Effects of strain on cardiac electrophysiology and microstructure

Does strain induce changes in the electrical properties of the heart? Does strain affect the microstructure of cardiac myocytes? Others have considered these questions, but have been limited in their findings. I addressed the first question by measuring conduction velocity in papillary muscles in rest conditions and during applied strain. I also applied streptomycin, a nonselective stretch ion channel blocker, in the above conditions. In control, conduction velocity increased with strain before conduction block occurred. When streptomycin was applied conduction velocity peaked at a higher strain, but conduction block remained unchanged. Changes in electrical properties of papillary muscle allowed for changes in conduction velocity. Although streptomycin did not alter the strain at which conduction block occurred, it did shift the peak conduction velocity to a higher strain. The second question was addressed by imaging isolated cardiac ventricular myocytes in varying degrees of contraction and strain using confocal microscopy. The length of transverse tubules (t-tubules), along with cross-section ellipticity, and orientation in myocytes were analyzed for cells in 16% contraction, rest, and 16% strain. Cells in contraction showed an increase in length of t-tubules with less elliptical cross-sections compared to cells in rest. Strained cells showed a decrease in length of t-tubules with less elliptical cross-sections than cells at rest. The orientation of t-tubule cross-sections changed in a similar manner when comparing contracted and strained cells with cells at rest. The transfer of strain to the t-tubule system supports the hypothesis that the motion of t-tubules during contraction and stretch may constitute a mechanism for pumping extracellular fluid.

EFFECTS OF STRAIN ON CARDIAC ELECTROPHYSIOLOGY AND MICROSTRUCTURE by Thomas Grant McNary A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Bioengineering The University of Utah December 2011 Copyright © Thomas Grant McNary 2011 All Rights Reserved The U n i v e r s i t y of Utah Gradu a t e School STATEMENT OF DISSERTATION APPROVAL The dissertation of _______________________________________________________ has been approved by the following supervisory committee members: , Chair Date Approved ____________________________________________ , Member ______________ Date Approved , Member Date Approved , Member Date Approved , Member Date Approved and by ________________________________________________________ , Chair of the Department of _______________________________________________________ and by Charles A. Wight, Dean of The Graduate School. ABSTRACT Does strain induce changes in the electrical properties of the heart? Does strain affect the microstructure of cardiac myocytes? Others have considered these questions, but have been limited in their findings. I addressed the first question by measuring conduction velocity in papillary muscles in rest conditions and during applied strain. I also applied streptomycin, a nonselective stretch ion channel blocker, in the above conditions. In control, conduction velocity increased with strain before conduction block occurred. When streptomycin was applied conduction velocity peaked at a higher strain, but conduction block remained unchanged. Changes in electrical properties of papillary muscle allowed for changes in conduction velocity. Although streptomycin did not alter the strain at which conduction block occurred, it did shift the peak conduction velocity to a higher strain. The second question was addressed by imaging isolated cardiac ventricular myocytes in varying degrees of contraction and strain using confocal microscopy. The length of transverse tubules (t-tubules), along with cross-section ellipticity, and orientation in myocytes were analyzed for cells in 16% contraction, rest, and 16% strain. Cells in contraction showed an increase in length of t-tubules with less elliptical cross-sections compared to cells in rest. Strained cells showed a decrease in length of t-tubules with less elliptical cross-sections than cells at rest. The orientation of t-tubule cross-sections changed in a similar manner when comparing contracted and strained cells with cells at rest. The transfer of strain to the t-tubule system supports the hypothesis that the motion of t-tubules during contraction and stretch may constitute a mechanism for pumping extracellular fluid. iv CONTENTS ABSTRACT.........................................................................................................................Ill LIST OF TABLES............................................................................................................. vll LIST OF FIGURES......................................................................................................... vlll ACKNOWLEDGEMENTS...............................................................................................x CHAPTERS 1. INTRODUCTION.......................................................................................................... 1 Straln Effects on Cardlac Tlssues and Cells................................................................... 1 Anatomy and Function of the Heart.................................................................................1 Cardiac Electrophysiology................................................................................................8 Strain and Heart Disease.................................................................................................16 References.......................................................................................................................18 2. EXPERIMENTAL AND COMPUTATIONAL STUDIES OF STRAIN-CONDUCTION VELOCITY RELATIONSHIPS IN CARDIAC TISSUE....... 25 Introduction.....................................................................................................................27 Background.....................................................................................................................28 Methods........................................................................................................................... 31 Results............................................................................................................................. 34 Discussion and Conclusions.......................................................................................... 37 3. STRAIN TRANSFER IN VENTRICULAR CARDIOMYOCYTES TO THEIR TRANSVERSE TUBULAR SYSTEM REVEALED BY SCANNING CONFOCAL MICROSCOPY.................................................................................... 44 Supplementary Information........................................................................................... 48 4. GEOMETRIC CHANGES IN RABBIT CARDIAC TRANSVERSE TUBULAR SYSTEM DUE TO CONTRACTION AND MECHANICAL DEFORMATION.......................................................................................................... 55 Introduction.....................................................................................................................55 Methods...........................................................................................................................57 Results............................................................................................................................. 65 Discussion.......................................................................................................................71 References.......................................................................................................................75 5. CONCLUSION............................................................................................................ 79 References......................................................................................................................83 vi Table Page 2.1 Experimental studies of the strain-conduction velocity relationship in cardiac tissue............................................................................................................................ 29 2.2 Computational studies of strain-conduction velocity relationships in cardiac tissue............................................................................................................................ 30 3.1 Statistical analysis of t-tubules.................................................................................... 47 4.1 Statistical analysis of t-tubules from confocal microscopic images of living cells. 67 LIST OF TABLES LIST OF FIGURES Figure Page 1.1 The human heart............................................................................................................ 2 1.2 Transmission microscopic image of a dog ventricular myocyte............................... 3 1.3 Schematic illustration depicting the architecture of a sarcomere.............................. 7 1.4 Schematic representing the circuit equivalent of a small sarcolemmal segment at rest................................................................................................................................ 10 1.5 Diagram representing the important proteins and ions involved in excitation contraction coupling.....................................................................................................15 2.1 Sample electrograms measured along a papillary muscle at different distances from the stimulus position.......................................................................................... 32 2.2 Exemplary activation time-distance relationships extracted from electrograms ....33 2.3 Exemplary strain-conduction velocity relationships in three papillary muscle preparations................................................................................................................... 34 2.4 Strain-conduction velocity relationship for control and after application of 100 |iM streptomycin...................................................................................................35 2.5 Hysteresis of strain-conduction velocity relationship for control and after application of 100 |iM streptomycin...........................................................................35 2.6 Simulation of mechano-electric feedback in a one-dimensional model of cardiac tissue............................................................................................................................ 36 2.7 Hypotheses for mechanisms of strain-conduction velocity relationships in ventricular tissue.......................................................................................................... 39 3.1 Image of myocyte segment before and during 15% static strain............................. 46 3.2 Reconstruction and analysis of t-tubule from rabbit myocyte..................................46 3.3 Statistical analysis........................................................................................................ 47 3.S1 Setup for imaging and applying strain to a myocyte................................................ 52 3.52 Glass microtool for applying strain............................................................................53 3.53 Reconstruction of t-system in a myocyte segment before and while applying 15% strain.....................................................................................................................54 4.1 Central cross sections from image stacks of segments from contracted myocyte... 59 4.2 Relationship between A-Z ratio and SL.................................................................... 61 4.3 Electrical schematic representing the components of the voltage clamp set-up..... 62 4.4 Current response to voltage clamp protocol applied to a ventricular myocyte....... 64 4.5 Processed images of cells in contraction, control, and strain...................................65 4.6 Statistical analysis of t-tubules segmented in confocal image stacks......................66 4.7 Raw sections from image stacks of segments from fixed cells labeled for actinin and WGA......................................................................................................................68 4.8 Processed sections from image stacks of segments from fixed cells in rest and contraction....................................................................................................................69 4.9 Electron micrograph images of cardiac tissue in contraction, control, and strain ...70 4.10 Change in angle between t-tubule minor axis and the longitudinal axis of the myocyte........................................................................................................................ 71 4.11 Distribution of normalized membrane resistance measurements............................ 72 5.1 Modified hypothesis based on measured changes in membrane resistance........... 82 ix ACKNOWLEDGEMENTS This work would not be as good as it is, if it were not for the help I've received from many people. I would like to thank Frank Sachse, who has helped me from the beginning, helping me to understand the work of science and learn the exactness needed for progress in such a field. I would also like to thank John Bridge and Kenneth Spitzer, who have also been mentors to me, for their patients and their guidance. Lastly, I would like to thank my family. They have not only been supportive, they have been encouraging, and I am deeply grateful for it. 1. INTRODUCTION Strain Effects on Cardiac Tissues and Cells Does stretch induce changes in the electrical properties of the heart? Can mechanical strain affect the microstructure of cardiac myocytes? These questions have been raised in many studies of cardiac physiology and pathophysiology. This dissertation is aimed at providing novel mechanistic insights into strain effects on cardiac structures and functions. I will devote this chapter to providing information necessary to understanding my experiments and methods. This will include a description of cellular and tissue anatomy of the heart, cardiac electrophysiology, and the influence of mechanical strain in heart disease. Anatomy and Function of the Heart The general anatomy and function of the heart are well established and explained in most physiology books1-3. The heart functions as a pump, pumping blood to the lungs and to the rest of the body. There are four chambers in the mammalian heart (Fig. 1.1), being divided into two atria and two ventricles on the left and right side. Blood returning from the body first enters the right atrium before entering the right ventricle. As the heart contracts the blood from the right ventricle is pumped to the lungs and on to the left side of the heart. The blood on the left side of the heart is pumped from the left atrium to the left ventricle, and then on to the rest of the body. 2 UT 4 \ \ 2 V y | ] Figure 1.1: The human heart. The left image depicts the human heart as drawn in Gray's Anatomy of the Human Body. 1918. The image on the right depicts a cutaway view of the heart where the blue represents the unoxygenated blood and the red represents the oxygenated blood. The right atrium and ventricle are numbered 1 and 2, respectively, while the left atrium and ventricle are numbered 3 and 4, respectively. To function as a pump, cardiac myocyte contraction in the atria and ventricles need to be coordinated, contracting in a coordinated manner. The signal to contract is initiated in the heart at the sinoatrial (SA) node, spreading over the atria. The atrioventricular (AV) node is the only electrical connection between the atria and the ventricles where the signal may pass from the atria to the ventricles. After the signal is delayed at the AV node, the signal propagates along the bundles of His and the Purkinje fibers, which make up the conduction system, to signal ventricular contraction. Myocytes Myocytes are both electrically and mechanically active. In the heart, myocytes are roughly 100 |im in length, 30 |im in width, and 15 |im in height; often being described as being "brick-shaped" although there are many irregularities in their shapes6 (Fig. 1.2). Myocyte size is dependent on species as well as hemodynamic load7, 8. The major 3 Figure 1.2: Transmission microscopic image of a dog ventricular myocyte. The vertical edges seen in this picture (marked by arrows) are locations where this cell may have connected to other myocytes via gap junctions. This image is courtesy of Dr. Kenneth Spitzer. anatomical structures that affect how the myocyte functions mechanically and electrically include the sarcolemma, the system of transverse tubules (t-system), and the sarcomere as part of the cytoskeleton. Sarcolemma The sarcolemma comprises the outer membrane of the myocyte and the t-system, which is described later in this section. The sarcolemma is mainly made of phospholipids, cholesterol, glycolipids, and membrane proteins. The following description will focus on phospholipids and membrane proteins. Phospholipids are amphipathic molecules, including a hydrophilic head group and a hydrophobic tail group. Due to these two chemical characteristics, the hydrophilic group is exposed to water and other charged molecules, while the hydrophobic lipids in a cell membrane are sandwiched in between the polar head groups. This arrangement of phospholipids prevents all polar molecules from crossing the membrane unless there is a pore, like an ion channel, to allow the polar molecules pass4, 9. For example, water would not be able to cross the membrane if aquaporin, a protein that forms a membrane pore for water, were not present in the sarcolemma10. Here I consider four types of proteins most relevant to my work: ion channels, ion exchangers, ion pumps and gap junction channels. Each protein type is known to affect myocyte electrical activity. These types of proteins can be involved in other types of signaling, but the function of interest in this dissertation is focused on their effects on electrical activity. Ion channels. There are myriad types of ion channels. Their function is to open or close a pore with different stimuli and allow or prevent ions to pass across the membrane. Commonly, channels exhibit selectivity to specific ions passing through their pore. Stimuli by which the channels may open or close include voltage, ligands, and strain. The duration of how long a channel remains in a specific state is variable depending on the type of channel. Ion exchangers and pumps. Ion exchangers move one type of ion out of the cell while moving another type of ion into the cell. For example, the sodium-calcium (Na+-Ca2+) exchanger in the sarcolemma exchanges 3 Na+ for 1 Ca2+ ion, depending on the electrochemical gradient of both ions11. Proteins that move ions against the concentration gradient at the direct expense of adenosine triphosphate (ATP) are ion pumps12. The sodium-potassium pump (Na+-K+ pump) pumps Na+ out of and K+ into the cell. Since this pump affects the concentration of Na+, it indirectly affects the function of the Na+- Ca2+ exchanger. Gap junction channels. Gap junction channels are built of two hemi channels called connexons that are composed of connexins. There are many types of connexins found 4 through out the body of which three are prevalent in the heart: connexin 40 (Cx40), Cx43, and Cx4513. For a functional gap junction channel to exist between myocytes both cells need to contribute connexons, the connexons need to be linked, and the resulting channels need to be open. Properly formed gap junction channels act as open pores that connect the intracellular spaces of myocytes together, allowing ions and small molecules to pass between myocytes14, 15. Depending on the connexins involved in forming a gap junction channel the conductance of the channel will be higher or lower13. For instance if the gap junction channel is formed with Cx40-Cx40 linkage, the conductance is 162 pS. A Cx45-Cx45 gap junction channel, on the other hand, will have a conductance of 32 pS. Further description of gap junction channels' role in the electrical activity of the heart will be described later in this chapter. Transverse Tubules Transverse tubules (t-tubules) are invaginations in the sarcolemma, which are prevalent in some types of skeletal and cardiac myocytes. In cardiac myocytes, these invaginations significantly increase the surface to volume ratio16, and allow electrical signaling to propagate deep into the cell. This is important because the high density of voltage activated calcium channels and Na+-Ca2+ exchangers that line t-tubules are involved in excitation contraction coupling17-19. Electrical signals propagate much faster along the sarcolemma than calcium ions diffuse into the cell interior. Thus, voltage activated calcium channels within the t-tubules will allow a fast influx of calcium and synchronous triggering of adjacent calcium release unit in the sarcoplasmic reticulum. This would not be possible in the absence of t-tubules. 5 Cardiac t-tubules are only found in mammalian myocytes17. The distribution of t-tubules varies depending on the type of cardiac myocyte 17 20 21 . Commonly, myocytes from atria have sparsely developed t-systems, while ventricular cells typically have well-developed t-systems20. The t-system in rats is more of a network of tubules because of the many longitudinal components22, while the t-system in rabbits is mainly composed of transverse components with few in the longitudinal direction23. Various studies have shown that there are many cytoskeletal proteins associated with t-tubules. This suggests mechanical stabilization of the t-system while the myocytes contract, during systole, and are stretched, during diastole24, 25. In addition to the proteins listed above, the inability of a study to electrically characterize nonselective stretch activated ion channels (SACNS) in adult cardiac myocytes has led some to believe that such channels are sequestered to the t-tubular membrane26, 27 This presupposes that mechanical deformation does occur in the t-tubules; otherwise these channels would not sense the mechanical signal. Thus, it is important to know if the t-tubule geometry changes during the cardiac cycle and if it does change, then to what extent. Such information would be important for understanding strain modulation of SACNS currents and subsequent myocyte electrophysiology. Cytoskeleton Proteins that make up the cytoskeleton maintain the shape of a myocyte and its ability to contract. The most notable proteins in the cytoskeleton of a cardiac myocyte are those directly associated with the contractile function, forming the sarcomere. These proteins are actin, myosin, troponin, and tropomyosin. Other cytoskeletal proteins are indirectly 6 involved in mechanical function by anchoring the contractile structures to the myocyte sarcolemma, which include actinin, vinculin, titin, and dystrophin. The principal components needed for contraction are thin and thick filaments. Strands of actin, troponin, and tropomyosin make up thin filaments, which extend from the Z-disk (Fig. 1.3). Troponin and tropomyosin interact with the actin preventing myosin from binding to the actin at rest28. Though troponin and tropomyosin move to allow contraction to occur, such movement does not directly contribute to the movement of contraction. Thin filaments remain essentially the same length throughout the excitation contraction process. Myosin is the protein that provides the contractile force at the cost of ATP. Multiple myosin proteins aggregate to form thick filaments, which extend from the M-line (midline of the sarcomere) towards the Z-disk. The process by which contraction 7 Figure 1.3: Schematic illustration depicting the architecture of a sarcomere. The Z-disk is represented in blue, the thin filaments in red, thick filaments in green, and titin in black. This is an adaptation from pages 962-963 of the textbook Molecular Biology of the Cell4. occurs will be explained in rudimentary detail later. Anchor proteins are essential for transfer of contractile force within the cell to the sarcolemma. Dystrophin, for example, is integral in costamere formation, which anchors Z-disks to the sarcolemma. Actinin binds to actin, anchoring actin to the Z-disk and integrin receptors in sarcolemma. Titin is an elastomeric protein that anchors the thick filament to the Z-disk29. Cardiac Electrophysiology This section will briefly explain how action potentials (APs) occur in myocytes, propagate to surrounding tissue, and signal the tissue to contract. Therefore, this introduction to cardiac electrophysiology begins with the individual myocyte, followed by increasing detail regarding interacting structures, which make AP propagation through the tissue possible. Cellular Electrophysiology Passive Electrical Properties As explained earlier, the sarcolemma prevents charged molecules from entering or exiting the cell without a protein in the membrane to allow such transport. Commonly, cells hold and maintain ion concentration gradients, which also establishes electrical gradients across the membrane due to the charge of ions. Na+ and K+ are the most important ions in establishing this electrochemical gradient. The cell maintains the gradient via the Na+-K+ pump, which pumps Na+ out of the cell while pumping K+ into the cell30. Calcium also contributes to the electrical gradient, but plays a larger role in excitation contraction coupling, which will be discussed in detail later. 8 These gradients establish electrical voltages for each ion type separated by the cell membrane and each voltage can be described by the Nernst equation: 9 RT [/] E, =-----ln-, o U ~z lF [ I \ with the voltage for a specific ion Eh the gas constant R, the temperature in Kelvin T, the valence of the specific ion zj, Faraday's constant F, the ion concentration inside the cell [Iji and the ion concentration outside the cell [I]o. The voltage described by the Nernst equation is also called ion equilibrium voltage. This is due to the voltage measured when electrical and chemical gradients come to equilibrium for a specific ion. As an example, the equilibrium voltage for Na+ is +70 mV when the respective extra/intracellular Na+ concentrations are 125 and 7.5 mM, at 295° Kelvin. Since the membrane is permeable to K+, Na+, and chlorine (Cl") a more comprehensive description of the voltage at rest is the Goldman-Hodgkin-Katz equation: E = R T ln PN [Nal, + Pk [K ]„ + Pg [C l], F P,a [Na], + Pk [K ], + Pg [C l\ with the permeability P of the respective ions as noted by subscript. In other words, the flow of ions across the membrane generates a membrane voltage dependent on the electrochemical concentration gradient of the ions as well as the permeability state of the respective ion channels. If you assume that Cl" permeability is very low, the Cl terms can be ignored. When a myocyte is at rest the permeability of K+ is roughly one hundred times larger than the permeability of Na+. Due to the high K+ concentration inside in contrast to outside of the cell the resting voltage of the mammalian myocyte is around -80 mV30, 31. The membrane permeability for a specific ion can be modeled as a resistance, and the equilibrium voltage for the same ion can be modeled as a voltage source. Using these models, an electrical schematic is commonly applied to describe a segment of the membrane (Fig. 1.4). The composite permeability of the sarcolemma to the various ions, as described in the Goldman-Hodgkin-Katz equation, determines the membrane resistance12. In order to have a capacitor, two conductors (the extracellular fluid and intracellular fluid) need to be separated by an insulator (the cell membrane). Capacitance is influenced the thickness, surface area, and electrical dielectric of the insulator. Mathematically capacitance C is described by: Extracellular 10 Intracellular Figure 1.4: Schematic representing the circuit equivalent of a small sarcolemmal segment at rest. It shows a composite membrane resistance of the permeable ions, Rm, and the membrane capacitance, Cm. The membrane voltage, Em, is dependent on ion concentration and permeability of all permeable ions. An extended version of this schematic, showing variable resistances and reversal voltages for certain ions, is found in Hodgkin and Huxley's work5. m by the 11 C = ""0A d with the dielectric constant of the insulator s, the dielectric constant of vacuum s0, the surface area A, and the thickness of the insulator d. Cells exhibit significant variability of their membrane area, but the relative dielectric constant s and the thickness d of their membrane is typically viewed as constant. In previous studies it has been speculated that the surface area of a myocyte may change with strain or contraction, leading to a change in capacitance32, 33. Another study reported membrane capacitance that was insensitive to strain, but the membrane area of the cell affected was small compared to the rest of the cell34. Membrane Excitability Many ion channels in the myocyte are voltage sensitive, with increased opening probabilities when the membrane voltage reaches specific thresholds. For example, the inward rectifying K+ channel has high open probabilities when the membrane voltage is close to the resting voltage. The sodium channel, on the other hand, opens when the membrane depolarizes to a threshold voltage and remains in an open state for a short period of time before inactivating35. For a more extensive description on ion channel function the interested reader is referred to pertinent textbooks, for example, Ion channels o f excitable membranes, chapter 212. An important property of sodium channels is their fast inactivation, which is maintained until the membrane is repolarized. This is important for activation of an AP. When a part of the sarcolemma depolarizes and the threshold voltage is reached, Na+ will flow through the channel further depolarizing the adjacent membrane and activating the 12 Na+ channels there. The newly activated channels will open, speeding depolarization of the membrane in a positive feedback loop9, 31, which forms a local circuit. This form of activation can happen only if the Na+ channels are available for activation, not Stretch Modulated Ion Channels Many types of ion channels alter their properties in response to deformation of the cell membrane. These channels are called mechanosensitive. An example for a of mechanical alterations are stretch-activated and swelling-activated channels. These channels respond to the deformation by either opening or closing. An example is the stretch-activated transient receptor potential cation (TRPC6) channels, which is thought to conduct stretch-activated nonspecific ion currents in cardiac myocytes. A number of models have been developed to describe currents through stretch-activated ion channels. An example from an early model assumed a reverse potential ENs of -30 mV, a maximum conductance GNs of 1 |iS and an exponential effect of stain on the current: inactivated. The more inactivated Na+ channels present the slower activation propagates until the myocyte and the tissue is inexcitable36. mechanosensitive ion channel is the inward rectifying K+ channel, which has been shown to exhibit reduced currents when strain is applied34, 37 Ion channels specialized in sensing with the sarcomere length SL and the membrane voltage Vm38. 13 Gap Junction Channels Gap junctions play a critical role in local circuit activation propagating from one myocyte to the adjacent. It is through gap junction channels that cardiac cells are electrically coupled together. If the gap junction channel conductance is too high, the cells will be highly coupled increasing electrical load on a myocyte, which will prevent sufficient charge accumulation needed for the voltage to reach the threshold of activation39. As the myocytes become less coupled the intercellular resistance increases promoting a decrease in conduction velocity until becoming effectively decoupled, leading to conduction block36. For those interested in more detail regarding the influence of gap junctions on conduction velocity see39, 40. Initial concepts of cardiac tissue electrophysiology have been derived from established model to describe propagation of electrical signals is the cable model: with the membrane resistance per area Rm, intracellular resistance R , membrane capacitance per area Cm, and membrane voltage Vm. The intracellular current (left hand side) equals the capacitive and resistive currents (right hand side) due to the membrane capacitance and resistance, respectively. As described earlier, there is some controversy regarding the effects of strain on membrane capacitance. Due to the strong effect membrane capacitance has on conduction velocity41, it would be important to know if Tissue Electrophysiology descriptions of electrical properties and conduction in neurons5. In both fields, an 14 strain does affect membrane capacitance. Similarly, it would be important to know if and how strain affects the intracellular and membrane resistances. More commonly in cardiac modeling, two- and three-dimensional mono- and bidomain approaches are used to describe propagation of electrical activation in cardiac tissue. These approaches need knowledge about cellular electrophysiology and electrical properties of the tissue. The bidomain model allows for calculating the currents through the intracellular and extracellular spaces as well as voltage generated by current crossing the cell membrane. A drawback to using the bidomain model is that it is computationally expensive, in particular, for large volumes. This calculation is done using intracellular and extracellular conductivities, which are dependent on the respective volumes. The monodomain is an alternative that is based on lumping intracellular and extracellular conductivities by a bulk conductivity tensor. The defining equation of the monodomain is: with the surface to volume ratio ! , bulk conductivity tensor G, the currents through the cell membrane Iion, and the stimulus current Is. Using the monodomain description can be an appropriate approximation when modeling AP propagation because there is little extracellular space to model defibrillation, for example43. Excitation Contraction Coupling Electrical activation of myocytes causes cellular contraction. For this to happen the electrical signal needs to be transduced to mechanical contractions. During this process of difference to bidomain simulations42, given there are no current sources within the 15 excitation contraction coupling APs are transduced to a calcium signal, which in turn triggers and modulates mechanical contraction. This topic has been extensively researched44-48 Depolarization of the membrane activates voltage sensitive calcium channels (Fig. 1.5), which open allowing calcium into the junctional space between the sarcolemma and the sarcoplasmic reticulum (SR). The increase in Ca2+ concentration in the junctional space leads to Ca2+ binding to ryanodine receptors (RyR) in SR membrane, causing the RyR to open releasing Ca2+ from the SR into the junctional space. The transient increase in calcium quickly decays after closure and inactivation of the calcium channels and RyRs, respectively. The sarcoplasmic reticulum calcium ATP-ase (SERCA) pump Figure 1.5: Diagram representing the important proteins and ions involved in excitation contraction coupling. Na+: Sodium ions; Ca: Calcium ions; RyR: Ryanodine receptors; SR: Sarcoplasmic reticulum; SERCA: Sarcoplasmic calcium ATPase (pump). returns calcium to the SR, and the Na+-Ca2+ exchanger together with a sarcolemmal Ca pump transport calcium to the extracellular space. As described earlier, troponin and tropomyosin cover the actin at rest preventing the myosin heads from attaching and contracting49. As the cytosolic Ca2+ concentration increases troponin binds to Ca2+ causing the tropomyosin to move; this reveals the binding site for myosin and induces contraction. Through a major part of systole the Na+- Ca2+ exchanger moves Ca2+ into the extracellular space while moving Na+ into the intracellular space. The removal of Ca2+ by way of the SERCA pump and the Na+-Ca2+ exchanger leads to Ca2+ unbinding from troponin, tropomyosin covering the binding region of actin, and myocytes relaxing49. It is interesting to note that the process of force development at whole heart but also cellular level has been reported to change due to mechanical deformation. The Frank- Starling law, for example, explains an immediate change in the force of contraction depending on the preload50. Further studies showed that, when strain is continuously applied for a number of minutes the force of contraction, along with the calcium transient amplitude, increases51. Another study suggested that the sarcoplasmic reticulum leaks more calcium into the cytosolic space when strain is applied, but the experiment showed a decrease from strained spark rate to control levels over the course of a minute52. Strain and Heart Disease Heart disease has been the lead cause of death among Americans for many years. In 2006 over 600,000 people died of heart disease, which is above 25% of all deaths that year53. A study examining the mechanisms of cardiac arrest in those suffering from heart failure found that only 10% of those who died were because of electromechanical 16 dissociation54. Thus, it may be implied that the majority of those who die of heart disease suffer from some form of electrical arrhythmia. It is has been speculated that strain is involved in arrhythmogenesis55. Furthermore, it is thought that strain induces changes in expression of proteins involved in electrical signaling56. Arrhythmias It has been hypothesized that remodeling of protein expressions in atrial fibrillation (AF) is caused by changes of strain and that this remodeling leads to further remodeling of electrical activity57. Some mechanisms that induce AF include mitral valve regurgitation, mitral stenosis, and heart failure58. When the mitral valve remains open or closes incompletely during ventricular contraction, pressure in the left atrium is increased. An increase in pressure in the left atrium also occurs when a valve is affected by stenosis, but the increased pressure is due to the incomplete opening of the valve. Though it is clear that mechanical stimulation plays a role in the development and progression of AF59, 60, the mechanisms involved in signaling protein remodeling are not clearly understood. Commotio cordis occurs when cardiac arrest follows a blunt trauma to the heart61. There may be few who die due to this induced ventricular arrhythmia, but it is evidence that mechanical deformation of the heart will cause immediate electrical changes55, 62. The effect of mechanical impacts on the heart has been modeled by activating stretch activated ion channels62, but may also be due to conduction block at large strain63, the mechanism of which remains unexplained. 17 Heart Failure Heart failure, like AF, also has a close connection to mechanical stimuli. One of the animal models used to induce heart failure involves surgically inducing aortic stenosis64- 66, which increases the mechanical load on the left ventricle. Another way heart failure can develop naturally occurs after a portion of the heart has become infarct67, 68. The dead tissue no longer contracts, increasing the mechanical demand on the remaining portion of the heart that is still functional. It is interesting to note that patients suffering with aortic stenosis, hypertension, dilated cardiomyopathy, and cardiac failure show increased sensitivity towards arrhythmias69, 70. This suggests that the pathophysiological contraction of the heart affects the electrical activity of the heart71. It is well-known that people who have an increased cardiac demand through exercise or pregnancy also have cardiac hypertrophy67. 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Prog Biophys Mol Biol. 1999;71:139-154 71. Kohl P, Hunter P, Noble D. Stretch-induced changes in heart rate and rhythm: Clinical observations, experiments and mathematical models. Prog Biophys Mol Biol. 1999;71:91-138 2. EXPERIMENTAL AND COMPUTATIONAL STUDIES OF STRAIN-CONDUCTION VELOCITY RELATIONSHIPS IN CARDIAC TISSUE Reprinted with permission from Progress in Biophysics and Molecular Biology 97 (2008)383-400 26 Available online at www.sciencedirect.com *•#' ScienceDirect Progress in Biophysics and Molecular Biology 97 (2008) 383-400 www.elsevier.com/locate/pbiomolbio Experimental and computational studies of strain-conduction velocity relationships in cardiac tissue T.G. McNarya,b, K. Sohna,b, B. Taccardia'c, F.B. Sachsea,b'* aNora Eccles Harrison Cardiovascular Research and Training Institute, University of Utah, 95 S 2000 E, Salt Lake City, UT 84112, USA hBioengineering Department, University of Utah, 72 S Central Campus Drive, Salt Lake City, UT 84112, USA cSchool of Medicine, University of Utah, 30 N 1900 E, Salt Lake City, UT 84132, USA Available online 29 February 2008 Abstract Velocity of electrical conduction in cardiac tissue is a function of mechanical strain. Although strain-modulated velocity is a well established finding in experimental cardiology, its underlying mechanisms are not well understood. In this work, we summarized potential factors contributing to strain-velocity relationships and reviewed related experimental and computational studies. We presented results from our experimental studies on rabbit papillary muscle, which supported a biphasic relationship of strain and velocity under uni-axial straining conditions. In the low strain range, the strain-velocity relationship was positive. Conduction velocity peaked with 0.59 m/s at 100% strain corresponding to maximal force development. In the high strain range, the relationship was negative. Conduction was reversibly blocked at 118 ± 1.8% strain. Reversible block occurred also in the presence of streptomycin. Furthermore, our studies revealed a moderate hysteresis of conduction velocity, which was reduced by streptomycin. We reconstructed several features of the strain-velocity relationship in a computational study with a myocyte strand. The modeling included strain-modulation of intracellular conductivity and stretch-activated cation non-selective ion channels. The computational study supported our hypotheses, that the positive strain-velocity relationship at low strain is caused by strain-modulation of intracellular conductivity and the negative relationship at high strain results from activity of stretch-activated channels. Conduction block was not reconstructed in our computational studies. We concluded this work by sketching a hypothesis for strain-modulation of conduction and conduction block in papillary muscle. We suggest that this hypothesis can also explain uni­axially measured strain-conduction velocity relationships in other types of cardiac tissue, but apparently necessitates adjustments to reconstruct pressure or volume related changes of velocity in atria and ventricles. Published by Elsevier Ltd. Keywords: Strain-conduction velocity relationship; Mechano-electric feedback; Cardiac electrophysiology; Strain-modulated ion channels; Strain-modulated tissue conductivity ^Corresponding author at: Nora Eccles Harrison Cardiovascular Research and Training Institute, University of Utah, 95 S 2000 E, Salt Lake City, UT 84112, USA. Tel.: + 1 801 5879514; fax: + 1 801 581 3128. E-mail addresses: [e-mail] (T.G. McNary), [e-mail] (K. Sohn), [e-mail] (B. Taccardi), [e-mail] (F.B. Sachse). 0079-6107/$ - see front matter Published by Elsevier Ltd. doi: 10.1016/j.pbiomolbio.2008.02.023 27 Contents 384 T.G. McNary et al. / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 1. Introduction............................................................................................................................................................................ 384 2. Back g ro u n d ............................................................................................................................................................................ 385 2.1. Factors contributing to strain-velocity relationships............................................................................................385 2.2. Review of experimental studies.................................................................................................................................385 2.3. Review of computational s tu d ie s .............................................................................................................................387 3. Methods .................................................................................................................................................................................... 388 3.1. Experimental stu d y ......................................................................................................................................................388 3.1.1. Papillary muscle preparation ........................................................................................................................ 388 3.1.2. Experimental setup and p ro to co l................................................................................................................ 388 3.1.3. Signal processing........................................................................................................................................... 389 3.1.4. Data selection and statistics......................................................................................................................... 390 3.2. Computational study...................................................................................................................................................390 4. Results....................................................................................................................................................................................... 391 4.1. Experimental stu d y ......................................................................................................................................................391 4.2. Computational study................................................................................................................................................... 393 5. Discussion and conclusions................................................................................................................................................... 394 5.1. Experimental studies...................................................................................................................................................394 5.2. Computational studies................................................................................................................................................ 395 5.3. Comparison with studies of atria and ventricles................................................................................................... 397 5.4. Summary....................................................................................................................................................................... 397 Acknowledgments .................................................................................................................................................................. 397 Editor's n o te ............................................................................................................................................................................ 397 Appendix A. Measures of strain ......................................................................................................................................... 398 References ............................................................................................................................................................................... 398 1. Introduction The relationship between mechanical strain and velocity of electrical conduction in cardiac tissues has been studied since the 1960s. Experimental studies have been carried out with different species and types of cardiac tissue (Penefsky and Hoffman, 1963; Spear and Moore, 1972; Dominguez and Fozzard, 1979; Rosen et al., 1981; Tavi et al., 1996; Zhu et al., 1997; Eijsbouts et al., 2003; Sung et al., 2003; Sachse et al., 2004). These studies showed differing effects of strain on conduction velocity. More recently, these studies were complemented by computational studies based on mathematical models of cellular and tissue electrophysiology (Rice et al., 1998; Sachse et al., 2000, 2002, 2006, 2007; Trayanova et al., 2004; Kuijpers et al., 2007). Those studies also showed differing results for various species and tissue types. The heterogeneity of experimental and computational findings, the biophysical mechanisms underlying strain-velocity relationships, and the physiological relevance of this mechano-electric feedback phenomenon are still not completely understood. In this work, we describe factors a t cellular and tissue level contributing to the strain-velocity relationship in cardiac tissue, followed by a review of experimental and computational studies of these relationships. In the review we provide quantitative data on strain-velocity relationships for various species and experimental conditions. Furthermore, we classified the experimental and computational data into different types of strain-velocity relationships: biphasic, constant, increasing and decreasing. We present then the design and results of our experimental study on rabbit papillary muscle. Conduction in rabbit papillary muscle has been well characterized in various studies in the past and the preparation allows for reliable measurement of one-dimensional mechanical strain.1 Our study was conducted to gain insights in biophysical mechanisms of the strain-velocity relationship in ventricular tissue and developing a qualitative description of this relationship. Our study showed novel phenomena of strain-velocity relationships, in particular reversible block of conduction for large strain and hysteresis of conduction velocity in a protocol with increasing and decreasing 'We refer to Appendix A for a description of strain measures used in this work. 28 strain. We explored hypotheses for biophysical mechanisms underlying the measured strain-velocity relationships in computational studies with a one-dimensional model of electrical conduction in cardiac tissue. In particular, we were interested in discriminating the effects of strain-modulated electrical conductivity of myocardium and activity of mechano-sensitive ion channels on conduction velocity. We conclude with discussing our findings, relating these to results of others, and proposing a hypothesis for conduction in uni-axially strained cardiac tissue. The hypothesis was developed by comparison of our experimental and computational findings and groups the effect on conduction velocity according to the level of strain. 2. Background 2.1. Factors contributing to strain-velocity relationships Cardiac conduction velocity is a function of cellular electrophysiology and electrical properties of tissue. In the following, we will list factors contributing to the strain-dependent modulation of cellular and tissue properties, which were suggested to affect strain-conduction velocity relationships. At the cellular level, strain and tension of the sarcolemma were found to activate and modulate current flow through various ion channels. Strain depolarized the resting transmembrane voltage Vrest of cardiomyocytes (Deck, 1964; Rosen et al., 1981), changed the shape of action potentials (Deck, 1964; Spear and Moore, 1972; Zabel et al., 1996a; Riemer and Tung, 2003) and reduced action potential duration (APD) (White et al., 1993; Hsieh et al., 1999). These changes were commonly explained by increased open state probabilities of mechano-sensitive channels, in particular the stretch-activated cation non-selective channels (nsSACs) (Zhang et al., 2000). Blocking of nsSACs is possible with gadolinium, streptomycin and GsMTx-4 (Franz and Bode, 2003; Calaghan and White, 2004; Sachs, 2004; White, 2006). Recently, the protein forming these channels in cells of vertebrates was identified as the canonical transient receptor potential channel (TRPC1) (Maroto et al., 2005). The increased Vrest due to opening of nsSACs was suggested to underly slowing of conduction velocity by voltage-dependent inactivation of fast sodium channels (Rice et al., 1998; Mills et al., 2005; Sachse et al.. 2006). These sodium channels are responsible for the upstroke of myocytes' action potential and upstroke velocity is known to be related to conduction velocity. Further channels with reported strain-modulation include those associated with inward rectifier potassium, sarcolemmal ATP-sensitive potassium and outward rectifier potassium currents (Ruknudin et al., 1993; Niu and Sachs, 2003; Li et al., 2006). The physiological role of the strain-modulation of these potassium channels and their significance in strain-conduction velocity relationships is unclear. A proposed role of the outward rectifier potassium current through two-pore domain channels TREK-1 was to counterbalance nsSAC currents when myocytes are stretched at end diastole (Li et al., 2006). This effect would reduce membrane depolarization by opening of nsSACs and sodium channel inactivation. It was also suggested that strain uncovers ‘‘surplus'' sarcolemma and expands sarcolemmal vesicles (Kohl et al., 2003; Calaghan, 2007). These changes would affect membrane capacitance and accessibility of transmembrane proteins. An increase of membrane capacitance would reduce conduction velocity by slowing depolarization. Further effects of strain on electrical properties were proposed at tissue level and characterized in computational studies of ventricular myocardium (Sachse et al., 2000). Here, strain-modulation of intracellular electrical conductivity was found to have varied effects on conduction velocity. A positive relationship of strain and intracellular conductivity led to positive strain-conduction velocity relationships. Strain-independent conductivity led to negative strain-conduction velocity relationships (see Section 2.3). 2.2. Review o f experimental studies An overview of experimental studies on conduction velocity is given in Table 1. We classified the experimental results in the following listing into four groups: biphasic, constant, increasing and decreasing relationships of strain versus conduction velocity. T.G. McNary et al. / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 385 29 386 T.G. McNary et al. / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 Table 1 Experimental studies of the strain-conduction velocity relationship in cardiac tissue Year Authors and reference Species Tissue Dim. Relationship 1963 Penefsky and Hoffman (1963) Cat Papillary muscle 1 Biphasic Cat Auricle strip 1 Biphasic Hamster Ventricular strip 1 Biphasic Squirrel Ventricular strip 1 Biphasic Chicken Auricle strip 1 Biphasic Chicken Ventricular strip 1 Biphasic Terrapin Auricle strip 1 Biphasic Terrapin Ventricular strip 1 Biphasic Carp Ventricular strip 1 Biphasic 1964 Deck (1964) Sheep Purkinje fiber 1 Increasing 1972 Spear and Moore (1972) Rat Papillary muscle 1 Decreasing Rabbit Papillary muscle 1 Constant Cat Papillary muscle 1 Constant Guinea pig Papillary muscle 1 Constant Frog Trabeculae 1 Constant 1979 Dominguez and Fozzard (1979) Sheep Purkinje fiber 1 Increasing 1981 Rosen et al. (1981) Cat Trabeculae 1 Biphasic Dog Purkinje fiber 1 Biphasic 1989 Solti et al. (1989) Dog Atria 1 CT increase 1996 Tavi et al. (1996) Rat Atria 1 Increasing 1996 Zabel et al. (1996b) Rabbit Ventricle 1 Delayed AT 1997 Reiter et al. (1997) Rabbit Left ventricle Increasinga 1997 Zhu et al. (1997) Dog Ventricles 1 Constant AT 2003 Eijsbouts et al. (2003) Rabbit Atria Decreasing 2003 Sung et al. (2003) Rabbit Left ventricle Decreasing 2004 Sachse et al. (2004) Rabbit Papillary muscle 1 Biphasic Abbreviations: CT: conduction time; AT: activation time. aIncrease of mean longitudinal conduction velocity only. Biphasic. A biphasic relationship of strain and conduction velocity was reported for papillary muscle, atrial and ventricular strips of various species (Penefsky and Hoffman, 1963). In cat and terrapin, a maximal velocity was found a t 100% strain corresponding to maximal force development. Conduction velocity increased in the low strain range (80-100%) and decreased in the high strain range (100% and above). Local activation times remained constant in the low strain range, but increased in the high strain range. All responses to strain were reversible. Similarly, a biphasic-shaped profile with a maximal velocity for strain closely associated with maximal force was described for cat ventricular trabecular (Rosen et al., 1981), Purkinje fibers from young and adult canine (Rosen et al., 1981) and rabbit ventricular muscle (Sachse et al., 2004). In the studies of adult canine Purkinje fibers, the increase of strain from 75% to 115% relative to slack length in an exemplary fiber was associated with an increase of resting voltage from -85 to -70mV and a decrease of upstroke velocity from 770 to 310V/s. Constant. An approximately constant conduction velocity, independent of strain, was reported in a study of papillary muscles from rabbit, cat and guinea pig and frog (Spear and Moore, 1972). The conduction velocity was determined by the ratio of distance between electrodes a t the muscle ends and the latency between stimulus artifact and membrane depolarization. In the study of rabbit, strain varied between 76% and 110% with respect to maximal force development and conduction velocity was in general below 0.4 m/s. Constant activation time (and thus velocity independent of strain) was also reported in a study of normal dogs and dogs with pacing-induced cardiomyopathy (Zhu et al., 1997). The measurements were carried out on the left ventricular anterior epicardium and tissue strain was increased by rapid infusion of intravenous saline. The amount of strain resulting from this injection was not measured. 30 Increasing. Increasing strain-velocity relationships were measured for Purkinje fibers of sheep (Deck, 1964; Dominguez and Fozzard, 1979). Increasing strain to 130% and 150% with respect to slack length resulted in 7.2% and 26% increase of conduction velocity (Dominguez and Fozzard, 1979). An increased conduction velocity for increased diastolic ventricular pressure (and thus increased strain) was found also in ra t atria (Tavi et al., 1996). The increase o f conduction velocity a t increased pressure disappeared after application of the nsSAC blocker gadolinium. Decreasing. A negative strain-velocity relationship was found for ra t papillary muscle (Spear and Moore, 1972). In this study, strain varied between 87% and 110% with respect to maximal force development. The reduction o f conduction velocity was approximately linear from 0.82 to 0.17m/s. A pacing site-dependent decrease of conduction velocity was reported for increased pressure in rabbit right atrium (Eijsbouts et al., 2003). Pacing a t the cranial p a rt of the crista terminalis resulted in no increase in conduction delays. However, pacing from the low right atrium revealed several lines o f block oriented parallel to the major trabeculae and the crista terminalis. The same study investigated stimulus rate effects (4.1 versus 8 Hz) on the strain-conduction velocity relationship. The increase o f rate reduced velocity in general. In an optical mapping study of rabbit ventricles, conduction velocity decreased by 25% after increasing ventricular end-diastolic pressure from 0 to 30mmHg (Sung et al., 2003). The pressure increase was associated with an anterior epicardial strain o f 104% and 103% in muscle fiber and cross-fiber direction, respectively. Application of 200 mM streptomycin did not change the overall conduction velocity. 2.3. Review o f computational studies An overview o f computational studies is given in Table 2. These studies were based on established models of electrical conduction in cardiac tissue extended with mathematical models of stretch-activated channels. Some of these studies included also models of strain-modulated tissue conductivity. Conduction is simulated in either cables, two-dimensional sheets or three-dimensional domains. The computational studies also showed differing relationships between strain and conduction velocity, which can be explained by the parameterization of models o f stretch-activated channels and strain-modulated tissue conductivity. A biphasic relationship between conductance o f mechano-sensitive channels and conduction velocity was found in simulations o f Purkinje fiber strands (Rice et al., 1998). The velocity increased for conductances in the range of 0-0.035 pS/mm2 and decreased rapidly for higher strain. Conductances above 0.045 pS/mm2 led to conduction block. Conduction block was explained by inactivation of fast sodium channels due to raised V rest by opening of stretch-activated channels. The same effect was suggested to underly slowed velocity in the high strain range (Mills et al., 2005), which was supported in a computational study of a guinea-pig myocyte strand (Sachse et al., 2006). In this study, the effect o f raising diastolic transmembrane voltage by opening o f stretch-activated non-selective cation channels and clamping o f the diastolic transmembrane voltage was similar. In both cases, the increased Vrest from -90 to - 60 mV led to reduction of upstroke velocity and conduction velocity. T.G. McNary et al. / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 387 Table 2 Computational studies of strain-conduction velocity relationships in cardiac tissue Year Authors and reference Species Tissue Dim. Relationship 1998 Rice et al. (1998) Mammalian Purkinje fiber 1 Biphasic 2000 Sachse et al. (2000) Guinea pig Ventricular 1,3 Variablea 2002 Sachse et al. (2002) Guinea pig Ventricular 2 Increasing 2004 Trayanova et al. (2004) Mammalian Ventricular 2 Variableb 2006 Sachse et al. (2006) Guinea pig Ventricular 1 Biphasic 2007 Kuijpers et al. (2007) Human Atrial 1 Decreasing 2007 Sachse et al. (2007) Guinea pig Ventricular 1 Biphasic aVelocity is related to strain-modulated conductivity. bVelocity decreased for cycle length shorter than 125 ms and increased otherwise. 31 Some computational studies indicated th a t the strain-conduction velocity relationship is effected by stimulus rate (T rayanova et al., 2004; Kuijpers et al., 2007; Sachse et al., 2007). In the high strain range, increased stimulus rate reduced current of the fast sodium channels, upstroke velocity and conduction velocity. F u rth e r studies examined the effect o f strain-modulated tissue conductivity on conduction velocity (Sachse et al., 2000, 2002; Kuijpers et al., 2007). Commonly, the underlying assumptions are th a t (1) the intercellular resistance associated to gap junctions is strain-independent and (2) the intercellular resistance associated to the cell interior is increased by strain. In previous work, we suggested to describe strain-modulation of tissue conductivities as a tensor transformation based on the deformation gradient tensor F, which is used in mechanics to derive various measures of strain (see Appendix A). Here, the conductivity tensor s is transformed by stretch to the tensor s s (Sachse, 2004): s s = --1 AsA T detA with the second order weighting tensor A and the determinant operator d et. The weighting tensor A is a function of the scalar weighting parameter 6: A = R (I + 6(U - I)) with the unit tensor I , the right stretch tensor U and rotation tensor R obtained by polar decomposition of the deformation gradient F = R U . Reasonable choices of the weighting parameter 6 are in the range [0,1]. A weighting parameter 6 = 0 yields a conductivity independent of strain and thus th a t the associated resistor is increasing with strain (Assumption 1). A parameter 6 = 1 leads to A = F and a scaling of conductivity, which keeps the resistor between given points constant and independent o f strain (Assumption 2). This setting would be appropriate if the gap junctions resistance is the dominant factor to intracellular conductivity. The suggested transformation applies a single scaling parameter to describe the effect of strain on conductivity. While this approach is sufficient to account for the upper assumptions, extensions of the transformation such as anisotropic nonlinear scaling parameters might be useful to describe, e.g., extracellular conductivities. However, experimental data for parameterization of the transformation are currently sparse. 3. Methods 3.1. Experimental study 3.1.1. Papillary muscle preparation The study was approved by the Institutional Animal Care and Use committee, University of Utah. New Zealand White rabbits (1-1.5 kg) were anti-coagulated with heparin (2500 USP units/kg) and anesthetized with intravenous administration o f pentobarbital (25 mg/kg). The hearts were rapidly excised and moved to a dissection tray filled with a low calcium oxygenized bathing solution containing (in mM) 126 N aCl, 11 glucose, 4.4 KCl, 1.0MgCl, 0.1CaCl2, 24Hepes and 12.9 N aOH. After opening the right ventricle, a non-furcated papillary muscle with a diameter smaller than 1 mm and length between 3 and 5 mm was selected. The muscle was excised including the onset of the chordae tendinae. The harvested muscle was then stored in the solution a t room temperature for 0.5 h. Afterwards, it was transferred to a horizontal flow-through chamber for mechanical fixation and measurement. Here, the papillary muscle was bathed with a similar solution as above. This solution (control) included 1 mM CaCl2. The streptomycin perfusate consisted of the control solution being supplemented with 100 mM streptomycin. The temperature of each solution was 37.0 ± 0.1 °C. The muscle was left in the bathing solution for a t least 0.5 h before the measurements began. 3.1.2. Experimental setup and protocol The experimental setup and measurement protocol were similar as previously introduced (Sachse et al., 2004). In short, electrograms were recorded using a silver-silver-chloride electrode, which was positioned along the muscle surface using a software-controlled micro-manipulator. The software was developed in 388 T.G. McNary et al. / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 32 LabVIEW 7.1 (National Instruments, TX). The locations for electrical measurements were calculated from the position of the distal and proximal muscle ends, which the user determined through positioning the recording electrode. The locations were digitally read into the computer. The software used the points to calculate 10 equidistant locations over the surface of the muscle. The location at the proximal end of the papillary muscle remained constant through the measurements, while the position at the distal end was reset manually as incremental strains were applied. This kept the measurement sites at the same position of the muscle as it was strained. Measurements started with a low strain of the muscle. Strain was increased incrementally every 2min after taking electrical and force measurements and until conduction block occurred. Straining increments were either 100 or 200 mm. In some experiments, we continued the measurements after conduction block and reduced strain every 2min until reaching the initial small strain. The bathing solution was switched after taking a set of measurements. If the muscle was initially immersed in a streptomycin solution, it was changed to control and vice versa. The muscle was left in the new solution for at least 0.5 h before measurements were resumed, allowing for wash in or wash out of streptomycin. Electrograms were low-pass filtered and recorded with a sampling frequency of 50 kHz. Force of contraction was measured using a force transducer (FORT10, World Precision Instruments Inc., FL) with a frequency of 1 kHz. Stimulus electrodes were of type silver-silver-chloride and were positioned at the proximal end of the papillary muscle. The electrical stimulus was biphasic with a duration shorter than 1ms. In preliminary studies, we found that biphasic stimuli produced smaller artifacts in the electrogram than monophasic stimuli. The stimulus frequency was kept at 0.5 Hz during the measurements. 3.1.3. Signal processing Acquired signals were analyzed offline using Matlab 7.2 (The Mathworks Inc., MA). All signals were digitally filtered using a third order Butterworth band pass (10-1000 Hz) and low pass (50 Hz) filter for the electrograms and force measurements, respectively. Each strain was normalized to the strain at maximal force development. The local activation time at each electrode position was defined as time of minimal temporal derivative in the extracellular unipolar electrogram in a time window after stimulation (Fig. 1) (Punske, 2000). The length of the stimulus artifact defined the start of the time window. Electrograms that were not biphasic or measured from proximal or distal sites were discarded when determining conduction velocity. Furthermore, only activation times that were a linear function of distance with a linear coefficient of r2 X0.99 were used to calculate conduction velocity (Fig. 2). The slope of the fitted line to the distance-activation time data determined the conduction velocity. T.G. McNary et al. / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 389 Time [ms] Fig. 1. Sample electrograms measured along a papillary muscle at different distances from the stimulus position. The distances range between 2.3 and 4.5 mm. The electrograms show truncated artifacts resulting from the biphasic stimuli starting at 4 ms with a duration of ~ 3 ms. The local activation times are identified with a down-stroke in the electrogram. Activation times increase with distance from the stimulus position. 33 390 T. G. McNary et al. / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 Activation Time [ms] Fig. 2. Exemplary activation time-distance relationships extracted from electrograms. The plots show relationships for three measurements under different strain conditions. Conduction velocity v was calculated after selection of electrograms showing a linear activation time-distance relationship. 3.1.4. Data selection and statistics Data sets with conduction velocity below 0.45 m/s at low strains were not included in statistical analysis as were data sets with peak velocity above 0.75 m/s. Several preparations showed velocities below 0.45 m/s, which is below the typical range for rabbit papillary muscle at physiological temperature (37.0 °C). The slow conduction might have been caused by partial gap junction closure due to damage during the extraction or mechanical fixation. Peak velocity above 0.75 m/s indicated the involvement of the fast conduction system such as Purkinje fibers with velocities in the range of 0.8 and 1.5m/s at resting length and up to 2.2m/s at high strain (Deck, 1964). The mean strain-conduction velocity relationship in the rabbit papillary muscle was determined by a piece­wise linear least squares fit. The fitting procedure yielded four continuous line segments specifying conduction velocities for strain in the ranges 80-90%, 90-100%, 100-110%, and between 110% and strain leading to conduction block. Statistics on the conduction velocities for control and streptomycin measurements excluded conduction block; the strains at which conduction block occurred were compared separately. Statistical comparison was evaluated using Student's t-test where p<0 .0 5 was considered to be significant. 3.2. Computational study The modeling was performed as previously described (Sachse et al., 2007). In short, electrical conduction in rabbit right ventricular papillary muscle was simulated by a computational mono-domain model of a one­dimensional strand. The strand consists of 24 cardiac myocytes coupled by gap junctions with a resistance of 1.25 MO. The chosen resistance represents high electrical coupling and led to physiological conduction velocity at slack length of the strand. This intercellular resistance was defined as independent of strain and intracellular conductivity was neglected (see Section 2.3, Assumption 2). Myocytes were represented by the Noble et al. model of guinea-pig ventricular cells (Noble et al., 1998). Currents through nsSACs were modeled by a Boltzmann-type relationship (Sachs, 1994) with reversal voltage of -30mV and half-maximal conductance of 0.02mS at strain l = 112.5%. The chosen reversal potential is in the range of potentials applied in related computational studies of -40 to - 20 mV (Sachs, 1994), -25 to -20 mV (Zabel et al., 1996a) and - 30 mV (Noble et al., 1998). Half-maximal conductance and associated strain were chosen to generate a membrane depolarization to -60mV for strain l = 125%. Simulations were carried out for various strain conditions of the papillary muscle. As a measure of strain the sarcomere length was varied between 1.68 and 2.52 mm. Here, a sarcomere length of 1.6, 2 and 2.5 mm represent 34 small strain (2 = 80%), resting (2 = 100%) and large strain condition (2 = 125%) of the myocyte, respectively. Stimuli were applied at one end of the strand with a frequency of 0.5 Hz, which is identical as in our experimental studies. Simulation results after 15 stimuli were analyzed. Conduction velocity was measured by detecting activation time of the 8th and 16th myocyte and assuming a myocyte length of 100 mm. Activation time was identified with the time at which the transmembrane voltage crosses -2 0 mV. Activation duration was defined to characterize the upstroke of the transmembrane voltage. As a measure of activation duration, we chose the difference between the time t90% at which the transmembrane voltages reaches 90% of resting voltage and the time t-20mV at which the transmembrane voltage exceeds -2 0 mV: activation duration = t-20mv - t90%. Activation duration was measured at the 12th myocyte. All calculations were performed in double precision floating point arithmetic. The system of ordinary differential equations underlying the myocyte model was solved with the forward Euler method using a time step of 1 ms (Press et al., 1992). Intercellular currents were updated every 1 ms. 4. Results 4.1. Experimental study Strain-velocity relationship in control. Conduction velocity was measured at 6-10 different strains for each papillary muscle. The measurements started by applying small strain and continued with sequentially increasing strain. We acquired relationships in 17 papillary muscles. From these, 5 and 3 papillary muscles showed conduction velocities below 0.45m/s at small strain or larger than 0.75m/s, respectively. We did not include these data in further analysis. In the remaining nine experiments, peak and mean conduction velocities varied over a large range, but the individual relationships showed a similar progression. Examples of the measured strain-conduction velocity relationships for control are shown in Fig. 3. The averaged progression is depicted in Fig. 4. Conduction velocity increased with strain until a peak value of 59.8 ± 1.9cm/s was reached at strain of ^ 100%, which is the strain leading to maximal active force of contraction. The mean conduction velocity increased by 5% for 80-90% strain and by 12% for 80-100% strain. Strain beyond 100% caused the velocity to decrease until conduction block occurred at 118 ± 1.8% strain. Strain-velocity relationship with streptomycin. With the same protocol as above, we measured the relationships in 14 papillary muscles bathed in a solution containing 100 mM streptomycin. Again, we excluded T. G. McNary et al. / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 391 Strain [%] Fig. 3. Exemplary strain conduction velocity relationships in three papillary muscle preparations. Measurement data were marked with the symbols x, * and +. Conduction velocity shows an increase for small and middle strains. Conduction block was found at high strain. Range of conduction velocities can greatly differ between preparations. 35 392 T.G. McNary et al / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 Strain [%] Fig. 4. Strain-conduction velocity relationship for control and after application of 100 mM streptomycin. Conduction velocity for control shows an increase in the range of 80-100% followed by a decrease before conduction block. Conduction velocity using streptomycin resulted in a smaller increase. However, conduction was blocked at similar strain. Vertical and horizontal bars indicate standard error of velocities and strains at block, respectively. Strain [%] Strain [%] Fig. 5. Hysteresis of strain-conduction velocity relationship for (a) control and (b) after application of 100 mM streptomycin. In these experiments strain was increased until block and then decreased. Mean conduction velocity for each strain was larger during the increasing phase than the decreasing. For control, conduction velocity at 100% strain is 5cm/s larger in the increasing versus decreasing phase. data with conduction velocities below 0.45 m/s a t small strain or larger than 0.75 m/s. The averaged progression is shown in Fig. 4. In the remaining 10 experiments, conduction velocity and progression were similar to control measurements for 80-90% strain. For 80-110% strain, the velocity was in general smaller and showed over this range only a moderate increase of 8%. Peak conduction velocity was 54.8 ± 1.5 cm/s at 110%, which is a statistical significant decrease of 9% in comparison to peak velocity in control. Conduction block occurred a t 119 ± 0.8% strain with no statistically significant difference to control. Block and hysteresis. We further investigated the mechanism of conduction block with an extension of the protocol described above. After block strain was incrementally reduced until the initial low strain configuration of the papillary muscle was reached. We found th a t the block is reversible by reducing strain (Fig. 5). The control measurements revealed hysteresis after block by comparing conduction velocities for increasing and decreasing strains. The average velocity and velocity a t 100% strain decreased to 2.5% and 7.1%, respectively, from the increasing to decreasing strain in the control measurements. With streptomycin in the solution the decrease was reduced to 1.5% and 2.3% for average velocity and velocity a t 100% strain, respectively. 36 4.2. Computational study We performed computational simulations of mechano-electric effects with the one-dimensional model of cardiac tissue described above. Simulated resting voltage, maximal upstroke velocity and conduction velocity versus sarcomere length as a measure of strain are shown in Fig. 6. The strain-conduction velocity relationship was strongly dependent on involvement of nsSACs (Fig. 6a). Without nsSAC currents, velocity was linearly related to strain. The conduction velocity at sarcomere length of 2.1 mm was 0.50 m/s. The velocity was 0.37 and 0.60 m/s at lowest and highest strain, respectively. A 10% increase in strain led to a 10% increase in velocity. With nsSAC currents, velocity displayed a biphasic relationship to strain with a peak velocity of 0.62 m/s at sarcomere length of 2.275 mm (Fig. 6a). The velocity was 0.37 and 0.43 m/s at lowest and highest strain, respectively. For sarcomere lengths between 2 and 2.35 mm, nsSAC currents augmented the velocity in comparison to the velocity without nsSAC currents. Above 2.35 mm, nsSAC currents slowed conduction. With increasing strain the resting voltage decreased from -9 3 to -5 9m V (Fig. 6b) and the maximal upstroke velocity decreased from 236 to 33V/s (Fig. 6c). The simulations revealed a biphasic relationship between nsSAC currents and activation duration (Fig. 6d). The activation duration decreased with increasing nsSAC currents to a minimum of 0.527 ms at sarcomere length of 2.25 mm. For larger strain and increasing nsSAC, the activation duration increased. T.G. McNary et al. / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 393 Fig. 6. Simulation of mechano-electric feedback in a one-dimensional model of cardiac tissue. Strain was quantified by sarcomere length. (a) The simulation yielded conduction velocity v as a function of sarcomere length. The strain-velocity relationship was determined with (solid) and without (dashed) involvement of nsSACs. Currents through nsSACs led to (b) resting voltage V rest increasing with strain, (c) maximal upstroke velocity dV max decreasing with strain and (d) a biphasic relationship between strain and activation duration. 37 5. Discussion and conclusions 5.1. Experimental studies Our experimental data on rabbit papillary muscle supported the biphasic relationship of strain to conduction velocity, which has been previously reported in studies of mammals, reptiles and fishes (Penefsky and Hoffman, 1963; Rosen et al., 1981). We applied a wide range of strain from 80% to 120% with 100% referencing to strain of maximal force development. Smaller strains led to bending of the papillary muscle. The upper strain limit was decided by occurrence of conduction block. In the lower strain range (80-100%), the velocity was approximately linearly increasing with strain. In the higher strain range (above 100%), the velocity was decreasing with strain and eventually culminated in conduction block. The block occurred with a probability of 100% was reversible and associated with hysteresis of velocity. The finding of a biphasic strain-conduction velocity relationship is in agreement with our computational studies. Biophysical mechanisms underlying the relationship are subsequently hypothesized (Section 5.2). Our discovery of conduction block at high strain is consistent with the occurrence of block reported for increased pressure in rabbit right atrium (Eijsbouts et al., 2003). In our studies, the block occurred at similar strain with or without streptomycin in the bathing solution. We conclude that the block is not related to activity of nsSACs. This conclusion is supported by our computational studies, which failed to reconstruct block with and without inclusion of nsSAC currents (Fig. 6a). Potential mechanisms underlying block are opening of the before mentioned K+ stretch-modulated ion channels and mechano-sensitivity of gap junction channels. Opening of K+ stretch-modulated ion channels would impose a larger electrical load on depolarizing myocytes potentially prohibitive for conduction. Closure of gap junction channels in the high strain range would prevent intercellular current flow and thus conduction. The latter hypothesis is supported by a recent single-channel and whole cell study of Cx46 hemi-channels (Bao et al., 2004), which showed that current through these hemi-channels is mechano-sensitive. However, Cx46 is not expressed in the heart and the mechano-sensitivity of cardiac connexins remains to be clarified. Application of the nsSAC blocker streptomycin reduced peak velocity, shifted the associated strain to 110% from 100% in control and reduced the extent of hysteresis. Differences between control and streptomycin data were insignificant for strains between 80% and 90% as well as for strain at block. We conclude that under physiological conditions currents through nsSACs are contributing to peak velocity and the initial phase of subsequent decreasing of velocity. The conclusion is supported by our computational studies, which showed that nsSAC currents boost and reduce conduction velocity for moderate and large strain, respectively (Fig. 6a). Furthermore, the nsSAC currents appear to be responsible for hysteresis. Under physiological conditions, the opening of nsSACs results in inward currents of sodium and calcium and outward current of potassium. We speculate that in the long-term these currents change intracellular ion concentrations, which directly or indirectly reduce conduction velocity. The mechanism could involve the electrogenic sodium-calcium exchanger (NCX). Increased concentrations of intracellular calcium increases the transfer of calcium out of and sodium into the cell by NCX. Assuming that the calcium concentration is sub-acutely raised, a persisting NCX activity could depolarize the membrane and cause sodium channel inactivation. Limitations. The measured velocities showed a high inter-preparation variability (Fig. 3). Several reasons can account for this variability: Firstly, several preparations showed very large velocities up to 1.3 m/s, which indicated involvement of the fast conduction system. We did not include data from experiments with peak velocity larger than 0.75 m/s in our analysis. However, we cannot exclude the possibility that excitation was partially carried by the fast conduction system in some of our preparations. Secondly, the diameters of the preparations were inhomogeneous. Velocity in a strand preparation is moderately dependent on its diameter (Roth, 1991). A strand with radius of 0.2 mm has an « 8% larger velocity than with 0.6 mm radius. Thirdly, the shape of the preparations was inhomogeneous. Some muscles had uniform circular cross-sections, others were slightly tapered toward the tendon. This shape variation might affect conduction velocity, but to what extent is unclear. Despite the high inter-preparation variability the biphasic relationship was consistently found in our measurements. 394 T.G. McNary et al. / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 38 The application of streptomycin to block nsSACs in tissue and whole heart preparations has been questioned in several studies (Lamberts et al., 2002; Sung et al., 2003; Cooper and Kohl, 2005; Garan et al., 2005). Application of streptomycin in sino-atrial node tissue from guinea pigs and mice did not eliminate strain related changes of the chronotropic beat rate (Cooper and Kohl, 2005). Application of streptomycin did not alter the frequency of ventricular fibrillation in a study of commotio cordis in pig heart (Garan et al., 2005) and did not affect electrophysiological changes related to increased ventricular filling in a study of isolated rabbit heart (Sung et al., 2003). Conversely, arrhythmias were suppressed in the presence of streptomycin when whole rat hearts were exposed to increased ventricular pressure (Salmon et al., 1997). The slow inotropic response of rat cardiac myocytes and tissue was reduced by streptomycin (Calaghan and White, 2004). Also, in myocyte preparations, nsSACs have been reportedly blocked by streptomycin (Belus and White, 2003). In our hands, the application of 100 mM streptomycin strongly affected the strain-modulation of conduction velocity in a manner compatible to the subsequently described hypothesis to explain this mechano-electric feedback phenomenon. However, the degree of nsSAC block by streptomycin remains unknown. In our studies, streptomycin sulphate was used. The upper concentration of the nsSAC blocker refers to the single streptomycin molecule (White, 2006). Our measurements were carried out with isometric condition of the tissue, while under physiological conditions cardiac muscle undergoes marked contractions during each beat. Isometry is an approximation of physiological conditions, where conduction occurs at the end of diastole while the heart is almost in a steady mechanical state. The condition was used in previous studies of strain-conduction velocity relationships in papillary muscle, Purkinje fibers and tissue strips. With our protocol, measurements were taken every 2min and immediately afterwards strain was increased or decreased. Thus, our measurements represent only steady state conditions and transient effects were neglected. 5.2. Computational studies Our simulations reconstructed a biphasic relationship of strain and conduction velocity similarly as revealed in our experimental studies of rabbit papillary muscle. The biphasic relationship resulted from the combined effects of two factors of mechano-electric feedback: nsSACs and strain-modulated intercellular conductivity (Fig. 7). Our choice of strain-independent resistance led to linearly increasing strain-conduction velocity relationships for all strains (Fig. 6a). Currents through nsSACs had varied effects. At moderate strain, nsSAC currents depolarized the membrane in such a manner that time to activation was reduced despite upstroke velocity was identical as for small strains. At large strain, the increased depolarization of the membrane led to inactivation of the fast sodium channels and their availability was strongly reduced. This reduction diminished upstroke velocity of the transmembrane voltage and slowed conduction. Our computational results are in qualitative agreement with previous experimental work with various tissues and species (Penefsky and Hoffman, 1963; Rosen et al., 1981; Sachse et al., 2004) as well as with computational studies on mammalian Purkinje fibers (Rice et al., 1998) and mammalian myocardial strips (Trayanova et al., 2004). Our findings are not in complete agreement with a computational study of strain-conduction velocity relationships in human atrial tissue (Kuijpers et al., 2007). This study indicated a generally decreasing relationship for strain 1X100% in accordance with studies in dog and rabbit atrial tissue (Solti et al., 1989; Eijsbouts et al., 2003). In part, the differences between the computational studies can be explained by different parameterization of nsSACs. The activation of nsSAC currents was shifted to smaller strains and conductances were sufficiently large to block conduction at high strain by inactivation of the fast sodium channels. Further differences are related to their definition of strain-modulated intercellular conductivity leading to constant or linearly decreasing strain-velocity relationships. The computational studies with and without inclusion of nsSAC currents did not reconstruct block of conduction, which occurred in our experiments with a probability of 100% with and without application of 100 mM streptomycin for extreme strain (Fig. 4). The simulations demonstrated that nsSAC currents can boost or lower conduction velocity, but with the given parameterization the currents were insufficient to depolarize the membrane to such an extent that cells were inexcitable and conduction was blocked. In principle, this would have been possible by increasing nsSAC conductivity. However, the occurrence of block in our T.G. McNary et al. / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 395 39 396 T.G. McNary et al. / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 Fig. 7. Hypotheses for mechanisms of strain-conduction velocity relationships in ventricular tissue. We suggest that four different mechanisms are relevant. Two of these, strain-modulated conductivity and depolarizing nsSAC currents / NS,SAC for moderate strain, lead to positive strain-velocity relationships. Depolarizing currents INS;SAC at large strain underly the negative relationship. A less understood mechanisms is suggested to be responsible for block. experimental studies in presence of streptomycin indicates that such an approach would be inappropriate. Currently, experimental data explaining conduction block at extreme strain are sparse. We suggest that studies of mechanical modulation of conduction and intercellular resistance in myocyte pairs will help to gain insights in biophysical mechanisms of block. Limitations. With our computational studies we aimed at a qualitative reconstruction of strain-conduction velocity relationships. We did not apply more detailed conduction models such as three-dimensional bidomain models, which we have used before for reconstruction of wave propagation in papillary muscle (Sachse et al., 2005). Also, we did not attempt a quantitative reconstruction of the experimental data. We suggest that optimized descriptions of nsSACs and integration of these in an electrophysiological model of rabbit myocytes will improve the reconstruction of our experimental data. We applied a Boltzmann-type relationship of nsSAC currents to strain (Sachs, 1994). Various other descriptions of nsSACs have been suggested (Rice et al., 1998; Noble et al., 1998; Zeng et al., 2000). Remarkable differences between the guinea-pig model of Noble et al. (1998) applied in our study and the model of rabbit ventricular myocytes of Puglisi and Bers (2001) can be found for resting transmembrane voltage and upstroke velocity. Both are important factors contributing to the strain-conduction velocity relationship (Section 2.1). The steepness of the simulated strain-velocity relationship in the low strain range is about twice of the steepness of the measured data. Thus, the assumed strain-independence of intercellular resistance (Section 2.3, Assumption 2) appears to be an oversimplification and an extreme choice. An intermediate behavior would reduce the large effect of strain on conduction velocity in the low strain range. 40 T.G. McNary et al. / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 397 5.3. Comparison with studies o f atria and ventricles In our studies on papillary muscles we applied one-dimensional strain in the muscle's long axis direction, which is also the myocytes' long axis direction. Assuming volume preservation of cardiac tissue and transversal isotropic tissue properties, increased straining in fiber direction 1fiber will lead to reduced strain in the two orthogonal cross-fiber directions 1cross-fiber: Similar straining conditions are commonly applied in studies of stretch-activated currents in isolated myocytes. The straining condition is different in studies of atria or ventricles, in which strain is modified by setting cavity pressure or volume (Solti et al., 1989; Tavi et al., 1996; Zabel et al., 1996a; Reiter et al., 1997; Zhu et al., 1997; Eijsbouts et al., 2003; Sung et al., 2003). In these studies, increasing pressure or volume caused an increase of strain in fiber and epicardial cross-fiber direction, which presumably is associated with a reduction of strain in the orthogonal direction. Ventricular filling studies indicated that the resulting strains in fiber and epicardial cross-fiber direction are significantly smaller than strain applied in studies on papillary muscle and Purkinje fibers (Sung et al., 2003). 5.4. Summary Major features in our experimental and computational studies of ventricular tissue were the biphasic strain-conduction velocity relationship and block at extreme strain. Our computational studies supported previous work done by us and others showing that this relationship is associated with a positive strain-resting voltage and negative strain-maximal upstroke velocity relationship at cellular level. Our computational studies did not reconstruct block at extreme strain and further experimental studies are necessary to gain data A summary of our hypotheses to explain the biphasic relationship and block is given in Fig. 7. We propose four partially cooperative mechanisms which are associated to specific strain ranges: • Over the complete strain range: strain-modulated conductivity causes a linear positive relationship. • Moderate strain: nsSAC currents lead to a positive relationship by reduction of activation duration. • Large strain: nsSAC currents yield a negative relationship by sodium channel inactivation. • Extreme strain: block results from an unknown mechanism, potentially currents through stretch-activated potassium channels and/or closure of gap junction channels. Only the first three hypothesized mechanisms have been supported by experimental and computational Our hypotheses might explain uni-axially applied strain-conduction velocity relationships in other types of cardiac tissue such as Purkinje fibers and trabeculae. However, the hypotheses necessitate adjustment to reconstruct pressure or volume related changes of velocity in atria and ventricles. Acknowledgments This work was funded by the Richard A. Harrison and Nora Eccles Fund for Cardiovascular Research and awards from the Nora Eccles Treadwell Foundation. on this effect. studies. Editor's note Please see also related communications in this issue by Zhang et al. (2008) and Loiselle et al. (2008). 41 Appendix A. Measures of strain Strain tensors. Different descriptions of strain are found in mechanics to specify deformation of a material (Bathe, 1982). For example, in continuum mechanics tensors of second order, e.g. the Cauchy strain tensor C and the Lagrange strain tensor E, are applied to quantify the deformation. These tensors are derived from the deformation gradient tensor F , which can be defined by differentiating the coordinates tx(°x, t) with respect to the reference configuration coordinates 0x in a cartesian system: 398 T.G. McNary et al. / Progress in Biophysics and Molecular Biology 97 (2008) 383-400 = One-dimensional strain. One-dimensional strain l is commonly described by the ratio of length under load I to resting length L : i = L. Here, strain is unit-less and has a value of 1 if no loads are applied. We used this notation for specifying strain at cellular level. In this work, we commonly quantified strain in cardiac tissue with reference to strain for maximal force development and in percentage: / 0tx1 0tx1 0tx1 \ 0% 0% 0% 0txi 0tx2 0tx2 0tx2 N 00x 1 0% 00x3 0tx3 0tx3 0tx3 ^ 0% 0% 00x3 j If / Lf ■100%. Thus, a strain of 100% would correspond to peak force development. The choice is motivated by simple accessibility of force in studies of papillary muscle, trabeculae, atrial and ventricular strips, and Purkinje fibers. References Bao, L., Sachs, F., Dahl, G., 2004. Connexins are mechanosensitive. Am. J. Physiol. Cell Physiol. 287, C1389-C1395. Bathe, K.-J., 1982. Finite Element Procedures in Engineering Analysis. Prentice-Hall, Englewood Cliffs, NJ. Belus, A., White, E., 2003. 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Sachse*** f Nora Eccles Harrison Cardiovascular Research and Training Institute, *Department of Bioengineering, and §School of Medicine, University of Utah, Salt Lake City, Utah ABSTRACT The transverse tubular system (t-system) is a major site for signaling in mammalian ventricular cardiomyocytes including electrical signaling and excitation-contraction coupling. It consists of membrane invaginations, which are decorated with various proteins including mechanosensitive ion channels. Here, we investigated mechanical modulation of the t-system. By applying fluorescent markers, three-dimensional scanning confocal microscopy, and methods of digital image analysis, we studied isolated ventricular cardiomyocytes under different strains. We demonstrate that strain at the cellular level is transmitted to the t-system, reducing the length and volume of tubules and altering their cross-sectional shape. Our data suggest that a cellular strain of as little as 5% affects the shape of transverse tubules, which has important implications for the function of mechanosensitive ion channels found in them. Furthermore, our study supports a prior hypothesis that strain can cause fluid exchange between the t-system and extracellular space. Received for publication 21 January 2011 and in final form 24 March 2011. Correspondence: [e-mail] Mammalian ventricular myocytes exhibit a transverse tubular system (t-system), which consists of membrane invaginations (1). Geometry and morphology of the t-system were found to be dependent on species and cell type (2). The t-system is an important site for excitation-contraction coupling and essential for rapid electrical signaling from the outer sarcolemma into the cell interior. Recent interest in the t-system has been renewed by studies demonstrating that transverse tubules (t-tubules) are less dense and their arrangement is disorganized in diseased ventricular cardiomyocytes (3,4). It has been suggested that t-tubular loss reduces the effi­ciency of cardiac excitation-contraction coupling (5). It has also been suggested that mechanical deformation of the t-system can contribute to fluid exchange between it and the interstitial space (2,6). Such a pumping mechanism would support transport of nutrients, metabolites, and ions into the myocyte. Any t-system deformation may contribute to mechanical modulation of ion channels. Mechanosensi-tive ion channels found in the t-system include stretch-activated transient receptor potential cation channels (TRPC6 ) and stretch-modulated inward rectifier potassium channels (Kir2.3) (7). The aim of this study was to characterize the transfer of strain at cellular level to the t-system. The study is based on our previous work, which applied three-dimensional scanning confocal microscopy on living isolated cardio-myocytes to characterize geometrical features of the t-system (2 ). We found that the rabbit t-system rarely exhibits longitudinal tubules. We demonstrated flattening of t-tubule cross sections and alignment of their short axis with the long axis of myocytes. We suggested that the flat­tening is related to the myocytes being at a slack length and is altered when they shorten or lengthen. Using this experimental and analytical approach, we studied mechanical deformation of the t-system of myocytes. Strain was applied statically by longitudinal stretching of the myocytes. We hypothesized that 1 ), cellular strain is trans­mitted to the t-system; and 2 ), mechanical deformation of myocytes contributes to fluid transport between the t-system cavities and extracellular space. We tested these hypotheses by imaging and comparison of geometrical features of t-tubules in quiescent myocytes at rest and during static strain. The protocol used for isolating rabbit myocytes is described in the Supporting Material. The myocytes were transferred to an imaging chamber, suffused with a mem­brane- impermeable dextran conjugated to fluorescent dye (Alexa 488; Invitrogen, Carlsbad, CA), and imaged using a LSM 5 Duo confocal microscope (Carl Zeiss, Jena, Germany). The setup for imaging and straining of myocytes is shown in Fig. S1 in the Supporting Material. Exemplary images obtained from a myocyte before and during strain are shown in Fig. 1 . The image stacks were deconvolved and corrected for background signals and depth-dependent attenuation (8 ). Longitudinal spacing of t-tubules, D, was determined by maxima in Fourier spectra of the three-dimensional images. Strain was defined as DStrained/DUnstrained with DStrained and Editor: Andrew McCulloch. © 2011 by the Biophysical Society doi: 10.1016/j.bpj.2011.03.046 46 L54 Biophysical Letters FIGURE 1 Image of myocyte segment before (A) and during (B) 15% static strain. Extracellular space and t-system exhibit fluo­rescent signal. Two corresponding t-tubules are marked in each image (arrows). Longitudinal t-tubular spacing D was (A) 1.80 and (B) 2.06 mm. Scale bar: 10 mm. Dunstrained describing the spacing after and before strain, respectively. Fractional volume of the t-system was calcu­lated based on fluorescence ratios (9). T-tubules were automatically segmented with the region-growing method (10). Characterization of t-tubules by prin­cipal component analysis was based on the image moments of spherical regions (10). The centers of these regions were regularly spaced (~0 . 2 mm) along the t-tubule longitudinal axis. Centroids of these regions x were determined by first-order image moments given by x - (x! X2 S3 )' = J 2 Xi /(Xi) / J 2 1(Xi), ie S ie S with the three-dimensional image I and the set of voxel indexes in the spherical region S. A matrix of second-order central image moments M2 was set up as / M 200 M 110 M 101 \ M 2 = I M 110 M 020 M 011 I i \M 101 M011 M002 ) with the moments Mpqr - ^ (Xi,1 - ST) P(Xi,2 - X2) ? (x,-3 - Sj) 7(x,). ie S Eigenvalues, 11 ,1 2, and 13, and eigenvectors, e1, e2, and e3, of M2 were calculated by singular value decomposition. Several measures served for characterization of t-tubule cross-sections: ellipticity and orientation. Ellipticity £ of tubules was defined as £ = 1 - \ ! I 3 / I 2 . With this measure, a decrease of ellipticity corresponds