margolis Foundation, and the UCAIR facilities. A generous allocation of extensive computer time from the Center for High Performance Computing at the University of Utah is gratefully acknowledged. ix CHAPTER 1 INTRODUCTION High Intensity Focused Ultrasound (HIFU) is a promising new cancer therapy (1­8) that uses ultrasound energy to kill tumor tissue. In this treatment modality, a beam of ultrasound generated by a transducer is focused to a sharp focus (up to the diffraction limit imposed by the wavelength of the ultrasound beam) - either through the use of a phased array transducer, a lens, a geometrically curved transducer face, or any combination of the three methods - and is coupled to a patient's body through an efficient transmitting medium such as water. Similar to sunlight focused with a magnifying glass, a portion of the energy at the concentrated focus is converted to heat, which causes tissue death at the site of the focus through thermal damage. Despite the potential of this treatment modality to present an effective, relatively noninvasive method of treating cancer, challenges still exist to its widespread clinical implementation. Foremost among these are long treatment times, with treatments of several hours common (3, 9, 10). Recent research (11, 12) has shown that these times can be reduced through intelligent selection of user controllable parameters, found through treatment simulation and optimization. Below is a concise summary of the physical and mathematical theory behind this research. 2 Background Theory For HIFU treatments involving therapies that cause tumor cell death due to heat damage, there are three main components of each treatment to consider in treatment simulation routines. These components are: the deposition of heat in the body due to the ultrasound, the time evolution of the deposited energy (in the form of heat) in the body (including the resulting temperature distribution inside the body due to conduction and perfusion effects), and tissue damage caused by high temperatures. An explanation of these three components and a derivation of relevant equations is included below. Ultrasound Physics Ultrasound is broadly classified as a group of sound waves with frequencies above the 20 kHz limit detectible by human hearing (13). The medical uses of ultrasound imaging are well established, with ultrasound fetal imaging, ultrasound imaging of blood flow through Doppler effects, and B-mode imaging of biological tissues being just a few of the more well-known examples among the many possible. Ultrasound waves propagate via the periodic compression and rarefaction of a medium. As with all waves, ultrasound waves have two primary components: a longitudinal (or compressional) wave that travels in the direction of the displacement of molecules in the medium and a transverse (or shear) component that travels perpendicular to the direction of molecular displacement. In biological tissues, the transverse component of the ultrasound tends to attenuate rapidly in all substances except for bone 3 (2), so in this treatment, we will consider only the longitudinal components of the wave equation. With only the longitudinal components of the wave equation considered, the classical wave equation reduces to the one-dimensional wave equation: (11) where is the average density of the material, is the compressibility of the material, is the excess pressure above static pressure, is the direction of wave propagation, and is time. This equation holds in the "linear" domain where the amplitudes of the pressure variations are assumed to be sufficiently small to only cause small disturbances in the medium. If the amplitude of the pressure wave is too large, this assumption of small disturbances breaks down and a more advanced treatment is needed. There are several possible solutions to equation (1.1). Though a complete treatment of these solutions is beyond the scope of this text, a few simple solutions suffice to demonstrate the physics behind this equation. In general, any function 2 tt satisfying the form p = p+f ( kx + o t ) will satisfy the equation above, where k = - is - A the wave number (and A is the wavelength), go = 2 n f is the angular frequency, and p+/ - is the amplitude coefficient. A specific example of a solution is the equation: p = p+cos (kx - w t ) (12) 4 This equation can be understood when considered as a plane compressional wave traveling in the direction. Other possible solutions include a Dirac Delta pulse at time t = 0 or a superposition of sine and cosine waves. The phase velocity (the rate at which the phase of the wave propagates through space) of the wave above is given by the equation c = ^. Substitution of (1.2) into (1.1) additionally gives a relation specific to the propagation of plane compressional acoustic waves: k2 = p0K o 2 which can be combined with the definition of phase velocity to form the equation = . V p oK Heating Due to Ultrasound Absorption When ultrasound energy is produced by a transducer and propagated through biological tissue, that energy is dissipated in a number of different ways. The first way is simply through the geometrical spreading of the wave due to diffraction as it propagates. Focusing reduces the effects of dispersion due to diffraction in the beam near field. The second way in which ultrasound energy can be dissipated is through attenuation (absorption and scattering) in the medium. Under the model of a decreasing ultrasound beam due to an exponential absorption envelope, the equation for the heating due to an ultrasound plane wave is (2): Q = 2 a l ; l = l0e"2ax (1.3) 3 where Q is the heat deposited in the tissue from the ultrasound [W/m ], I 0 is the initial 2 2 ultrasound intensity [W/m ], the ultrasound intensity [W/m ] after the ultrasound has penetrated distance x, and x the penetration depth of the ultrasound into the tissue in 5 meters [m]. The equation for Q can be derived from taking the derivative with respect to x of both sides of the equation = /0e~2ax . The equation for Q follows from the assumption that heating in the tissue is entirely due to energy loss from the ultrasound beam as it passes through the tissue. One of the main purposes of beam focusing in HIFU is to increase the ultrasound intensity at the focal point, effectively increasing by increasing / . Modeling Heat Diffusion and Loss in Biological Tissue The evolution of the heating inside the body as a function of time can be modeled using the bioheat transfer equation (14): pc ^ = Vk(VT) - W( T - T o ) + Q (1.4) 3 where p is the density of the tissue [kg/m ], c is the specific heat of the tissue [J/(kg*C)], k is the conduction coefficient [W/(m*C)], W is the perfusion coefficient [kg/(m *s)], and Q is the applied power density from the ultrasound [W/m ]. The bioheat transfer equation can be derived by tracking the heat flow through the body through conservation of energy. Read from left to right, the time derivative of the temperature vector is equal to the heat dispersion due to conduction plus the heat lost due to perfusion plus the heat deposited due to the ultrasound. The perfusion term is often called the Pennes term and is what makes the heat equation become the Pennes bioheat equation. In this model, the process of perfusion is modeled as a uniform heat sink that removes heat from the equation based solely on the temperature difference between the 6 tissue temperature and the ambient body temperature. This is in contrast to more complicated models of heat flow that model the perfusion term as a tensor that is dependent on the specific geometry of the underlying vascular network. Modeling Heat Damage in Biological Tissue Finally, the damage done to tissue due heating can be modeled using the empirical formula (15) CEM = rC/ R T - 4 3d t (1.5) to where CEM are the cumulative equivalent minutes of thermal dose delivered to the tissue, is the integral starting time, is the integral end time, is the temperature of the tissue in Celsius, and dt time differential (in units of minutes), and R and 4 3 are empirically determined reference constants where R = 4 if 3 7 < T < 4 3 degrees and R = 2 for T > 4 3 (16). This formula was derived from experiments in which cell cultures were heated and the percentage of cell populations remaining alive at intervals were recorded and fitted to the model using a computer program. While more refined models have been developed by subsequent research, this equation remains a good approximation for the amount of thermal energy that needs to be deposited in tissue in order to cause cell death, and it is still used by many researchers when investigating HIFU and other hyperthermia treatments. 7 Optimizing Treatment Times In the process of mathematically optimizing treatments in order to reduce treatment times, there are several constraints that are often imposed to ensure the goals of treatment safety and efficacy. One such constraint to ensure treatment efficacy is that all tumor locations receive a minimum thermal dose by the end of the treatment. Additionally, concern for the health of the normal tissue surrounding a tumor often dictates that safety constraints are imposed, whereby either a temperature limit or an accumulated thermal dose limit are set for the normal tissue (outside of a small "margin" near the tumor edges). A more detailed explanation of these requirements are available in several places, for example, in Chapter 2. Mathematically, the efficacy requirement can be expressed as: M in (Dj'Umor) > Dfi0or (16) Where D Tumor is the thermal dose deposited in the tumor(15) by the end of the treatment and is the minimum allowable thermal dose for an area to be "treated". In most cases, value of DF10or is taken to be 240 CEM (15). Similarly, the safety requirement for a temperature constraint in the normal tissue can be expressed mathematically as Max(TNT) < TLimit (17) 8 where is the temperature in the normal tissue at any point during the treatment and Tu m it is the maximum temperature allowed for any part of the normal tissue. As a corollary, the safety requirement for a maximum dose constraint in the normal tissue can be expressed as Max (Dn t ) < Dlimj t (18) where is the maximum thermal dose deposited in the normal tissue by the end of the treatment and is the maximum allowable thermal dose in the normal tissue at the end of treatment. A tightly focused focal zone from a HIFU transducer typically has dimensions on the order of a 1mm diameter in the transverse direction and 1cm in the axial direction (for example, see (11)). As the typical dimensions for breast tumors are typically on the order of several cubic centimeters (17), it is often necessary to scan the focal zone between several points in a HIFU treatment. Indeed, in most HIFU treatments, the typical set of user-controllable parameters consist of the transducer power output (possibly as a function of time); the transducer power on and off times; and the focal zone size, shape, and path through the tumor, as explained more fully in other research (18). For most HIFU treatments, the combination of the six user-controllable parameters mentioned above means that there are multiple treatment configurations possible on the same tumor geometry. Because the number of possible treatments scales as the factorial of the possible user-controllable variables, in practice it is not possible to evaluate every possible treatment for an initial tumor geometry. Therefore, it is usually 9 highly desirable to select a treatment from the large space of possible treatments through the use of an optimization scheme. Many optimization schemes exist, and a comprehensive review of these schemes is beyond the scope of this work; although, it is available in several other places (19). In brief, most optimization schemes follow the same basic heuristic to find an optimized solution in a large treatment space: 1. Evaluate the objective function (possibly subject to one or more constraint functions) at a "starting guess." 2. Use selection criteria to select a new point for evaluation. 3. Evaluate the treatment at the new point, possibly subject to constraints. 4. Repeat steps 2-3 until the stopping criteria have been met. For the optimization schemes presented in this work, the evaluation criterion was the total treatment time (i.e., the treatments were optimized to minimize the total treatment time). Mathematically, this can be described as t trea tmen t = ^ n=1t he a tn t co o ln (19) where ttre atme nt is the total treatment time, the atn is the heating time at position n and tCo o l n is the interpulse cooling time for the position n. The constraints on this objective were exclusively equations (1.4) and (1.5), although the use of equation (1.6) instead of equation (1.5) would also have been possible. New points were mostly selected by using an interior point method (19), sequential quadratic programming (19), or a heuristic grid 10 search algorithm (11). Stopping criteria were chosen as the convergence of the function to below a user specified tolerance. Outline of Dissertation The outline of the dissertation is as follows. Chapter 2 and 3 are papers that have been accepted and published by the International Journal of Hyperthermia (in 2011 and 2012). Chapter 4 is an addition to the main body of research in Chapter 3 that will be submitted for publication as a technical note in the near future. Chapter 5 contains the major conclusion of this work and directions for future research. The Appendices which follow Chapter 5 contain explanations of and examples of the code used for this research, simplified for user readability. References 1. Fennessy FM, Tempany CM. MRI-guided Focused ultrasound surgery of uterine leiomyomas. Academic Radiology 2005;12(9):1158-66. 2. Hindley J, Gedroyc WM, Regan L, Stewart E, Tempany C, Hynnen K, et al. MRI guidance of focused ultrasound therapy of uterine fibroids: Early results. American Journal of Roentgenology 2004;183(6):1713-9. 3. Illing RO, Kennedy JE, Wu F, ter Haar GR, Protheroe AS, Friend PJ, et al. The safety and feasibility of extracorporeal high-intensity focused ultrasound (HIFU) for the treatment of liver and kidney tumours in a Western population. Br J Cancer 2005;93(8):890-5. 4. Hynynen K, Pomeroy O, Smith DN, Huber PE, McDannold NJ, Kettenbach J, et al. MR imaging-guided focused ultrasound surgery of fibroadenomas in the breast: A feasibility study. Radiology 2001;219(1):176-85. 5. Hesley GK, Felmlee JP, Gebhart JB, Dunagan KT, Gorny KR, Kesler JB, et al. Noninvasive treatment of uterine fibroids: Early mayo clinic experience with magnetic resonance imaging-guided focused ultrasound. Mayo Clinic Proceedings 2006;81(7):936- 42. 11 6. Daum DR, Smith NB, King R, Hynynen K. In vivo demonstration of noninvasive thermal surgery of the liver and kidney using an ultrasonic phased array - Comparison of strategies using phased array systems. Ultrasound Med Biol 1999;25:1087-98. 7. Damianou C, Hynynen K. Focal spacing and near-field heating during pulsed high temperature ultrasound therapy. Ultrasound Med Biol. 1993;19(9):777-87. 8. McDannold NJ, Jolesz FA, Hynynen KH. Determination of the optimal delay between sonications during focused ultrasound surgery in rabbits by using MR imaging to monitor thermal buildup in vivo. Radiology 1999;211(2):419-26. 9. Coon J, Payne A, Roemer R. HIFU treatment time reduction in superficial tumours through focal zone path selection. International Journal of Hyperthermia 2011;27(5):465-81. 10. Payne A, Vyas U, Blankespoor A, Christensen D, Roemer R. Minimisation of HIFU pulse heating and interpulse cooling times. International Journal of Hyperthermia 2010;26(2):198-208. 11. Christensen DA. Ultrasonic Bioinstrumentation. New York: Harper & Row; 1988. 12. Pennes HH. Analysis of tissue and arterial blood temperatures in the resting human forearm. Journal of Applied Physiology 1948;1(2):93-122. 13. Sapareto SA, Dewey WC. Thermal dose determination in cancer therapy. International Journal of Radiation Oncology Biol Phys 1984;10:787-800. 14. Cheng KS, Roemer RB. Optimal power deposition patterns for ideal high temperature therapy/hyperthermia treatments. International Journal of Hyperthermia 2004;20(1):57-72. Epub 72. 15. Fisher B, Slack NH, Bross IDF, Investigators C. Cancer of the breast: Size of neoplasm and prognosis. Cancer 1969;24(5):1071-80. 16. Payne A. Minimization of thermal dose delivery time and development of an isolated kidney phantom: Applications for high intensity focused ultrasound [Ph.D.]. Utah: The University of Utah; 2008. 17. Nocedal J, Wright SJ. Numerical Optimization. Secaucus, NJ, USA: Springer; 1999. CHAPTER 2 HIFU TREATMENT TIME REDUCTION IN SUPERFICIAL TUMORS THROUGH FOCAL ZONE PATH SELECTION Reprinted with Permission from Informa UK Ltd. International Journal of Hyperthermia, Vol. 27, No. 5, Pages 465-481 Joshua Coon, Allison Payne, Robert Roemer lot I lUfwnfceenu iXmakuil&S from *fc«n.4w.iltfkiirecafn h> I HI C‘rculxii« * >Wik‘ > l fcJMt-iu«k> lidc« 11.* 1V12 f*cr pncttd m cMkly- 13 Int. 3- Hyperthermia, August 2011; 27(5): 465-481 informa hcattrtcjre RE SEA R CH ART IC L E HIFU treatment time reduction in superficial tumours through focal zone path selection JOSHUA C O O N 1, ALLISON PAYNE" ', & ROBERT ROEMER- ' * 1 Department o f Physics atld Astronomy, Unh'ersity of Utah, Salt Lake City, 2Department of Mechanical Engineering, University o f Utah, Salt Lake City', yUtah Center of Adi'anced Imaging Research (UCAJRJ, University o f Utah, Salt Lake City, and ^Department o f Radictogy, University c f Utah, Salt Lake City\ Utah, USA (Received 22 A f jv 2010; Revised I February 2011; Accepted IS February 2011) Abstract Purpose: This study evaluates the hypothesis that optimising the path of a high intensity focused ultrasound (HIFU) treatment's N focal zone heating pulses can significantly reduce treatment time, and identifies the underlying bio-thermal principles. Ataierijls and meihodr. Thirty-one scanning paths were investigated using 3D simulations, with a minimum thermal dose delivered to every tumour position. Treatment rime was calculated as the sum of the N , individually optimised heating and cooling periods. Tumours were superficial (skin to tumour distance ranging from 1.3 to 2.5 cm), but always deep enough so that the pre-tumour normal tissue was routinely heated to its constraint temperature (range: 42-45 C). Properties were uniform and constant, and a range of blood perfusion and phased array powers were studied. Resuhr. The best paths signiiicandy reduced treatment times, with the largest gains occurring when (I) temperature superposition inside the tumour was maximised by successively heating the focal xone positions located in a ‘stack' along the transducer's axis, and (2) the focal zone was moved laterally to an optimised location and another stack was applied. Stacking takes advantage of the focal zone's elongated shape, which produces axial temperature superposition within the tumour. Reduced tumour heating times also reduced energy* deposition in the normal tissues, thus reducing o r eliminating the need for inter-pulse cooling. Cvncluskmr. HIFU treatment times can be significantly reduced by taking advantage of axial temperature superposition in tumours. Further reductions are obtained by correct choice of the transverse scan path. Keywords! High intensity jbeused ultrasound, AtRgHIFU, p*i/A cprimisMon, umuLitirns, treatment time Introduction High intensity focused ultrasound (HIFU) has been shown to be a promising treatment method for several types of cancer and for uterine fibroids [3-8]. However, when considering large tumours embed­ded in critical normal tissues, the requirement of precisely placing and applying a large number of heating pulses can result in very long treatment times [3, 9, 10], with McDannold et al. [10] recommend­ing at least 50-60 s of cooling between pulses and Fennessv and Tempany [3] using 20-40 s of heating followed by 80-90 s of cooling. For example, 100 pulses with 30 s of heating and 60 s of cooling per pulse would take 2.5h just for delivering the desired dose, not including treatment preparation time, adjustments and complications. Such long times pose a major challenge to HlFU's broad clinical acceptance. To reduce treatment times, clinicians can control: the electrical power delivered to the transducer; the sequence of focal zone positions; the heating pulses' periods; the inter-pulse cooling periods; and, for a phased array, the size and shape of the focal zone [1 1 ]. One way to reduce treatment times is to simulta­neously optimise all of those parameters. However, because of the computational intensity involved ______ C or f y u r u l i c a : >.-«hu j C o o n , I ) « p s ia M n i a l F t r a i and A « re * u im y . t-'n iva n tiy o f L 'n h , Salt I j i r C ity . T i l : l*OI> 4 I 7 -1 J » V P n i'BOI'i S l l - i M I. K-nual ( c l o j JTiitoocna 1S SX ©2o > -o 7 S© petm IS SN l* »V 5 l i 7 online C 2011 InOirmj V K l - i i OOt ia.SI0«O2a>e79o.a0ll.»»4i07 IfiC J .il'.TVrtb.'OTi 14 iKvftakVJiiJ Ic-.Vii thIlWi£aialifeaJJfdCGB1 t>\ I ILl JilV - A-J-iL'V HjM fcUUHU I.CJ C* 1 1 ,'Ii'll Hv [UTHL-Ail uj ‘.'■aly 14 in simultaneously optimising the large number of possible combinations of parameters, prior research [J, 4, 6, [5, 12-14| has commonly addressed i fixed treatment path and parametrically changed one of the other treatment variables, including the: applied power magnitude [1 J j ultrasound frequency [[5] and; inter-sonication delay period [10]. Most inves­tigators have used fixed beating pulse and inter-pulse cooling periods to both provide standardised heating conditions and to avoid normal tissue overheating [3, 4, fi, 14-16], Because af cificacy and safety concerns, such protocols used conservative heating and cooling periods, resulting in very long treatment times [6, IS]. To help reduce those times, recent research has developed an approach that minimises each individual pulse heating and inter-pulse cooling period during a treatment, resulting in significantly reduced treatment times [17]. That study also showed that larger applied powers always shortened treatments for focused transducers, a non-obvious result when normal tissue constraints are active. They employed the strategy of developing separate optimising approaches for individual treatment parameters (e.g. heating and cooling periods), with the goal of eventually combining all individual approaches into a comprehensive optimisation approach. The current study extends the use of that strategy by optimising one more treatment variable, the focal zone scan path. Only a few studies have investigated the effects of scan padi, and none have been concerned primarily with treatment time - except Payne et al. [17] which only compared two path?-. Fan and Hynvnen [13] considered three two-dimensional planar paths applied sequentially to two planes perpendicular to the transducer's axis. They used fixed beating and cooling period; and thus did not study treatment time; however, they did show that the volume of tissue ablated was palh dependent. Liu et al. [19] performed a numerical study of two heuristic paths (least possible distance and greatest possible distance between sequential small rapid scanning volumes) and showed Lhat cumulative heating time differences {rooling times were fixed at I min between sonica-tions) of several minutes were possible, depending on which pith t o used. More recently Kohler et al. [20|, in an experimental study that was extended by Enholm et al. [21], and was based on that group's earlier work with nested spirals [22, 23], used a foca] zone at a fixed axial depth that was rapidly electron­ically steered ill concentric 2D circles going sequen­tially from inward to outward. They used fixed heating times for their circles and thus they did not provide any comparative information on optima] treatment times. lrinal]yh in a 2D and 3D (spherical tumour) computational study, Alalinen et sL [2-1] developed an optimisation algorithm that found the 466 J. Coait et aS. scan path that minimised the total dose delivered to the tumour while guaranteeing minimal dose at all locations. Again, treatment time was not the study's focus, hut a more uniform dose delivery would, presumably, help shorten treatments - a reasonable belief bolstered hy comparison of their results to those from a ‘standard, non-optimised' path. In summary, while several investigators have studied the role of separate physical mechanisms in reducing treatment times, no study exists that concentrates on the effects of scan path on treatment time. Thus, although several different palhs have been proposed and studied by individual investiga­tors, at present no type of scan path has been shown to be preferable - regardless of differing claims by various investigators. The current research attempts to help shed light on thi* problem by providing direct comparisons of l£ie treatment times needed by a range of scanning paths to treat the same tumours under simple, standard conditions of fixed, uniform tissue properties. Such results will help guide, and be a reference base for, future studies on mone complex clinical situations. Methods The goals of this study were- to determine whether significant treatment time gains could he obtained by optimising the scan path when significant normal tissue heating was present, and toidentiiy the thermo­physical mechanisms underlying those gains. To do so, numerous treatment scenarios were simulated using different scanning palhs, tissue perfusions, transducer powers, tumour sizes and depths, and normal tissue constraints. In this study we concen­trate on superficial tumours, hut with all such tumours located at a sufficient depth so lhat there was sufficient 'pir-focaJ1 normal tissue between the skin and tumour so that normal tissue overheating due to scanning-related thermal build-up was a significant factor in differentiating among scan paths. Treatment time Each scan path involved a sequence of X discrete focal zone locations, at each of which a heating pulse was applied and a subsequent power off, inter-pulse rooling period was initiated (if needed) to avoid heating the normal tissue past its constraint value (generally C) during the next heating pulse. Each palfi's treatment time (Ztkeat) wbs calculated as the sum of its N heating and >J-1 inter-pulse cooling periods: K I lK lL lT = ^ + ^fCorf.n) (1) n = I R I G H T S LI M K4^r IfiC J .il'.TVrtb.'OTi 14 iKvftakVJiiJ Ic-.Vii th IlWi£ a iaJifeaJJfdCGB1 t>\ I ILl L'rt&il JilV - A-J-iL'V HjM fcUUHU I.CJ C* 11,'I i'll Hv [UTHL-Ail uj ‘.'■aly 15 Here, and art the pulse heating period and the subsequent inter-pulse cooling period for ihe nlh heating pulse. Each heating pulse was applied at the same total transducer power magni­tude it every fatal zone position within a tumour. In order to find die palh that minimised Iiukjit a scan palh was set, the pulse's heating and Inter-pulse cooling periods were Individually minimised at each of the X sequential focal ion: positions, and Itkiht mas -calculated and evaluated with respect to all other paths' treatment times values. To find the minimal heating and cooling times at each focal zone position, the simulations, used the approach of Payne et al. [IT in which each pulse's heating period was made just long enough so that the desired thermal dose was delivered to the focal zone {as determined both during that heating pulse and during ihe immediately ensuing decay of the focal zone temperature); and power was then turned off during an inter-pulse cooling period that was also optimised. This approach ensured that every path studied was standardised to consistently meet the same important conditions; ihe same applied power magnitude was used far every pulse, and every heating and cooling period was individually optimised. The thermal dose [25 was monitored in the hottest voxel of the fid] width half maximum region of ihe focal zone's specific absorption rate (SAR) pattern, and the inter-pulse focal zone spacing was made small enough to ensure that the tumour was treated to at least 240CEM43 C at all locations (as verified after each treatment). Any ‘prior dose' delivered (i.e. delivered to the -current focal zone position during earlier heating of other faca] zone positions) was subtracted from the target dose before the optima] heating and cooling periods were calculated. Conversely, no accounting for future dose was implemented. That is, the dose that will be delivered to the currently heated position by later pulses was not anticipated, an approach that results in the (clinically conservative) overdosing of some tumour locations. The metric used for comparing scan paths, the treatment timeh is equivalent to a rate of thermal ablation when a feted tumour volume is divided by the treatment time. Thermal model Temperatures i c e calculated u s in g the Pennes bio-heat transfer equation [2b]: f C ^ = lrfl T -W C l{ T - T l ) + 1l t (2> in tvherc T is temperature ( C],. p is the tissue density (kg-'m3), C is the specific heat of tissue C), k is the thermal conductirity of the tissue (Wm C), 0_-f, is the applied power density deposited by an external applicator [F Is the Fennes ptrfusion parameter (kg'fu' s), Cf. is the specific heat of blood and Tt Is the arterial blood temperature. Although this equation has its limitations, it has been shown to adequately predict the major aspects of in vivo experiment [26-29], An explicit finite-difference approximation of Equation 2 was implemented with a temporal resolution of one second and a spatial resolution of 3 x 3 k 1mm. These resolutions ace similar to those in Malinen's study [24| which used an isotropic 2-nim finite element nodal spacing, and 0.5-s time steps. Their preliminary studies showed that finer spatial resolutions did not significantly affect their results, a finding similar to ours for the ] -s time step. Also as In that study: all boundary conditions were kept at 3 7 ^ , as were the initial conditions; tissue properties were constant: and iheir computational region size was chosen to include the major features of the scanning process (primarily the heating of the proximal and distal normal tissues, and the tumour), while being mindful of the computa­tionally intense optimisation problems being solved. The present study used a comparable computational region size for the same reasons. We applied i range of normal dssue temperature limits [42 , 45 , and ■(5 C) on constraint planes located I cm behind and in front of the tumour - which Is the location where the maximum normal tissue temperatures almost always occurred due to thermal build-up, a phenom­enon that is minimal in the transverse direction due to ihe rapid transverse fall-oiT of the focal zone's SAR pattern. PiUiw dcpositwu The power deposition pattern was determined as in Fayne et al. [17] using the HAS (hybrid angular spectrum,) method [30] to simulate the SAR field from an existing ultrasound phased array with 25b elements arranged randomly on a spherical surface (Imasonlcs, Kesancon; France), with the focal zone steered electronically In the axial direction and mechanically in the transverse direction (Image Guided Therapies, Bordeaux France). The HAS method is an extension of the traditional angular spectrum, melhod to Inhomogeneous tissues and has been found to he bolh accurate and much faster computationally lhan olher methods (i.e. the Raylelgh-Sommerfeld Integral) [50], The resulting focal zone size, expanded to adjust for scattering and transducer element variability, is * 10 mm yPJiUM) which is lery close to that seen when using this phased array to heat agar phantoms and ex vivo tissues [3]'. The simulated tieatment geometry is shown In Figure 1. Every tumour studied was treated wilh heating pulses at three focal zone depths along the trans­ducer's axis (a direction). Thus, three electronically hitimatiemd Jamud of Hyperthermia -167 R I G H T S LI M K4^r I«i llvfotfttonu IXr* akuvkd from AloanJ^*jlihca(CCi«ih> I HI (Vculxiuft >V&k) Udt* ll.'l V!2 Vet f&MWl m oaly. 16 468 J. Coon et al. steered power deposition distributions mere simu­lated for each tumour, one for each focal zone depth. Each of those distributions was translated in the x-y plane at its fixed depth to obtain the SAR Figure 1. Geometry of the treatment domain. The origin k located in the ccntrc of the transducer's face. The geometric focus of the transducer is at 13 cm and the water fined distance from the transducer to the skin is 11..I cm (11.0 for some simulations, as measured from the ccntrc of the face of the transducer). A small <1.1 cm1) and medium (2-6 cro*) volume tumour were studied svith this geometry. A deeper medium and a larger (4.5 cm1) tumour were studied with a slightly modified geometry using an expanded simulation region. distributions for the tumour's (N. 3) transverse posi­tions at that depth. This approach simulates mechan­ical scanning in the transverse directions. The focal zones' peak absorbed power density values (Wm 5) used were all below the conservative limits set by the FDA [32] to avoid cavitation. For every scan pattern the total applied transducer power was the same at all N locations, and was fixed at a value that gave a maximum absorbed power density (in the hottest voxel) of 0.67 x 10' \V m' when the focal zone was centred on the front plane of the small, superficial tumour studied (Figure 1). This power density value is close to optimal in the sense that lower values yield significantly longer treatment times, while larger values give only small gains in treatment times, a prior result [17] that was confirmed in the current study (Figure 6). The property values used arc shown in Table I. Tumour models Four tumour geometries were studied (Table II), labelled as small superficial, medium superficial, Tabic I. Thermal and acoustic properties used in all simulations [1, 2]. Thermal conductivity, * (W.'m' Q Spca&c heat, C (J kg Q Speed of sound, c (ms) Attenuation coefficient, u (nP m MHz) Density, p Paines' perfusion, i r (kg mVs) 0.5 4190 1 Wood and tissue) 1500 (tissue 2nd water) 4.8 1000 0.5, 1.0-10 Pertustan kg^tn^s) Figure 2. Treatment time vs. perfusion for three focal zone paths treating the small superficial tumour with 45 positions with the standard total applied power and a range of perfusions. Also shown are the percentages of the treatment time spent cooling the normal tissue. The lines arc for the AS (MBF}, XY ;Ra) (squares'; 3D Kn (circles) and PL (BMF), XY Ra [triangles) scan panems. R I G H T S L I N K<^- IfiC J .il'.TVrtb.'OTi 14 iKvftakVJiiJ Ic-.Vii thfaffil£aiaJifeaJJfdCGB1 t>\ I ILl L'rt&il JilV - A-J-iL'V HjM fcUUHU I.CJ C* 1 1 ,'Ii'll Hv [UTHL-Ail uj oaly 17 Inttmational Jmmtd of Hypwthirmm -869 iT.cidiu.rn deeper, and Larger. The choice of geome­tries was mad: in ondcT 1o prohide (1J a reasonable range of sizes (ihe largest tumour dimension in the current study was - 2 cm, a value near the middle of the range for the largest tumour dimension reprc'- senting approximately ] 3 of breast tumours [33]J, {2) tumours it several depths, including depths where significant axial electronic steering was needed, wilfi its concomitant foca] zone SAR reduc­tion, and (3) tumour sizes and dimensions similar to those used in other pith studies, e.g. Liu et al. ind Malinen et a], 115, 24]. The tissue region dimensions for the small and medium superficial tumours were 3.3 x 3.3 x 3.] cm, while for the medium deeper and larger tumours ihey were 3.3 x 3.3 x. 5.1 cm. Ttiese region sizes ire close to those used by Malinen et al. [24|. Ta verify lh.it the region size was large enough to prevent boundary condi don induced changes in scan pith rankings, multiple additional simulations were performed using a larger, region up to 1*8 x L8 v 1.4™1, The larger region gave the same rank ordering of scan paths as the smaller region. Ttie focal locations woe spaced 3mm apart in all three directions for all tumours except for the larger tumour, for which the foca] zones were 6 mm apart in the c-direction. The 3-mm axial spacing had considerable axial SAR overlap among the three axial focal zone positions wilhin a ‘focal zone stack' and was thus a conservative spacing ensuring that all voxels within ihe tumour achieved a minimum dose of 240 CE.M.This matches the recommendation of a prehious study [IK] that some foca] zone overlap is present to avoid untreated regions in the tumour. This 3-mm spacing is on ihe same order as ihe 2-m.m spacing between focal zones used by Fan et al. [34] [which is more conservative than the 5-mm axial and 3-mm lateral spacing used by Hynynen [ti|), and is similar to the 4-mm inner annulus diameter used by Kohler et al. |20|. The 6-mm aaal spacing used in the larger tumour provided a Larger spacing that could treat ihe tumour in a reasonable amount of treatment time while still prodding enough SAR overlap to avoid region?, of untreated tumour tissue between focal zones. FinaJly, for the more difficult to treat ‘medium deeper' and ‘larger1 tumours a higher normal tissue temperature limit was used (45 C) for the constraint locations, which were deeper in the tissue and thus further from the skin's nerve endings. Post-treatment analysis of the normal tissue temperatures showed that this higher limit (.imposed to speed treatments) was approximately equivalent to a 30 CEM dose limit. Even ihough the tumours studied were super­ficial, near-flcld thermal build-up activated the nomial-tissue tissue constraints requiring interpulse cooling for approximately 9(V% of the paths studied. {>alhs llue to the extremely large number of possible paths (approaching Nr) an exhaustive search was not practical. The 3] paths studied are a combination of ones that are exactly or roughly equivalent to those used previously [13, 14, [3, 20,. 24], plus several that appeared promising due to- potentially improved tumour heating an&'or decreased normal tissue heating. The paths are broadly categorised as: axially stacked (AS), planar [PIJ, and 3-dimensional (31>J. TTithin each category multiple patterns were studied, as summarised in Table [II, while Figures 3 and 4 ahow example patterns. For the axially stacked patterns, when the trans­ducer is located at a given transverse (X-Y) location these patterns first treat aJl three axial focal zone positions in an ordered 'stack' (e.g. successively in a straight line alon g the z-axis in one of the six possible sequences invoking the back (B), middle (Al), and front (F) treatment deplhsj. That axial stack sequence is then repeated at multiple, sequential, transverse locations which, taken together, cover the complete tumour. These transverse patterns include raster scans, which have been used by [5, [3], Annular scans, which have been applied clinically in hyperthermia treatments and HIFU experiments [20, 22, 35-37], and knight jumps (the L-shaped moves from a chess gamc^, which were studied in an attempt to reduce normal tissue cooling times by using a transverse pattern lhat had a fixed distance Table ]J. 5unu[3[ian cvr.ri^jruLioir.. All dssmnjcra arc cnicn ir. err. from Die [ransduccr'^ ocixcre, the ltj r.v.l'j'j j-r pjc-jnciric focus- Is ac 13 n n , and j II duncr-sLcr-s at? in err.. coar-iinact oriar ii X , ¥, Z. SmiU .Medium, superficial Medium, deeper Larger Number cfFZs 45 IDS 1CIS tas Treatment -gid 1 * 5 x 3 6 x 6 x 3 6 x 6 x 3 6 x 6 x 3 Skin disun ce 114 ] 1.4 11.0 ] LQ TrcjttDcnn plane dinanccs 12.7, Li.D, 13.5 12.7, 13.0, L3.3 0 .5 , 13.S, ] L.l 12.4, 13.0, LJ.fr Coauniuu plane dis-ianccs 11.7, 1-L.i I].7, ]J.3 in ] L. l, L4Ji Tiunour dimensions 1.5 x 0.9 x 0.S ljfl x l.B x £LS ].3 x i.ftxo.a L.Sx L.S x 1.4 NT ennsnjim f C)i 43 J2, J2.5, 11 45 IS OdstiDK from tumour to 5-tin 1.3 ] .l 2.5 1.4 R I G H T S LIIM K^> loci llvfotfttonu iK.rttkuJcd frctn AloenJ«j]ifccj(CCc«oK I HI ('*culxio* >V&kt Udta ll.'I.Vll f or fw^eu] um; caly. 18 I«i llvfotfttonu lXr* akuvkd from AloanJ^*jlihca(CCi«ih> I HI (Vculxiuft >V&k) Udt* ll.'l V!2 Vet f&MWl m oaly. 19 International Journal of Hyperthermia 471 IT 10 2r, 21 22 5 6 7 K * * 16 1 2 9 24 * 1$ 4 y lo 25 M 14 13 12 II 2«v » 3o 27 2* 27 1 22 34 8 2«> 16 33 13 .Vi 15 23 7 21 i 9 6 17 28 12 31 14 24 35 5 25 20 X li> 27 18 32 II 26 19 4 36 1 2 3 io II 12 S 9 4 17 18 13 7 6 5 16 15 14 19 2» 21 2s 20 30 26 27 35 36 31 25 24 23 34 33 32 1 2 3 4 5 6 14 15 16 17 18 7 13 12 II Id 9 8 19 2i> 21 23 24 32 33 34 35 36 25 31 30 29 2S 27 26 Figure 4. Axial view of four tnmsverve, XY paths used to scan an axial suck: inner middle outer (IMO), concentric annuli (top left), knight (top right), adjacent vquarc annuls (bottom left), and adjacent rectangular annuli (boctorn right). diagonal in the treated volume, etc.). resulting in numerous small separations at the end of the treatment, (2) a ‘3DMaxLast' path (generated by-reversing the order of the maximum first path), and (3) a ‘3D knight' path, generated with 3D knight jumps between successive (x.y.s) focal zone locations, thus providing a relatively large fixed distance between all successive scan locations for the complete treatment. Finally, 100 randomly generated 3D paths were studied for the small superficial tumour. Elemental reference cases Four elemental reference cases that are composed of "building blocks' from which more complex paths are constructed were developed and arc presented in Appendix A. These cases serve as a reference base against which to compare the treatment time gains seen in the individual paths developed below. Results Results arc presented in terms of the scan path treatment times. For most cases the ‘standard treatment conditions' of a fixed applied transducer power level (giving a front treatment plane maximum power density of 0.66 x 10' Vi'm5 for the superficial tumour), a perfusion magnitude 0.5 kg m's (typical for muscle tissue [1]), and a 6 C normal tissue constraint temperature were used. Due to the large number of paths and treatment conditions studied, and the lengthy computations required for the optimisation of the heating pulse and inter-pulse cooling period at every focal zone position along each path, computation times of over a week on a large, multicore computing node were sometimes required to find the treatment time for a single path. Thus, when it was clear that a scan path being studied had treatment times far from optima] (e.g. the optima] treatment time was already significantly exceeded after only half of the tumour was scanned), the treatment times were extrapolated to an estimated final time, and the results indicated by asterisk. Effects of scan path To illustrate the large effect of scan path, Figure 5 presents the treatment times for fourteen scan paths with the standard treatment conditions for the medium superficial tumour. Clearly the axially stacked X-Y raster scans with the heating pulses starting in the middle of each stack (the AS (MFB), XY Ra and AS (MBF), XY Ra scans) arc the fastest, with treatment times that are a factor of 5.5 better (6.7 vs. 36.7 min) than the worst case simulated, i.e. the PL (BMF), XY raster scan that successively treats the back, middle and front planes with XY raster scans. (They arc also a factor of 4.5 better than the case of all N pulses applied indcpcndcndy, i.e. than the "independent pulse' case given in the appendix (6.7 vs. 30 min).) The small superficial tumour was also studied with most of the paths in Figure 5, and the resulting R I G H T S L I N K<^- IfiC J .il'.TVrtb.'OTi 14 iKvftakVJiiJ Ic-.Vii thIlWi£ a iaJifeaJJfdCGB1 t>\ I l!-l JilV - A-J-iL'V HjM fcUUHU I.CJ C* 11,'Ii'll Rv [UTHL-Ail tat! L*]V- 2 0 472 J. CtwuetnL (MFEfl |M 3 F | (MFB) I RE Ml (3= MB) Man H a n Kn |FHM| iJErHj i|E,VF| (BHUT| (BMF) [BMFj KYRJi XYRa XVRa XVRa X V R i La sl First SCYKn KYRa KYHa XYKn XYRa XZHa F D C i z o n e p a lh Figure 5. Ttdacmcivi time tv. scanning path sypd Jar the mcdaum s-irpcrficiaE tu rn o n r (106 focal zari£ positions.'; and the itandardl rrca orient conditions. A lia shown are the pcrccnia.£cs a f lh c trcBnneni time spem cooling she normal tissue. WTicn the oaaLing lime pcncenitagM arc nearly identical, only w h value (located bciewecn che p n h s with similar v a ly « ) u shown. relative path rankings n m unchanged from those in Figure ?. The small superficial tumour was also treated with 105 randomly generated paths, with their treatment times all lying roughly midway in the relative pith rankings. Effxts 0/ applied pjiL'cr Jiid perfusion Figures b and 1 show the effects of applied power and perfusion magnitude on the treatment times and the relative rankings of die scan padis. Results are shown for one of die best (AS (MBF), XV RiJ, worst (PL (EMF), XY Ra) and middle (3DKn) scans from Figure 5. (The odier scans from Figure 5 that were studied at different powcm and perfusions followed the trends in Figures S and 2, and are thus not shown.) H e trends of decreasing treatment times with increated power in Figure 6 are the same as shown previously [17] and illustrate why the stan­dard power density level of 0.66 x ]0TWi'm' was chosen - since larger powers yield only margina] treatment time gains, while lower powers greatly increase the treatment times. Figure 2 shows that far the best cases (e.5 . AS (MBFf, XY Ra scan) far which no normal tissue constraints are activated even at Low perfusions, increasing die perfusion magni­tude provides no additional benefit in the normal tissue and makes it harder to heat the tumour, thus increasing the treatment times. Conversely, for the slowest scan patterns (e.g. the FL (BMP), XY raster scan), which already have long treatment times at low perfusions (since they activate the normal tissue constraints so frequently), increasing the perfusion cools the nocma] tissue, and ihus reduces the treatment times. A small number of scans were also performed in a tumour model with heterogeneous perfusions, where the tumour perfusion level was twice the normal tissue perfusion. These scans used a subset of the paths described above, and in all cases the ranking of the paths was unchanged from those in Figure 5. To illustrate why the axiaJly stacked scans have the shortest treatment times and other scans have much longer treatment times. Figure 7 shows the heating and cooling times at each successivc position for the AS i.MBF), XY Ra and ihe FL IB.MF), XY raster paths for ihe medium superficial tumour. In Figure 7A, the benefits of axial stacking can be seen by noting that the axially stacked case has one long (initial) heating pulse (at M) followed by two much shorter pulses (at E and Fj within each axial stack. The short pulses arise since axial stacking aJlows for sequential pulses to build up the tumour tempera­tures (before they decay) in the direction in which the most SAR overlap can be utiUsed, i.e. axially stacking takes advantage of the elongated nature of R I G H T S LIIM K^> IfiC J .il'.TVrtb.'OTi 14 iKv ftakV JiiJ Ic-.Vii th I lW i £ a ia life a JJfd CGB1 t>\ I ILl JilV - A-J-iL'V HjM fcUUHU I.CJ C* 1 1 , ' I i ' l l J-OjT [UTHL-Ail Ud i."ifil V. 2 1 Inttmationtd Jmmtd of Hyperthermia J73 FiDivcr Densltydl D* (VYVtn3} Figure 6. Trea.unent time vs. power density For three- scjb* paths. trcaciiiin ih e imaO superficial rurncKiT vrith 45 positions. T h e standard perfbssan and. co n tirain t values were used bun the local applied power was varied. Also shown are the percentages o f the treatment o n e spent cooling the normal tissue. T h e lanes arc fa r th e AS (ME1F), XY (Ra] [sq[uarc-s); 3D Kn (circles) and P L CBASF', XY Ra Cmangl«) scan paLierni. the focal zone. In contrast, [hi PL (BMF); X Y raster path has nearly constant long beating times at each focal zone position in iveiy plane (Figure 7A) since it does rot tab; advantage of such SAR overlap. In addition, It treat! the back plane fust, thus spending the most time (ihe first pulses) at locations for which the ratio of SAR in the focal zone to that in the norma] tissu.es is the lowest, thus activating the cnter-pube cooling much more frequently. Figure 7B shows how these longer heating dir.es for ihls planar scan result in much Longer inter-pulse cooling periods. A second trend in Figure 7A is the steady reduction in heating times as the treatment progresses for both scan patterns, corresponding to Increased lheimal build­up in the turr.our, an effect present for both scan patterns, but to different degrees. The bio-physical mechanism by which the treat­ment time benefits are gained through axially staddng is illustrated in Figure E, which shows the temperature vs. time curves in the centre of the first focal zone treated (M) for a heating pulse applied to the middle of the larger tumour. It also shows the corresponding curves for the voids that are imme­diately proximal (F), distal (K) and transversely adjacent to the focal zone. Here one can see that if after heating the middle position, the focal zone is rapidly moved to the front position for the second heating pulse, that the temperature elevations result­ing from the second pulse will be superimposed on the -already significandy elevated tumour tempera­tures at the front posltlon; and thus the front pulse will need a much shorter heating period. Since this superposition occurs it high temperatures it also tabes m:\imum advantage of the gains to be obtained from the non-linear temperature-thermal dose rela­tionship, liius further reducing the needed heating times. Similar but smaller heating time gains would occur If one immediately moved to the back position when applying the second pulse. However, if one moved oiT-axis by a transverse motion, then not only would there only be a small amount, of temperature gain due to superposition, but also ihe temperatures In the front and back axial locations would tv allowed to decay, and thus when they are heated at a later time, long heating periods will be required to bring them back up from basal conditions to the desired target temperature. Such longer heating times will increase the energy deposited in the normal tissues, thus necessitating additional inter­pulse cooling times (as tan he seen in Figure 7B for the PL (E.MF), XY Ra scan), thus further lengthen­ing the treatment times. Finally, the largest time gains arise from heating the middle position first since this generally maximises the total p o w c T (and energy) deposition in the tumour during the first (and longest) -asial heating pulse, thus producing a larger Lpre-heated' temperature base at the other two axial focal zone locations. TrjjrK'eiTt path pattems c f axially siaeked scam Since the axially stacked scans starting in the middle position gave the shortest treatment times for a wide range of conditions when studied wilb the XV R I G H T S LIIM K^> I«i llvfotfttonu lXr* akuvkd from AloanJ^*jlihca(CCi«ih> I HI (Vculxiuft >V&k) Udt* ll.'l V!2 Vet f& M W l m oaly. 2 2 474 J. Coon el al. (a^20 IB 1C ! " w 12 c H 10 I -0 4 . 2 0 " " * « • • • • • • • • • • • 1 . . Position number IB) 60 E S> 40 0 30 S £ 10 Jj20 40 00 BO 100 120 Position number Figure 7. Pulse heating and inter-pulse cooling times (s) during treatment of the medium, superficial tumour under the standard treatment conditions: (A) The heating times at each sequential focal zone position for both the axially stacked (MBF), XY raster path (squares) and the planar (BMF), XY raster path (x). (B) The cooling times at each sequential focal zone position for the planar (BMF), XY raster path. The cooling times for the axialh' stacked (MBF). XY raster arc not shown because they are zero for almost all positions in the treatment and are only a few seconds for the remaining positions. transverse raster path treating the superficial tumours, additional transverse patterns were studied with the AS (MBF) axial stacking sequence to see if further treatment time gains could be realised. These treatments were performed on the medium superfi­cial tumour with standard treatment conditions. In addition, since a primary safety concern in treat­ments is thermal build-up in normal tissues, in order to study more difficult treatment conditions the more stringent normal tissue temperature limit of 5 C was also studied. Figure 9 show's (ranked in order of the treatment times for the 5 C limit) the resulting treatment times for the following axially stacked AS (MBF) transverse scan patterns: AS (MBF) XY raster; the AS (MBF) adjacent annuli; the six permutations of the AS (MBF) O, M and I annuli for the concentric annuli scans; and the AS (MBF) Figure 6. Temperature vs. time for the middle, front, back, and transversely adjacent (to cither skte of the middle posidon in the plane perpendicular to the transducer axis) locations with respect to the FZ location when the beam is focused on the middle (M) position- Results arc shown for the first heating pulse for the larger tumour under standard treatment conditions. XY knight jumps. In the 6 C constraint ease there was essentially no inter-pulse cooling needed for any scan patterns (the adjacent square annuli case used 3% of the time for cooling; all others were zero or < 1%), and thus normal tissue considerations were not significant. For the 6 C constraint case, all of the transverse scan patterns had very similar treatment times, and as expected since tumour heating was the dominant consideration, the fastest scan paths were generally those with the most adjacency among focal zone stacks (the adjacent square annuli had the shortest treatment time - 4J8s) while the longest treatment times had the least adjacency (the AS (MBF) XY knight pattern - 4o9s). However, once the normal tissue constraint conditions become very active (i.e. the 5 C limit), then path choice became significant, and the ordering of the paths essentially reversed - with the path with the least focal zone adjacency (knight) becoming the fastest and the path with the most adjacency (squares) becoming the slowest. This change clc3rlv illustrates the problem dependency of the optimal scan paths when normal tissue constraints are very active. It should also be noted for this 5 C normal tissue constraint that while all transverse patterns (except the adjacent square annuli) still gain from tumour temperature superpo­sition (their treatment times arc less than the 1860 s independent pulses treatment time - sec Appendix A), some paths lose part of that advantage due to activation of the inter-pulse cooling periods. This is evidenced by the monotonically increasing cooling times as the treatment time increases. Finally, for this stricter normal tissue constraint limit, the shortest treatment times are for the AS (MBF) transverse patterns of concentric annuli R I G H T S L I N K<^- I«i llvfotfttonu IXr* akuvkd from AloanJ^*jlihca(CCi«ih> I HI (Vculxiuft >V&k) KlMmtu*. Udt* ll.'l V12 Vet f& M W l m oaly. 2 3 International Journal of Hyperthermia 475 E 2000 1 | 1300 i to o o - 3- c cos train 37"* *** /♦ -V 0 constraint - A ----- A - Rav MOl OMI OIM Transverse path Sq Figure 9. Treatment time n . transverse scan path for axially stacked (MBF) stacks treating the medium, superficial tumour for 6 C and 5 C normal tissue temperature limits under the standard treatment conditions. The scans arc rank ordered based on their times for the 5 C constraint case. The path abbreviation* arc: Kn for the AS (MBF) XY krught rumps; inner I, middle M, outer O for the AS (MBF: concentric annuli; Ra for the AS (MBF; XY raster; Rec for the AS (MBF) adjacent rectangular annuli; and Sq for the adjacent square annuli. Paths where the treatment times were extrapolated hare an asterisk. The percentages of treatment time spent cooling the normal tissue for each path with the 5 C limit are shown. The percentages for the 6 C limit arc not shown because they were all less than and were not a significant factor m determining total treatment time. starting at the tumour ccntrc (1MO and IOM); the XV knight jumps, and the XY raster scan. Note that at the 5 C limit these four patterns have treatment times that arc less than the treatment times for all of the Figure 4 cases at the 6 C limit (except the AS (MBF) and AS (MFB) raster scans), so no other patterns from Figure 4 were worth running since their treatment time would only increase if run with the 5 C limit. These four transverse patterns are an interesting combination of quite different transverse scans which all balance the goal of optimising the gains from increased adjacency inside the tumour, with avoiding overheating the normal tissues due to SAR overlap in the near field. Deeper and larger tumours: SAR overiap To study the effects of path selection in other, more difficult to treat situations, treatments were also performed on the medium tumour moved to a deeper location and on an axially larger tumour. Since the o C constraint limit resulted in large amounts of normal tissue thermal build-up and thus unpractically long treatment times for these tumours, the NT constraint temperature was set at 8 C for these studies. (This 8 C temperature con­straint is approximately equivalent to a thermal dose limit of 30CEM43 C since in retrospectively exam­ining the results for these cases, a NT dose of greater than 30 CE.\l was observed for at most one NT voxel in every treatment.) Figure 10A and B show the resulting treatment times for the medium deeper tumour and the larger tumour for the four fastest transverse scanning patterns from Figure 9, Le. the AS (MFB): XY knight jumps; IOM and IMO concentric annuli: and XY raster. The results for these medium and deeper tumours differentiate these four transverse paths even further, showing that the AS (MFB) XV raster and AS (MFB) IMO concen­tric annuli paths arc the most consistently fast scans for all cases examined. Finally, scan path treatments were also performed on both this medium deeper and this larger tumour using all other five permuta­tions of (M, F, B) for the axially stacked XY raster path. In all cases, the treatment times were slower than for the corresponding MFB scans, thus reinfor­cing the optimal nature of the MFB axially stacking sequence. In order to better understand the effects of transverse path on treatment times, the heating times for each axial stack during the treatment (i.e. for all 36 stacks) for each of the five paths of Figure 10 are shown in Figure 11 (A-E), where stacks which were preceded by a previous stack requiring a long cooling time (>30 s) arc marked with a tilde. The heating time of the initial stack for all paths was 39 s and decreased for later stacks in all paths as focal zone adjacency came into play and R I G H T S L I N K<^- IfiC J .il'.TVrtb.'OTi 14 iKvftakVJiiJ Ic-.Vii th IlWi£ a ialifeaJJfdCGB1 t>\ I l!-l JilV - A-J'iL'V HjM i^iCp.yk I.CJ C* 11,'I i'll Rv [UTHL-Ail tat! L*]V- 2 4 476 J. Coanelal. £ 4-CO 200 0 __________ i__________ i__________ i__________ i IMO IOM Ha QMI Kn A S ^MFB) transverse path A3 (MFB} transverse! patti Figure 10. T re a tm en t time ctl transverse path fa r (A) the medium deep (lap) and (B) Larger tumour (bgiiDtn) for the standard treatment conditions an d a N T tcmpcranixc Lirni: o f 6 C .T h c :ndependent smclc pulse tre atm en t sane^ for the se tumoura aje 3-B52 an d 1556 s, respective]}" 'I'Appcndax'!. T h e percentage o f ucacmcrK time :,pen: cooling is. shown i tw c each path. (o r between points in caser. where the percentages were essentially id e n tic a l. llit rmal build-up in the tumour accumulated. Also note the 'spikes' in the heating time that occurred either after a Lung cooling period or because of a large change in the pith petition that reduced the adja­cency between successive focal zone stacks. Discussion The results presented confirm ihis study's primary hypothesis, lhat large treatment time reductions can be realised by judicious scan padi selection, at least for ihe tumours and condition; studied herein. They also identify-' and nuantiiy the effect of the underly­ing iheimo-physical principles lhat make scan paths ‘fast', thus prodding guidance for future studios with more complicated conditions (e.g. changing blood How and attenuation coefficients). The most impor­tant effect is ‘axially stacking1 of successive foca] aones in tho tumour, which arises fiom ihe combi­nation of axial SAR overlap and temperature super­position due to the focal zone's elongated shape. More specifically, the .MFE axiaJly stacked paths studied are .generally fastest sincc they apply iheir Longest heating pulse (Al, the initial pulse of each stack) when the focal zone is depositing the most power inside the tumour, and then move to the tumour location that was piehcatcd the most (F) by the initial pidse in older to take maximum advantage of temperature superposition in the tumour. This effect is shown to hold for a wide range of perfiision and transducer power levelst and multiple tumour conditions that activate the normal tissue constraints. In summary, while most previous scan-related stud­ies have concentrated on the problem of avoiding thermal build-up in the norma] tissues by haning successive focal zone locations spread far apart, the current study shows how in many cases the completely opposite approach of placing successive pulses close together (in an axial stack and with maximum stack adjacency) can shorten treatment times considerably'. The second most important thermo., physical factor, is adjacency of successive transverse stacks, an effect important in treatment paths used in other research [20]. The effect of adjacency can best be seen by comparing the heating times for the AS (MFB) XV knight path (Figure 1 IE) which has Little adjacency, to the other AS (.MFEj paths of Figure 11 which all have considerable adjacency. This reduced adjacency leads to much longer average stack heating times for the AS yj\lFK) XY knight pattern at the start of the treatment, and thus creates Longer treatment times both directly because of those Longer heating periods and indirectly because the normal tissue is also being heated for Longer times. This results in higher normal tissue temperatures and an increased need for inter-pulse cooling following Later heating pulses. The current study concentrates on superficial tumours with fined properties, and extends previous treatment time optimisation studies by showing that the time gains from path selection add to those obtained by optimising the individual pulse heating and cooling times [17]. The results shed light on the best approach for treating the presented tumour configurations, and protide a basis for further studies with more complicated conditions. An interesting topic for such future studies is temporally changing tissue properties, both changing tumour and normal tissue perfusion, and increased tumour attenuation. Attenuation changes have been observed both exper­imentally [IE-10| and when matching simulation data to previous experimental resulls [4!].The scan-related convention that has been followed by several previous investigators is to treat fra m the back to the R I G H T S LI M K4^r IfiC J .il'.TVrtb.'OTi 14 iKv ftakV JiiJ Ic-.Vii th I lW i £ a ia Jifea JJfdCGB1 t>\ I l!-l JilV - A-J-iL'V Hjfrl fcUUHU I.CJ C* 1 1 , ' I i ' l l Rv [UTHL-Ail tat! L*]V- 2 5 hrtematsomf Jmrmoi of Hypirthmriin 477 (A) 40 33 2 30 5J E 23 2D 13 10 3 0 c 13 E ■6& T ' ' l«F « * 33 1 A5 (UFBj; XY raSef • 5 sa 1 AS fUFH); 5fY IMD M A A A / m 20 3 % 13 { j 10 V m / w 3 0 Stack number 13 2 0 23 Slack number (C^ 40 33 £ 30 c- I 23 f 20 I ,D » ia T (B) AG . - . . . \ Ji 33 \ 11 A3 [MFH|; KYIDM £ 30 V I 23 £ 20 0 i ,D 1 AS (W.FEj; XY C-VI 5 tn ia 3 a■ V 13 20 23 Slack number Stack number Stack, number Figure 1 1 T h e s-mck he aring time vs. stacfc n um b e r for the path* in Figure II0 .The graphs.. in o rd er from short e tt to longest tre atm en t time., are for the AS (AIFE); fA) raster, (B ) 1MO concentric annuli, (C ) IOM concentric tumuli, >;"□) OMI concentric annuli, an d (H) knight- Cooling times o f greater than 30 s in. a preceding stack are marked vriih a tilde. front in a tumour (e.g. using a planar BMF, XY ratter-scan), with ihe idea being dial if Ac front of the tumour is treated tint that any resulting increased attenuation would black the ultrasound from reach­ing the deeper positions. The current study indicates that if indeed such a PL (BMF!, XYraster scan strategy is adopted, that treatment times will be very long. Thus, it is important to study this question in much mane depth in the future to quantify the treatment tint: trade-offs invoked. While several studies have begun investigating tissue attenuation changes during ihermal therapy treatments, much remains to be determined experimentally in viro befotv definitive conclusions tan he drawn about the R I O H T I LIIM K^> IfiC J .il'.TVrtb.'OTi 14 iKvftakVJiiJ Ic-.Vii th IlWi£ a ialifeaJJfdCGB1 t>\ I l!-l JilV - A-J-iL'V HjM fcUUHU I.CJ C* 11,'I i'll Rv [UTHL-Ail tat! L*]V- 2 6 4h3 J. Coon tin 1. p u s e s iopllrri m e ) axial slacks pairs oi slacks Relerence case c om e r IrlpilEl stacks pati Figure 12. T re a tm en t time vs. refcrcn.cc ease fa r the medium superficial, medium deeper, an d Larger rumour crcared wich "indcpcndens' pulss-i and snacks u n d e r ihe :-u r.iard trcauner-i conditions-. A h a shovm arc chc wimcs for she fas-esi scans obtained Era this study fee ihe same creaimenjc conditlxMis- T h e fastest case far each o f th e tu c n cu n was.; AS I'MFBj XTF ratter for b oth ih e medium superficial tym o u r ar.d fa r ihe- larger sumour, an d AS, AlETi IMG can centric annuli fee the medium d eeper rumour. rale- of attenuation change in path optimisation. Ill particular, die speed with which i ttfnmlinn changes occur during an in live HIFU treatment is not precisely known (i.e. whether such changes occur within seconds of ablation or on a scale of minutes, etc.). Previous e* vivo studies hive shown that the level and rate of tissue attenuation changes due to thermal ablation depend on the temperature to which the tissue is healed [42-lb ] , the frequency of the ultrasound beam [4 0 , 4 1 , 4 4 , 4 6 ] , and both the rate of dose delivery and the maximum dote delivered [42], with tissue attenuation changing more after it has been heated and then cooled, vs. when it is ktj't in a heated state [45'. Further study is needed to determine what affect tissue attenuation changes have on the optimal path choice, and whether an axial treatment which starts in the middle of the tumour could be sufficiently ‘fast1 to treat an axial stack before the tumour's attenuation changes sig­nificantly. However, the evidence presented in Figure 4 shorn that, if further research shorn that tissue attenuation changes are both fast enough and large enough in magnitude to make a back-to-front focal aone path necessary for some treatments, slatting with a baek treatment plane and axially stacldng the focal zones is still faster than a transverse raster scan path that does not use axial stacking. Similar timing and magnitude considerations are present for possible changes in tumour and normal tissue perfusion changes during treatments. Overdosing (tumour positions above 2 4 0C E .M ) was also examined but was found, I' .nil through post­treatment analysis and exploratory simulations on selected paths, to not be a significant -enough effect to change the rank ordering of the paths presented for the treatment conditions studied herein - although reductions in treatment times would be possible on all paths through the reduction of overdosing. Avoiding large amounts of overdosing in practice could only be done by anticipating all future doses to be delivered to a given position, a difficult task that would rely on accurate modelling. The problems of overdosing and attenuation changes are interrelated; that is, attenuation changes will likely be very significant in treatments that go to very high tem­peratures and thus deliver very high tumour doses (with concomitant overdosing for treatment efficacy ‘insurance'). One of the main results from ihe simulations conducted in this paper was an examination of the physics present in treatment paths that have signif­icant levels of axial stacking. Even though the temperature increase due to this stacldng may vary for a particular treatment, the results of these R I G H T S LIIM K^> IfiC J HjpertMWi 14 iKvftakVJiiJ Ic-.Vii tSfaffil£ a ialifeaJJrdCGB1 t>\ I l!-l L'rt&il JilV - A-J-iL'V HjM fcUUHU I.CJ C* 11,'I i'll Rv [UTMOOil tat! L*]V- 2 7 simulations Lend credence to the belief that the underlying physics of axial stacking and stack adja­cency will be a useful tool for treatment acceleration in many, and more complicated, clinical situations. In summary, these results provide useful guidelines for reducing treatment times through path selection in many tumours, and a reference base for future studies of more complex situations, e.g. for treating larger, deeper tumours with heterogeneous perfu­sions, irregular geometries and temporally changing properties. Given the very large treatment time gains realised in the current study, it is reasonable to expect that by applying the basic bio-thermal approaches identified in this study, those gains will translatej in some proportion, to other cases. Given the immense scope of an exhaustive search over all tumour anatomies and physiologies, transducer con­figurations, focal zone sizes and shapes and spacing, and NE paths for any tumour, it is unlikely that a truly universally optimal scan path will ever be found, nor be needed since it is likely that some "close to optimal' patterns will give practical treatment times. Conclusion Optimisation of the focal zone scan path in HIFU treatments yields significant treatment time savings. The optimised treatment paths use axially stacked [along the transducer axis) focal zones, with each such stack starting with the focal zone in the tumour centre. These time savings occur primarily because the optimised axial focal zone stacks take advantage of SAR overlap and temperature superposition in the tumour in successive axial focal zone heating pulses. The tumour is generally best treated by multiple such stacks scanned through the tumour in an optimised transverse pattern that maximises the amount of "stacking adjacency11* with the best path being depen­dent on the normal tissue constraint. These time gains are present over a range of transducer powers and tissue perfusion levels, and for several different tumour configurations. Such treatment time reduc­tions will be very important clinically, thus motivat­ing further path studies and searches for even better thermophvsics-based heuristic guidelines for a wider range of expected clinical conditions. Acknowledge mentis We greatly appreciate the help of Dennis Parker, U n i Vyas, and Doug Christensen, and use of the UCAIR facilities for this work. An allocation of computer time from the Center for High Performance Computing at the University of Utah is gratefully acknowledged. Declaration o f interest: This work was partially supported by grants from NIH (RG1-CA134599), Siemens Medical Solutions, the Focused Ultrasound Foundation, a University of Utah Synergy Grant and the Ben B. and Iris M, Maigolis Foundation. The authors alone arc responsible for the content and writing of the paper. Itrt&mationat Journal of Hyperthermia 479 References L. Chaio JC, Lee RC. Tbs future of biotharnaa] engineering. In: Diller RK, editor. Heat i n i Mass Transfer in Living Systems. >serv York: New York. Academy of Sciences; L99B. pp 1-20. 2. Christensen DA. Ultrasonic Bio instrument at ion.. Chichester: Wiley; L9SS. 3. Feruiessy F.VL, Teen piny CM. MRI-guided formed ultra­sound surgery of uterine leiomyomas ],. Acad Radiol 2M5;] 2:1 L5S-L166. 4. Hindi cy J, Gedrove WM, Re-gin L, St emit E, T « n party C, Hyiuwn K, « al. MRI Guridjnee nf Focused Ultrasound Therapy of Uterine Fibroids: Early Results. Am J Roentgenol 20M;] Bi:17] 3-17] 9-. >. 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Worthington AE, Sberar MD. Changes m ultrasound prop­erties of porcine kidney tissue during heating. Ultrasound Med Biol 2001;27:673-682. Appendix A Four eases that represent the most elemental ‘building blocks' used to construct all 31 of the scans studied arc presented to investigate the thcrmo-physical mechanisms underlying the scans' differences in treatment times. These idealised eases include ‘independently optimised': (1 ) pulses; (2) single axial stacks; (3) pairs of adjacent axial stacks; and (4) comer triplets of adjacent axial stacks. All reference stacks used MFB axially stacking since this stacking order always gives the shortest treat­ment times of all six stacking orders. All four of these cases are ‘independent' in the sense that for the independent pulses, each pulse is applied under the idealised conditions that it is not affected by, i.e. is independent of, all other pulses. Such pulse R I G H T S L I N Kiy- IfiC J .il'.TVrtb.'OTi 14 iKvftakVJiiJ Ic-.Vii th IlWi£ a ialifeaJJfdCGB1 t>\ I ILl JilV - A-J-iL'V HjM i^iCp.yk I.CJ C* 11,'I i'll J-OjT [UTHL-Ail Ud L*]}-. 29 ‘independence' could arite if there was 3 high blood perfusion everywhere, and the- sequential heating pukes were widely separated in space so they did not affect each other. Similarly for independent stacks, each stack is applied so that it is not affccted by any other stackt, and similarly far the pairs and triplets of slacks. Each ease is ‘optimised1 since the pulse heating and inter-puke cooling periods arc optimised separately for each case. That is, the independent single pulse case uses one heating puke period that is optimised for the independent heating of on; location, the independendy optimised single axial slack has three heating periods and twa tooling: periods that an: optimised for the treatment of the three a3dal positions within one independent stack, etc. I n d e f a i d e n d y o p tim is e d single pu!scs If each heating pulse was independent of all other pukes then it would begin its heating puke with the tumour at basal conditions and treat its focal zone location to the needed dote, but would hive no effect on my other location. This means that there would be no treatment time gains at that location from 3-D SAR overlap among successive pulses, nor from long term thermal build-up in the tumour, nor from the delivery of prior or future dose. Similarly, there would be no treatment time delays tom inter-pulte cooling since there would be no ihermal build-up in the normal tissues (i.e. = 0 for all ?r) other than from the tingle puke, which will rot require inter-pulte cooling by definition. The resulting treatment time is dius X times the independent puke's optimised heating time, which it die same for all pultes due to their independence. l u d e f o i d e n d y o p tim is e d sin g le a x ia l s ta c k s N o t , a series of ‘independent' MFE stacks, whote three pulse heating and two intei-pulte cooling times were optimised within lhat stack, was studied. This approach takes advantage of SAR overlap and temperature superposition within the tumour to reduce the second and third pulse heating times (when compired to the first pulse). In the tumours studied it also resulted in some normal tissue thermal build-up due 10 the three heating pulses, but never enough to reach the constraint temperature, so normal tissue thermal build-up was not a considera­tion (Jfc™t„ = ti for all pj). There it no interaction with other stacks, and ihus there is no long-term thermal build-up in the tumour or in the norma] tissues. The difference between ihis casehs treatment times and the independent single pultc cate's treatment times is thus a measure of the heating time gained by using axial stacking. The resulting total treatment time is Jv'3 times the optimised independent axial stack heating time, which is the same for all stacks due to their independence. Independently optimised parrs of adjacent axial stacks Next, since in most transverse scan patterns studied, suceettive stack are placed adjacent to each other (in x or y, but not diagonally), those pairs gain from their adjacency (.the second stack wdl have lower heating times since it will have been preheated by SAR overlap heating and transverse conduction from the first stack). I f such pairs are independent, they mil hive interactions between themselves, but not with any other stackt. Comparing the treatment time for the optimised independent pairs of adjacent stacks to that for independent single asial stacks gives a measure of the time gains obtained tolely from the ‘two stack adjacency1. The retulting treatment time is M/d times the heating time needed to heat one such pair of stacks, which is die same for all such pairs due to their independence. Again, for this cate, the normal tissue constraint temperature was never reached during die sis pulset used by a pair ofttacls, and dius Afr^_r_ = 0 for all ?i. Independently optimised comer triplets oj axial s Finally, the sequence of three adjacent slacks that form comers (e.g. stacks [, 2 and 3 at the beginning of ihe AS (MFB), IMO pattern of Figure 3) not only gain from the immediate adjacency of each pair of successive stachs, but also from the diagonal heating between slacki 1 and 3. When compared to the paired stack times they give a measure of ihe time gains realised tolely from adding a third stack to form a ‘comer triplet' . Their treatment time is JJ19 times the time required for one such triplet. Again, in these cases there is little thermal build-up due to the nine heating pulses and thus normal tissue constraints were never activated 0Jfc.»r,„ = 0 J0- The ‘reference cate' result! for the standard treatment conditions are presented (Figure 12} to both show the gains attainable from the different ‘building blocks' scanning approaches, and as a baseline for comparison with the results for the 31 pattu studied. Also shown are the results from those paths (out of all of the 31 paths studied; with the shortest treatment times. Xotc that those 'fastest' paths have the additional benefits (not present in any of ihe ‘independent' reference cases! of both (]) thermal build-up in the tumour, a benefit that results in further shortening of the treatment times, and (2) accounting for prior dose' to reduce treatment times. These results clearly illustrate the gains achievable through optimising the use of the thermal physics (primarily axial stacking and secondarily stack adjacency) during treatment path selection. Lrtematiomd Jamurf of Mypeithentiia -IS L R I G H T S LI M K4^r CHAPTER 3 HIFU TREATMENT TIME REDUCTION THROUGH HEATING APPROACH OPTIMIZATION Reprinted with Permission from Informa UK Ltd. International Journal of Hyperthermia, Vol. 28, No. 8, Pages 799-820 Joshua Coon, Nick Todd, Robert Roemer be J IK fv n tu rm u iXiwakxiJed torn iftktfrrutaikfecjre a «ni b«. I ljf id i) X(jr-<A« c« 11, 19,12 Ji.ir tat: L*]y. 31 Int. J. Hypenhmnia, Diccmbcr 2512; 28(B): 799-825 informa hcjfctore RESEARCH ARTICLE HIFU treatment time redaction through heating approach optimisation JO S H U A C O O N J, X I C K T O D D '1, & R O B E R T RO E .M ER ' 1,1 Salt Lake City, and ‘Department of Radiology, Unixvnity of Utah, Salt Lake City, Utah, USA (R c te itv d 3 0 M a rc h 2 0 1 2 ; Furciscd 6 OirjcitiT 20 1 2 ; Accepted & October 2012} A b s t r a c t Purpose: T h is sti*dy evaluated th e H IFU tre a tm en t tim e red u c tio n s attainable fo r several scan p aths w h en optimising the he ating a p p ro a ch u s e d (single, discre te pulses versus volumetric scanning) a n d the paths* focal zo n e h eating lo cations'; n um b e r (N m ) , spacing*, sequencing order, n um b e r o f h eating cycles (N c r c u a X a n d heating tiroes. Also evaluated were the effects o f focal zone size, in cre ased tissue absorptivity d u e to heating, a n d o p tim isatio n technique. A laJerials an d methodr. T re a tm en ts o f h om ogeneous co n s tan t propern* tum o u rs were simulated for several simple generic tum o u r shapes an d sizes. T h e c o n c en tra ted heating a p p ro a ch (which delivered the d esired th erm al dose to each location in o n e d iscrete h ea ting pulse (N c y c u s - 1}) was com p a red to th e fractionated heatin g ap p ro a ch (which d o sed th e tum o u r using m ultiple, sh o rte r pulses repeatedly s c an n ed a ro u n d th e h eating p a th (i.e. ‘volumetric sc an n in g ' with X c v c l e s > I))- T re aim er.t times were min imised using b o th sim u ltan eo u s, collective pulse o p tim isa tio n (which used full a priori knowledge o f th e in te rac tin g effects o f aO pulses) an d sequ en tial, single pulse o p tim isatio n (which used only the information from previous pulses an d cooling o f the currc ru pu lse). Results: Op tim ised c o n c en trate d heating always had sh o rter tre a tm e n t times th an o p timised fractio n ated h eating, and co n c en tra ted h c ad n g resu lted in less normal tissue heating. W h e n large, rap id tissue absorptivity changes were p resen t (d o u b led o r q u ad ru p led immediately after heating) th e o ptim al o rd erin g o f the scan p a th 's sequence o f focal zone locations changed.. Conchtsianr. C o n c en tra ted h e a ting yields significant tre a tm e n t bmc red u c tio n s a n d less n o rm a l tissue h eatin g w h en comp ared id all fractionated sc an n in g approaches, e .g. voCumetric scanning. Keywords: H IFU , treatment plamung, treatment optimization, focal zone size Introduction 1 Department o f Physics and Astronomy, University o f Utah, Salt Lake City, 2 Utah Center for Advanced Imagntg Research (UCAIR), University o f Utah, Salt Lake City, Department of Mechanical Engineering, University etf Utah, HIFU has been shown to be a promising treatment (FZ) locations) in the tumour^ tfiie order in which modality for several types of cancer and uterine these locations are treated; the number of times they fibroids [1-8]. While many factors will affect its are each heated; and the focal zone size and shape. ultimate clinical acceptance, long treatment times Finding an optimised set of treatment parameters [9, 10], sometimes several hours [5], can present a that will make a given treatment short enough to be serious obstacle to wider clinical implementation. clinically viable presents a complicated problem. This limitation will become increasingly important Although many studies have looked at treatment time when larger malignant tumours (whose irregularly as a factor when studying HIFU treatments, including shaped volumes must be completely dosed) in critical studies on dose homogeneity inside of the tumour and locations are treated. Reductions in treatment time new transducer systems [11-22], only a few studies arc possible through user selecdon of the HIFU have focused solely on the development of a set of treatment operating parameters, including: the trans- optimal treatment scanning parameters to specifically ducer power; the pulse heating times; the focal zone reduce treatment time [23-26]. The problem is made Tol: SOI-Hl-oflfll. K-mxI cma J hie ws»H.«Ju. ISiSVOJoi D T t o r n n i l iS S 1.464-3157 unlina i ‘ ' PS 1 Inii>r=u I K E.-J IM I : JD .U IH L > M d » TM .201.2.TJ-Sfl+6 C tm i p i n J a i n : 31c T.'■ hua C m s , Ocparimmc n f r i i p i a and R I G H T S L t I bc J j U^cd-iijnu JKmibk'uJL'il Irf.cTi ifi.kc^ul'iii H-l j l ‘ a*riby I jjflftfe Jrtjram i* I L 'l^ 'I i J-it jvfsiiiil tat: i>aly. 32 especially difficult because tfi-c large dimensionality of the problem combined with long computational times makes a lbrute force* search through all treatment parameter space unfeasible [25]. Because of this difficulty with exhaustive searches far optima] treat­ment parameters* previous research has optimised each user-selectable parameter independently [23* 25]. So far, optimisation research specifically focused on minimising treatment time has been done on the transducer power levels [23], heating and cooling times at each position [23] * and the path of the focal zone through the tumour [25]. This study expands that research to compare treatment times of a concentrated and a fractionated pulse heating approach (defined below). It does so while also studying the effects of an increasing number of focal zone heating locations used to heat a tumour of a fixed size (focal zone packing density), and for a range of focal zone spacings* both axial and transverse, for a fixed number of focal zones heating a tumour of a fixed size. Additionally, this study investigates the effects of heating-induced absorptiv­ity changes on the optimal path for treatments using focal zones in an axial stack. Concentrated Terms fractionated fx a l zone heating The question, of whether to use a single heating pulse to completely deliver a desired total therapeutic thermal dose to each successive focal zone location individually before moving to another location {herein called concentrated heating), versus an approach that successively passes the focal zone over a fixed set of positions in a cyclical fashion that only delivers a fraction of the desired thermal dose to each location during each such pass (herein called fractionated heating) has been the subject of much speculation. These two approaches have different advantages and disadvantages. This paper concen­trates on comparing the speed with which they can treat tumours under comparable conditions in order to determine which approach has the potential to be clinically faster. Although several speculative claims have been made regarding treatment speed, no systematic studies have been performed to evaluate their relative heating times under comparable condi­tions. Many HIFU applications have used concen­trated heating in simulations, animal experiments and clinical treatments [4* 16* 17, 27-37]. The concentiated HIFU method was developed, in part, to overcome the long treatment times present in standard hyperthermia [30, 3S] by using small, concentrated, high power density focal zones that produced high temperatures in. short times. By heating tissues rapidly, that approach both reduced the time available for coaling to occur and took advantage of the non-linear temperature versus SOI} J. Cametal. thermal dose relationship [30* 39]. Concentrated healing was also introduced to reduce the cooling effects of the (unknown) tumour blood flow: [30* 31 ] by inducing more dependence on thermal conduc­tion. Unknow n blood flow effects are now less of a concern since the temperatures present during treatments can be measured with magnetic reso­nance imaging (MRI) [4, -10-12]. One wray to obtain more concentrated treatments is to use a more highly focuscd beam with a. tight focus (with dimensions of approximately II mm by 5mm* e.g. [-I]). However, such smaller focal zones require treatment of a larger number of focal zone locations to cover a given tumour, potentially resulting in more heating in the norma] tissue due to build up from the larger number of points heated [43* 44]. Other research [21* 45-50] has subsequently modified the concentrated heating approach in one of two wap. Firsth investigators have studied the use of a larger focal zone (produced either electronically or mechanically) that is then scanned discretely through a reduced number of locations [46* 47, 50]. Focal zones as large as I x 1 x 2 cm1 [47] have been used, ajid one simulation, study investigated the use of a large, single focal zone that was optimally shaped to yield a uniform thermal dose in the tumour, thus potentially minimising the total energy5 needed to treat the tumour [511]. Second, o ther investigators have proposed using a single focal zone (or multiple foct) to rapidly scan a large volume by using repetitive heating pulses that cyclically heat a sequence of focal zone locations (called volumetric scanning), including extensive research on animal models [21, 45, 49]. These volumetric heating approaches use rapid electronic switching to repeat­edly progress through successive treatment locations, and have the potential advantage of giving a. more uniform temperature distribution in the tumour. Howeverf problems exist with this approach as well. Due to the smaller power density ratio between the tumour and that in the normal tissue, more near-field heating may occur in. these treatments, a trend noted by Damianou and Hynynen. [3II ]. Also* when trvin g to minimise treatment times* research has indicated [23, 2 5] that it is always desirable to have the maximum possible power density" at each treatment location to take advantage of both the reduced time available for coaling and the non-linear rate of thermal dase deposition, factors whose effects are reduced by the dilution of power present in the larger* or repeatedly scanned, focal zone approaches. Finally, some researchers have investigated a mix of concentrated and diluted focal zones in simulation studies [52]. Though strong opinions exist regarding which treatment strategy (concentrated or fractionated) will achieve optimal results when considering a treatment time metric, little work has been done to directly R I G H T S LIN bc J j U ^ c d -iijn u JKmibk'uJL'il Irf.cTi ifi.kc^ul'iii H-l j l ‘ a*rifey I Uflftfr Jrtjram i* I L 'l ^ 'I i J-it jvfsiiiil toe l*]}'. 33 compare the Ewo methods. This paper directly compares these methods with the end goals of bath gathering quantitative evidence on, and explaining the underlying physics of both heating approaches, in order to help resolve this timing question. F o ca l zo n e p o t k in g , sp a c in g a rid sca n n in g p a th Most studies using a discrete scanning approach use conservative spacings between focal zone locations to avoid thermal dose ‘holes1 of untreated tissue inside the tumour, with a spacing of about 3 mm laterally [-1, 25] and 5 mm or less axially between treatment planes [4, 25, 23] being typical. However, Little work has been done an treatments that employ a more aggressive axial and transverse spacing, and Little work his been done an the trade-offs involved between the optimal spacing of a smaller number of focal zones versus increasing the focal zone packing density. This need reflects a similar need for systematic studies of different focal zone sizes, which have only been studied for a few isolated cases, often as part of a Larger study whose main focus is another phenomenon [11, 17, 20, 22, 53, 54]. Thus, the effect of focal zone size on treatment time remains unclear. Several previous studies [11, 33, 23, 25, 45, 49, 50] have examined the efFect of scanning path in magnetic resonance guided high intensity focused ultrasound (MRgHIFU] treatments. Hoxvever, much work remains to be done in this area, including an examination of the path when other parameters, including the spacing between focal zone locations in the tumour, have been optimised. The results of previous research strongly suggest that, even, in non-optimal scanning co^ditions^ repeated use of 'axial stacking' of the focal zones (e.g. where an initial focal zone is placed in the centre of the tumour and subsequent focal zones are placed proximaL'distal to this focal zone in a ‘stack1 along the axis of the transducer) can. dramatically reduce treatment times. Tissue absorptivity changes during treatment Increases in the ultrasound absorptivity coefficient as 3 result of heating have been observed both exper­imentally [55-57] and when matching simulation data to experimental results [58]. Ftevious ex vivo studies have shown, that both the magnitude and the rate of increase in the tissue ultrasound absorptivity coefficient due to heating depend on the temperature to which the tissue is heated [59-63], the frequency of the ultrasound beam [57, 60, 61, 63], and both the rate of dose delivery and the maximum thermal dose delivered [59]. However, Little research has been performed on the quantitative efFects of these changes on HIFU treatments, including whether the presence of absorptivity changes mil increase or Optima! scanning 301 decrease treatment times, or alter the optimal path for a given treatment. The only guideline present for such choices is the general observation that if very Large absorptivity changes are present during a treatment, that treating the proximal tumour loca­tions first should be avoided since the subsequent ultrasound pulses will possibly not be able to then penetrate to the more distal tumour locations [53]. However, though this conclusion is logical given its assumptions, the definition of ‘very large' still remains to be quantified, as does the temporal speed with which absorptivity changes occur relative to a treatment's scan times. It has, however, been shown that tissue absorptivity changes more after it has been heated and then, cooled versus when it is kept in a heated state [62]. That study showed the absorptivity increasing up to, and plateauing at, values of up to twice the unheated values. Optimisation technique Several previous studies have examined the problem of optimising HIFU treatments using a variety of techniques and objectives [13, 25, 26, 64-68]. The objectives used for HIFU optimisation generally have the primary goal of cither shaping the thermal dose delivered to the tumour and the surrounding tissue 113,26,64-6S] or of reducing treatment time through parameter optimisation while treating a fixed volume to a desired dose [25, 26]. The optimisation tech­niques previously used include an adjoint approach (in one dimension) [64], a. series of simulated treat­ments that step through the parameter space at fixed values [65], use of a cost function-based algorithm to minimise tumour overdosing [13, 67], an analytical solution for the thermal dose distribu tion in a single pulse treatment [66], and a sequential optimisation technique that optimises treatment times at each Location without considering future doss [25] beyond the current pulse's effects. This research expands on previous research by comparing two techniques for optimising HIFU treatments to minimise treatment times: the sequential optimisation technique used in previous research [25] and a method of ‘simulta­neous, collective pulse optimisation' that uses all available knowledge for a given, treatment, including the a priori knowledge of the heating due to and thermal dose deposited by all pulses during a. treat­ment, to optimise treatments. That latter technique is similar to that used in previous research [13]. Methods Dvjfpjrivrj lime and tissue constraints The total time needed to administer a treatment (which served as the objective function for the R I G H T S L IN Kiy- bc J j U ^ c d -iijn u JKmibk'uJL'il Irf.cTi isn.kc^ul'iii H-l j l ‘ a*rifey I Uflftfr Jrtjram i* I L 'l ^ 'I i J-it jvfsiiiil toe l*]}'. 34 optimisation routine) was calculated as the sum of its focal zone location pulse heating times plus (if necessary to prevent norma] tissue damage) the related inter-pulse cooling times: -V *iTMiwnii = y^A-jr. + fwdj (1} n= I where t,„aiorcui is the total treatment time, ls the heating time at position tt and i*/, is the subsequent inter-pulse cooling time during which power is off before initiating the next heating pulse. In the current studies the normal tissue temperature constraint (see below) was never violated (except for a small subset of non-optima! runs)* so inter-pulse coaling was never invoked, and thus the sum of the heating times always equalled the total treatment time. Additionally, a computational constraint that no individual heating pulse could be longer than 300 s was imposed on the solver for almost all treatments. To ensure efficacy, a thermal dose constraint {which was a constraint function for the optimisation routine) ensured that all voxels in the tumour were treated to a minimum of CEA1240 by the end of the treatment (a value commonly used in previous research [69, 70] }* where CEM is the "cumulative equivalent minutes* of dose at 43 C [39]. This included the dose accumulated during the cool down period fallowing the last heating pulse of each treatment. To ensure safety, a strict temperature limit (which was an additional constraint function for the optimisation routine) was imposed in twio normal tissue constraint planes located I cm proximal and distal to the tumour. That requirement was M i4 r jv r J s f r :C (2) where Af4L\(!T*T) is the maximum normal tissue temperature in the constraint planes. This tempera­ture limit replicates the conservative temperature limit used in previous research [23* 25, 64] that triggers normal tissue coaling before significant dose is deposited in the normal tissue due to thermal build up. The location of the CE.M30 dose surface in the tissue was also monitored and is reported for the cases where it is of interest (previous research has shown this to be an approximate limit above which irreversible tissue damage occurs [69, 70]). Additionally, several computational tolerance con­straints were imposed on the optimisation routine for the purpose of ensuring convergence. A tolerance for the evaluation of the objective function and each of the individual heating times (generally <10-1 for both} was imposed on the solver for all simulations, and the simulations were terminated if this tolerance was met (Le. the change of any value from one iteration to the next was less than the tolerance). Also, a maximum allowable number of 3000 802 J. Cametal. iterations per optimisation was imposed on the salver, and the optimisation routine was halted if the maximum number of iterations was reached. In cases where the optimisation routine halted after the maximum number of steps without reaching a solution* a new starting guess for each treatment time (in the range {0, 300)) was input* and the solver was restarted until a feasible solution was found. Pith? heating approaches Two pulse heating approaches were used, concen­trated and fractionated. There were focal zone locations along the scan path in any given treatment, where Nr a _ ranged from 1 to 25, depending on the tumour being treated. Each such location wtss heated N cy cu a times. Concentrated heating used a. single pulse to heat each focal zone position to the desired thermal dose, and the focal zone did not return to heat any position a second time, i.e. Ncrrc-jj-s = 1 for this approach. The important independent variable for tins approach is thus the pulse heating time at each location, In fractionated heating, each focal zone position was heated wilh multiple shorter pulses as the focal zone cyclically scanned the focal zone locations multiple {Ncvcajl3;> l} times. Each fractionated pulse heating period was a fraction of the single pulse heating period, and delivered only a fraction of the desired thermal dose to that location. Important user-defined variables are the number of cycles used (Ncv^tjj) and the time taken to execute the individual pulses within, each cycle. For the fraction­ated heating approach two methods of implementa­tion were investigated. First, since there are a total of Nra_ Nr-v.-i ■■ * individual heating periods for each treatment* each of those times could be optimised, herein called the fully optimised, fractionated heating approach. Second, a simpler, more clinically practi­cal version of fractionated heating involves the same fixed heating'dwell time at each location (equivalent to a constant scanning speed), with the cyclic scanning continuing until the complete tumour volume reaches the desired thermal dose* a. fraction­ated heating approach previously characterised as 'volumetric' scanning [45, 49]. For high velocity volumetric scanning there is not enough time for the tissue to cool, between cycles* and thus the high velocity fractionated heating approach becomes the equivalent of a single, large effective focal zone with the transducer's focal zone power diluted over the complete scanning volume. Conversely* as the scan­ning speed decreases the heatingdwell time at each position increases* the number of cycles needed to treat each position decreases* and the fractionated approach becomes closer and closer to the R I G H T S L I N Kiy- bc J j U^cd-iijnu JKmibk'uJL'il Irf.cTi ifi.kc^ul'iii H-l j l ‘ a*rifey I jjflftfe Jrtjram i* I L 'l^ 'I i J-it jvfsiiiil toe l*]}'. 35 concentrated approach, with Neverjss = 1 converg­ing to the concentrated heating approach. Optimisation techniques tu ^ : t c ^ For a given treatment with all other treatment parameters, fixed, (e.g. scan path, number of focal zone locations heated] the optimal values for the individual heating timet at each focal zone location were found using a gradient search routine. Two different optimisation techniques were used to deter­mine those times: simultaneous, collective pulse optimisation, and sequential, single pulse optimisation. Simultaneous, collective pulse optimisation was the primary technique used. It represents a. "best case1 limit since it assumed, and utilised, complete, a priori knowledge of all of the thermal interactions among all heating pulses at all locations at all times during a treatment to find the set of pulse heating times that minimised the total treatment time. This technique minimised all heating times by reducing overdosing in. the tumour by accounting for the SAR overlap and thermal conduction interactions among all pulses in a. treatment It worked by selecting initial guesses for the heating and cooling times at every focal zone heating location during the treatment, and then finding the optimal values of those times that minimised the total treatment time. This involved simultaneously optimising Np;cl- heating times for the concentrated heating approach and N , ^ x K,- ,,1 heating times for the fully optimised* fractionated heating approach. The finincon algorithm was run from several random guesses (Le. in a Monte Carlo fashion} for starting times at each focal zone location to ensure convergence to a global minimum. Either the interior-point method or sequential quadratic programming method was used to generate itera-tis. ely updated times [71]. Since the simultaneous optimisation technique requires full a priori knowledge of the thermal effects of all treatment pulses, and such knowledge would be very difficult to realise clinically, it was important to determine whether its resulting treatment time gains would be worth the effort of trying to obtain that knowledge when compared to a more clinically practical technique. Thus, when concentrated heat­ing was used, the collective pulse optimisation technique's treatment time predictions were com­pared to those of sequential, single pulse optimisa­tion, which required very little a priori knowledge. That technique optimised each successive pulse's heating time individually, on a pulse-by-pulse basis. It used knowledge of the thermal history at each location arising from prior heatings* i.e. knowledge of the prior temperatures and thermal doses in the volume to be heated. The only future efFeet it anticipated was the dose that would be delivered during that pulse's subsequent (post-heating) cooling period. Thus, in contrast to the simultaneous opti­misation technique* the sequential optimisation tech­nique did not antiripate'compensate for any dose delivered by future heating pulses. Thcwmf simitfntimt All thermal simulations were done using a. finite difference approximation to the spatial derivatives in the bio-heat equation [72]: ^ ^ A v - r - i r c ^ r - T ^ + a , , o ) that converts the Fennes equation into a set of simultaneous ordinary differential equations that were solved using the Matlab function QDE45, which uses a Runge Kutta approach. Here, T is the temperature ( C) at the point being analysed, p is the tissue density (kgm1) * C is the specific heat of tissue (pkg'1 C), jk is the thermal conductivity of the tissue (W/m-'C), QJf, is the applied power density depos­ited by the external applicator £W/m3)* W is the Fennes perfusion parameter (kg-mVs), C* is the specific heat of blood and Ft is the arterial blood temperature. All simulations used a 1-mm isotropic spatial grid and a. time step of 0.1 s or less. Thermal dose values were calculated using the approach of Sapareto and Dewey [39] using a 1-s time step. Pmver dcpcsitmi The power deposition distribution was determined as in previous research [23* 25] using the hybrid angular spectrum (HAS) method [73] to simulate a 256-element phased array (Imasonic, Paris, France) with a diameter of 14.5cm* a geometric focus of 3 3 cm, and a central frequency of 1 AlHz. Resolution of the ultrasound field w^as 1 mm isotropic. The transducer (which was used in the associated phan­tom experiments (see belaw) was simulated to produce the smallest possible focal zone consistent with the diffraction limit, yielding a full width at half maximum (FWHM) focal zone specific absorption rate {SAR) volume of 1 x 1 k 12 mm1. The total power from the transducer was set at a fixed value for all treatments (with a few exceptions as noted). The maximum power density used occurred when the focal zone was centred at the back face of the larger ( I x l x 30mm1) axial tumour, and was 0. 6 x 10JW.'m\ The associated fixed transducer power magnitude was used in all studies since it has been shown in previous studies [23, 25] that a ‘‘knee' occurs near this power density, below which the treatment times become significantly longer, and above which only minimal time gains are possible. This peak power density was similar to that used in Optima! stunning 303 R I G H T S L I N Kiy- bc J j U^cd-iijnu JKmibk'uJL'il Irf.cTi ifi.kc^ul'iii H-l j l ‘ a*rifey I Uflftfr Jrtjram i* I L'l^'Ii J-it jvfsiiiil toe l*]}'. 36 804 J. Coon e ld . Simulation Schematic Tunrwfrj Gotc-up 3.0 raifn Figure 1. .Model used far axial focal zone spacing and pacldng optimisation studies. The simulation region (left) and a close-up (right ) of an " axial tumour*' arc shown. The black dot at the centre of the tumour (right) marks the location of both the centre o f the tumour and the geometric focus o f the transducer. Both axial tumours (1.6 and 3.0 cm long! had at least 2.0cm (slightly more for the smaller tumour) o f normal tissue between the sldn water interface and the proximal tumour ia.ee i d aQow for a significant space in which normal dssue heating c o u l d occur. previous work [23* 25] and well below Limits set by the US Food and Drug Administration (FDA) [74]. The beam was steered electronically along the z-axis