Control of cardiac output studied with computer techniques.

This thesis concludes with an analog model which has limitations but provides a solution to the control of cardiac output. This solution is not unique and as a model is used to predict the response to different types of stimulation, changes, will be made. However, a basic model has been presented based on the just described experiments which show that peripheral resistance is a very important factor in controlling cardiac output, both by its effect on the baroreceptor reflex and its direct mechanical effect on stroke volume. At this stage of experimentation the most important role of the model has been to explicitly give numerical values to parameters of the system but to give insight into the type or research that must be carried out to fully describe this control system as well as insight into the possible nature of relationships not yet known.

CONTROL OF CARDIAC OUTPUT STUDIED WITH COMPUTER TEClINIQUES by William Sanforo Topham A thesis submitted to the faculty of the University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Biophysics and Bioengineering University of Utah August, 1965 R:EED. M GARDNER .. This Thesis for the Doctor of Philosophy Degree by William. Sanford Topham has been approved August, 1965 ChaJ.nnarl, Superv�sory COmnu ttee Reader, Superv�sory Corrrnittee Reader, supervisory comrra:ttee Reaaer� Supervisory cornmittee Head, Ma:j or Diiparbnent fi!an, Graduate SChool ACKNOWLEDGMENTS Without the able assistance of many people. it would have been impossible for this completed work to have become a realityo A special thank you is extended to nro Homer Ro Warner for his encouragement, advice and patient guidance during the experimental wor.k and preparation of this Thesis and also for providing a most stimulating atmosphere 0 Acknowledgment and appreciation are also offered to the American Heart Association and the National Institutes of Health under whose grants and fellowships the work was done, to John Gadd who spent many hours assisting with experiments and preparing figures for the manuscript, to Miss Rowena Bowers for her excellent preparation of the manuscript, to William Day for the photography and to Allan Pryor for his capable assistance in the writing and operation of the digital canputer programs 0 iii INDEX Page Introduction 0 0 0 0 o ~ 0 • 0 e 0 0 0 0 0 0 0 GOO 0 QQ. G 0 0 000 1 Experimental Results Experiment I -- Normal Responses to Exercise Q Q 0 ~ 0 Q (I 0 (I 36 GOO 44 o Experiment II -- Controlled Constriction of Descending Aorta Experiment III -- Constriction of the Brachiocephalic Artery ~ Analog Computer Model tl 0 References 0 00.., • " 0 0 .0 0 Q 0: 0 C " o (i) 0 0 Q 0 o 0 Appendix A Equations for Analog MOdel 0 (I 0 Appendix B Constants from Analog Modele 0 0 Vita 0 0 0 o 1.11 Q 0 0 0 0 m Q " 0 0 0 0 00. 0 " 0 0 0 " • 0 Q 0 '" 10 () Q 18 • <:I 54 " 000 Q 57 o 0 o 0 t) 0 o 0 o • 60 </I 0 0 <1! 1.1 0 Q 0 62 (;) " 0 /) the nnre we investigate the action of the heart, the rrore we must be filled with wonder and admiration at the marvelous way in which it is fitted by nature for the task which it has to perform; and the elucidation of the laws which determine its power of adaptation, as suggestive of purpose as that of a sentient being, presents an interest as enthralling in the thousandth experiment as it was in the first 0 ,,24 This was stated by Starling in his famous Linacre Lecture on the Law of the Heart in 1915 The concepts presented in this 0 lecture were pemaps scme of the earliest, most significant contributions made in regard to the regulation of cardiac output He showed 0 that the heart, in an isolated heart and lung preparation, had an inherent control system because the cardiac muscle responded similarly to skeletal muscle, i(l)e o as the end-diastolic volt.Dne increased, stretching the fibers, the muscle contracted more forcibly causing an increased e jectioo from the heart 0 When venous inflCM increased, the end-diastolic voltune increased and within a few beats the flCXtJ out equaled the flCM in 0 By this mechanism it was postulated that be- cause the venous return increases during exercise due to the additional pumping action of muscles and deeper respiratory movement, a distension of the ventricle takes place and an increase in stroke volume results 0 Also, due to the increased venous return, an in- creased tension on the venous side of the heart appearedo It was 2 proposed that the increased tension in the right atrium evoked reflexly an increased heart rate probably due to the inhibition of vagal tone but possibly by reflex stimulation of the sympathetics.. The oveI'-all result of this increased venous return was additional stroke volume and increased .heart rate which increased the cardiac outputo Further evidence to indicate the importance of end-diastolic volume in the role of cardiac output was shONll. when the venous return was held constant and the arterial pressure was increasedo l2 During the first three to ten beats the heart output was reduced but as the end-diastolic volume increased because of the constant inflow the output increased until the original value was attained o Starling explained a possible control mechanism: if there is a sudden dilitation of the arterioles which causes an increase in capacity and lowering of resistance. the lowering of resistance causes a fall in arterial pressure and a rise in venous pressuree The fall in arterial pressure and the rise in venous pressure contribute to cardiac acceleration, the rise in venous pressure also aids the increase in output because of the increased venous return 25 0 Further investigation showed there was a proportional relationship between end-diastolic volume and heart oxygen consumptiono 27 Assuming the oxygen consumption is proportional to the energy released or the work done by the heart, end-diastolic volume is related not to arterial press1.lt'e or venous return alone but to the product of the two since the work of the heart is proportional to the amount of blood it pumps times the pressure against which it pumps" When the heart was 3 failing, the relationship of end-diastolic volume and oxygen consumption remained, indicating a decrease in efficiency because of the decrease in useful worko With the injection of epinephrine the oxygen constunption increased for a given diastolic volt1l'Ie, but the proportiooal relationship remained 0 With same modification this idea was extended by Sarnoff in later investigations 19 ,20,22 which showed that there was not only one curve which related the end-diastolic pressure and the stroke-work of the ventricle, but there was a whole family of such curves, and it was possible to move from one curve to another by injection of epinephrine and also by stimulation of the sympathetic nerves 0 The reflex action of the baroreceptor'S also prompted the movement from one curve to another in this family of ventricular function curves Q In these studies stroke-work in gram-meters was calculated by the follONing equation: CIf:' ~= (mean arterial pressure - mean left atrial pressure) X stroke volume rna and the recorded mean atrial pressure was asS\.ml.ed to be end-diastolic pressUI.'e o 1m. effort was made to establish a relationship between other parameters such as right atrial pressure and left ventricular strokework, atrial pressure and stroke volume, and atrial pressure and cardiac output 0 No consistent relationship was found to existo While it is evident from the experiments of Starling that the heart does have an inherent regulatory mechanism, the last series of experiments demonstrate that it can be modified by neural control(l 4 Further evidence seems to indicate that in the intact animal this basic control is so completely modified by other mechanisms that it appears to be almost nonexistento Gregg 4 describes experiments in which the relationship of end-diastolic pressure to stroke-work and stroke volume was considered in three types of experiments ~ 1) the anesthetized, open-chest dog during ventricular loading with whole blood; 2) the anesthetized, closed"""chest dog during ventricular loading with whole blood; 3) the trained, normal, tmanesthetized dog before and inm.ediately after exercise 0 From the data obtained in the first two types of experiments, there appears a good positive co~lation between the changes in left ventricular end-diastolic pressure with stroke-work and stroke volumeo Although in the closed-chest dog this positive correlation appeared only in 50 to 10 percent of the comparisanso the co~lations With the exercising dog, almost disappeared and in some cases an increased stroke-work was observed with a decreased end-diastolic pressUr'eo It should be noted that the exercise measurements were made immediately after exercise and the variation during exercise may be different. In both the exper:i.m=nts of Sarnoff and Gregg the end- diastolic pressure was measured rather than the ventricular volume which is a difficult para.m:!ter to measure in an intact animalo It was felt by both investigators that a reliable measurement of ventricular volume would help to better understand the observations of Starling in the intact animalo 5 Fran roentgenkymogralIlS at rest and exercise the results of Reinedell have shown that in the athlete the end-diastolic heart size gets smaller during exercise while at the same time the stroke volt.Une may be markedly increasedo The increased stroke volume is apparently due to more canplete emptying of the ventricle o Other studies shGV that the tmtrained persoo also reduces his end-diastolic heart size during work 3 0 By measuring the ventricle diameter in an intact dog Rushrner has confirmed these results~17 During exercise the diastolic diameter decreases or remains at the sa.rre value as the resting control systolic diameter decreases slightlyo 0 The When exercise is stopped, there is an increase in both diameters as the heart rate decreases o This type of response does not agree with the response that would be predicted by Starling's Law, namely, at rest the volt.Une would be relatively small, .during sleep a little smaller and during exercise the volUl'le of both diastole and systole would increase markedly and then decrease at the end of exercise 0 The only similar relationship which the diameter measurements showed was a decrease in ventricular diameter from the resting state to the sleeping state 0 The effect of venous return in determining the cardiac output has been an area of popular interest and while this return has a great effect on the in vitro preparation, Guyton has shown that in vivo the venous return is a function of many variables and may be defined by the follcwing equation ~ 5 = f(MCFP) a v feD) 0 (MCFP _ RAP) a C 6 where. C :: dimensional constant MCFP :: mean central filling pressure RAP :: right atrial pressure v :: blood viscosity feD) :: a function of the different dimensions of the peripheral circulating system Many of these variables are changed as cardiac output is changed indicating the venous return changes are probably a result of cardiac output changes and are not the cause of cardiac output variances 0 Because of the conflicting ideas of the relationship between cardiac output, venous return Il arterial pressure, end-diastolic volume, end=diastolic pressure, neural effects and hormonal effects in the literature, Rushmer perfonned a series of experiments in which an effort was made to isolate the cause and effect of some of these parameters in an-intact animalo 14 t lS ,18 After exercising a dog on a treadmill and obtaining a nonnal response, experiments were done on the same dog in an effort to simulate the responses of the dog during exercise of these was to increase the venous retum o 0 The first This was done by infusion and also by sudden compression of the abdomen to further empty the large venous vessels o There was some modification in left ventricular per- formance but the response did not simulate the response to exercise o To test the role of peripheral resistance in causing changes in heart rate and ventricular function, two methods were usedo Isopropyl arterenol was injected manually at a rate sufficient to 7 produce changes similar in magnitude to the exercise response o This caused a marked drop in peripheral resistance and effected a change on ~ocardial contractility with the over-all response being very similar to that of exercise o HCW'ever, this substance is not found in signifi- cant amounts in the normal animal 0 'Ihe second method to test the role of peripheral resistance was an experimental arterial-venous shunt between the femral artery and the femoral vein with a pump used to accelerate the blood flow from the artery to the vein a marked reduction in peripheral resistancea 0 The result was Increase in heart rate occurred but ventricular function was not that of exercise" Wi th exer- cise there was a marked increase in ventricular press~ in peripheral resistance produced no increase o The ventricular diameter while the drop remained nearly the same with a slight decrease more evident during exercise 0 Epinephrine and norepinephrine infused at rates based on the estimated secretion of the adrenal medulla during exercise did not simUlate the exercise response at alIa In fact, there was a slight increase in heart rate after which bradycardia occurred, probably due to the increased blood pressure and the receptors l~flex action of the bare- 0 Stimulation of the autonomic nerves which go to the heart reproduced a response which was remotely related to that of exercise, however, sympathetic stimulation produced profound changes in the left ventricular function if the heart rate was maintained constant by an artificial pacernakero Because this change of ventricular function was 8 found. exploration of the higher centers in the central nervous system was in! tiated G It was found that stimulation of the hypothalamic and diencephalic an:!as produced responses which were very similar to those of exercise both in heart rate change and also in change of ventricular function" Because the diencephalon is probably a cross-roads for nerve impulses coming from many portions of the cerebral cortex and other areas of the brain , it is possible that stimuli entering from the external sense organs and also impulses from the motor cortex which initiate movement in the skeletal muscle can initiate the appropriate cardiovascular and respiratory responses that occur during exercise 0 The type of reasoning which states that the control of the cardiovascular responses during exercise is essentially originated from the higher centers of the brain allOW's some cause for question because it means that there is no closed loop system controlling the response and the change is only modulated through the effect of barereceptors and chemoreceptorBo In examining some other control systems of the body, the changes seem to be directly related to need o Furthe~ more ,. it has been ShC1NIl that the cardiac responses to exercise are closely related to the metabolic needs of the muscle, ioeo changes in oxygen uptakeo The fact that cardiac output is changed because of a changing need was demonstrated by experiments on dogs with the A-N node destroyed by electrocauteryo 32 With an atria-ventricular block thus produced, the heart was driven at a desired rate by an external stimulatoro As the dog exercised at three miles per hour on a treadmill, the heart rate was 9 varied from 80 beats/minute to 240 beats/minute put VS 0 A plot of cardiac out- heart rate shONed that the cardiac output remains reasonably constant for different heart rates 0 However, as soon as the treadmill speed was increased to four miles per hour, the cardiac output also increased fran 7 liters/minute to 12 liters/minute demonstrating that as exercise or metabolism increased the cardiac output increasedQ With the indication that cardiac output was under closed loop control a series of experiments was conducted to see if the controlling factor could be determined o EXPERIMENTAL RESULTS EXperiment I. -~ Normal Responses Mongrel dogs, weighing about 15 to 20 kg t were anesthetized wi th intravenous nembutal (30 mg/kg) and a left thoracotomy was perfomed at the third interspace 0 Pm incision which was parallel to the phrenic nerve was made in the pericardium 1 1/2 centimeters belON the nerve e The root of the aorta was freed from the connecting tissue and was carefully dissected away from the aorta exposing the the excess circumference of the aorta for a distance of about three centimeters fran the point whe~ it emerges from the hearto After making sure the aorta was free of all connective tissue t a 400 cps gated sine wave electromagnetic fla..nneter probe 9 ,10 was placed around the aorta by partially collapsing the aorta and sliding the aorta through a slit in the of the probe A keeper was then inserted into the slit and through a small hole in the keeper t a roved was advanced into aorta 0 gauge needle with the hub re- Attached to the proximal end of this needle was a fine polyethylene tube which was used later in the measurement of pressure 0 The two flowmeter leads were brought out through the fourth intercostal space with the polyethylene pressure tube! and threaded subcutaneously to the back the dog where they were brought out through the skino The incision was then closed and the dog was allowed to recover four to five days in order that the effects of the operation would be greatly diminished o 1m effort was made to 11 determine if the dogWs responses had returned to normal by comparing the time course of heart rate prior to the operation to that obtained after the recovery perioda Comparison was made both at rest and during exeI'= cise t 'generally at four and six miles per hour with a slight incline on the treadmillo If recovery seemed complete t the pressure catheter was connected to a Statham P23Db transducer t which had a sensitivity of about 600 microvolts/mmHg with an exciting voltage of ten volts o The output of the gage was fed into a differential amplifier with a gain of 300 0 The output of the amplifier was then connected to a PM channel of a magnetic tape recorder and also to the analog computer 0 The signal fram the flow probe was adjusted to eliminate any bias voltage 9 ,lO and was fed to the analog computer and to a second PM channel of the tape recorder 0 'Ihis flow probe had been found to be linear by previous cali= bration with dye curves From a miniature tachometer on the treadmill a voltage was obtained which was proportional to treadmill speed o This was also recorded as was a BCD tape code which was used for marking events on the tape during the experiment 0 From the aortic flow signal f(t) and aortic pressure trans= ducer output pCt) the following variables were calculated in the analog canputerg 1) Heart Rate HR ::; 1 2) Stroke Volume SV 3) Cardiac Output co = HR x = ,; where T :; period between heart beats f(t) dt SV 12 Mean Pressure 5) Peripheral Resistance ¥ = I~ R= 1'" '4-) -rt pet) dt A circuit which is basic to the calculatioo of these para- n:eters is an integrate track and hold circuit as sha..m in Fig. 1. This circuit consists of two operational amplifiers, one camected as an integrator the other connected as a lag cirellit. Ass\.DI\e that a con- stant is integrated in the first amplifier with relay 1 open. Relay 2 is closed and the output of amplifier 2 becomes the negative of the output of al'Iplifier 1. Variable When relay 2 is opened, it is seen that there EKG 1 - ' \ , . . - - - ' 1 , . - - - Fig. 1 Schematic Diagram of Track and Hold Circuit with EKG Trigger 13 is no disCharge path for the feedback capacitor on amplifier 2 except through the high input impedance of the amplifier o The output voltage of amplifier 2 will then :remain constant for a time which is dependent upon the RC time constant of the feedback capacitor and the input im- pedance of the amplifier or until :relay 2 is closedo By closing relay 1 the feedback loop of amplifier 1 is shorted, setting the amplifier to zeroo Opening this relay again allONS integration to begino Using this cireuit i t was possible to obtain a voltage on the output of amplifier 2 which was proportional to the period between heart beats With a constant voltage applied to the input of amplifier 1, 0 relays 1 and 2 were closed with every QRS complex of an EKG o This was done by differentiating the EKG, biasing the differentiated signal and clippingit to eliminate noise and provide a single spike with which to trigger 0 This spike was then fed to the sawtooth generator and the two pulses which operated relays 1 and 2 were generated at controlled points on the sawtooth", Since the amplifiers were reset with every heart beat a voltage proportional to the period between heart beats was obtainedo The pulses which close relays 2 and 1 are approximately three milliseconds in duration and about two milliseconds aparto It is necessary that the pulse which closes relay 2 be long enough t or the time constant of the lag of amplifier 2 be short enough, for the true voltage of arrplifier 1 to be reached o It is also necessary to separate the pulses which operate the relays by the two milliseconds so that the track· and hold circuit does not sample during the tine when the inte- grator is being reset 0 The pulse which operates relay 1 should be of 14 sufficient duration to allaN complete discharge of the integrating capacitor. HaNever, it cannot be too long or it will be a significant amoun.t of the period between heart beats and the voltage obtained by integration will not be accurate but will be biased by a significant level. Using a similar integrate track and hold cireuit and triggering with the EKG, the flaN f(t) was integrated beat by beat to J p(t) I PRE SSURE i TRACt< P AND R~ HOLD f CON STANT STRIP .------. CHART f RECORDER CoO--4 TRACK HR T ANoIJ HOLD r r FLOW TRACK sv AND X • HOLD -f-co r 1 EKG TRIGGER CIRCUIT Fig. 2 Block Diagram of the Calculation of Mean Pressure, Resistance, Stroke Volume, Heart Rate, and Cardiac Output in Analog Canputer 15 obtain stroke volume o The pressure pet) was also integrated using an integrate track and hold circuit 0 To complete the calculation of mean pressure t resistance t stroke volume t heart rate and cardiac output as defined above, multiplieI'-divider units were used as schematically shown in Fig 0 20 A strip chart recorder was used to obtain a pennanent record of the time course of these variables e '!Wo records showing typical responses to exercise are shown in Fig 0 3" The records are of two different dogs and shOW' the differences that can be obtained from the same amount of exercise of four miles per hour on a treadmill inclined 15 0 <:I Record A of Figo 3 show'S a rather slav change in the variables as compared with those in record B" Table I Time Constants with Onset of Exercise (see Fig~ Dafining 3) Heart Rate Cardiac Output Resistance Record A 13 sec o 16 seco 7 0 0 sec g Recor.... 3 8 sec o 2 9 sec o 2 0 0 sec o 0 0 time constant as though single lags exist, ioeo the time constant equals the time it takes for the variable to change 63 percent of its maximum change, it is seen that the time ccnstants of A are in the order of ten seconds and those of B are about two seconds Q In both cases, resistance has a shorter time constant than does heart rate or cardiac outputc The change in heart rate with the onset of exercise is from 160 beats/minute to 215 beats/minute in A while in B the change is from 120 beats/minute 16 to 192 beats/minute; this represents a change of 28 percent and 60 percent of resting values respectively. Perhaps the heart rate change in A was smaller because the resting rate was considerably above nonnal. It is interesting to note that while the heart rate changes were not the sane the changes in resistance and cardiac output were very similar with both records ShONing a drop of about 50 percent in resistance and increase of 75 percent in cardiac output. "Y-..-----..,---- 'OOp~~......, ......_ ...::.-.::::::-.....::••::,••::~....:::.......·::::.......... .... 10 SEC. (A) -- ----.. .-----... ..........:...:._-_ _ _._-: ",.-...-."'- - .' J _---_ I SEC.:;' ..... ........ -. PRESSURE .• \ • -.- - •••. 0 '.' • ....__.. oJ.RESISTANCE ......-.-". ".....,.J"......_ _ _ ........................_ ~. ....-.--.-.-_.:....... ., • .' ••_ ......_ ...._.--.......- . . . . _....... ___ ... . ..._ _ _ _ _.._ •• 'V"----.. -.: _. -_ - .-...••: ..:~.~.:..~......-.:.~...:.•~¥~'~.•:.,..:-....~~~.• ........-.....:.~::-',..:••:.:•.-......-:••-.:... - F. c.o. " ...... -"0 180...... .--. --'. I • ...... ., .... - . ..................... .....,..- •. "'---...,..... -- - ................. - :... .....,. -.. . HEART RATE • ..... • . - - - -...- . ADMILL 60 (8) o Fig. 3 Records Shooing the Normal Response to Exercise of '!Wo Dogs as Calculated with the Analog Computer 17 The overshoot seen in the heart rate of record B was observed in many dogs and was apparently caused by anticipation and excitement of the treadmill being turned one absent from Ao This type of response is completely In fact, in this record there is an unusual delay before the rise in heart rate o This delay was not observed in other dogs o When the treadmill is turned off there is usually a rapid drop in heart rate, pressure and cardiac output with the tirre constant being about one second, as is shown in record Bo This is probably caused by activation of the vagus system which in turn causes a sudden decrease in heart rate CD Since stroke volume, which is not shown on these records, changes only about five percent, the drop in heart rate causes cardiac output to decrease and because the resistance does not return to resting value for 35 to 40 seconds after the end of exercise, the pressure also drops 0 From the data just described, two factors indicate that changes in peripheral resistance influence cardiac output changes: 1) The drop in peripheral resistance is faster o 2) There appears to be a correlation between cardiac output and resistance independent of heart rate change (I It is probable that the influence of resistance on cardiac output is mediated through the baroreceptor'S because the rapidly decreasing tance causes a decrease in pressure of 8 to 16 percent jj resis~ The idea that press ure is maintained constant by adj usting cardiac output to canpensate for changes in resistance is alluded to in the literature 7 0 18 E;xperiment II -- Controlled Constriction, of ,])ascending .Aorta A second series of experirrents was designed to test the relationship of cardiac output to resistance Q Much of the operating and experimental procedure was the same as has been described but significant changes should be discussedo It was found in many dogs that after the pressure needle which was inserted through the flowmeter keeper had been in the aorta for approximately one week, clots would fonn on the end of the needle although heparin was injected daily. Pieces of the clots would break off forming embuli which were transmitted through the circulatory system'and lodged either in the cerebral vascular system or at the bifaroation of the aortaQ This usually caused death of the dogo Also, unless the probe was exactly the right size, the needle enlarged the initialpuncture and caused constant bleeding or ruptured the aorta o Two other rrethods for obtaining pressure were usedo The first of these was to insert a carmula through the right or left thyroid artery and thence through the carotid artery into the aortic arch o The secood method of obtaining pressure was removal of the left kidney and insertion of a cannula through the left renal artery through the descending aorta to the level of the aortic arch o Both methods seemed to be satisfactory 0 There was some question whether the carmula which was inserted into the carotid artery was blocking much of the blood flCM and inter'fering with the baroreceptors in the carotid sinus area, but it was felt 19 that this effect would be very small since the aortic arch was still intact as was the carotid sinus on the opposite side The difficulty 0 of using the renal artery for the measurenent of pressure was the removal of the kidney and the additional major surgery that had to be perfornedo In both of these methods of obtaining pressure, heparin was infused daily through the catheter to keep it patent but in some cases clots still formed on the tip of the catheters and in the catheter ltl1len o These clots did not present the problem of embuli as did the needle preparation but good pressure measurements were sometimes difficult to obtain~ The EKG was somewhat unsatisfactory for providing a trigger pulse because of noise and also because during exercise the EKG leads broke loose and the signal was lost 0 A better method for providing a trigger was devised using the floo curve, Fig 0 40 is seen, the As derivative of the flow curve is rectified so that only the negative derivative is used o This negative derivative is then integrated and the integral at each point in ti.Jre compared to a constanto When it is greater than the constant, the diode in the fourth amplifier will tum off providing almost infinite impedance in the feedback loop and the amplifier will saturateo This provides a pulse which resets the integrator and also triggers the sawtooth generator The constant on CD the integrator input is about 002 volts and is used to offset the forward bias voltage of the diode of the first amplifier 0 Taking the derivative tends to amplify the noise on the signal 0 However, most of this noise will be sharp spikes and the 20 area under these spikes will be much less than the area under the negative derivative of the flcw curve. Thus, by proper control of the constant on the fourth amplifier, it was easy to eliminate any triggering except at the point desired, and by adjusting this constant, it was possible, within a limited range, to determine where the trigger would occur. This was adjusted as close as possible to the end of systole. ---- - -r -Rectify Integrate I Derivative and Compare ---A- -----------, Trigger Amplifier (]) Flow I @ (j) I~~rtic Flow I Curve I I Sawtooth I I . ®Rectified ive I I I r\ ~ -m,--o ® minus bias voltage :! Trigger ® Amplifier I I L 1::'l --- (i) of TRIGGER I I U I I I Reset CIRCUIT L ___ _ ----, I I I Fig. 4 Diagram of a Trigger Cireui t Using the Flow Curve I I -.J 21 The main purpose of this second series of experiments was to control the effective peripheral resistance by placing a constrictor around the descending aorta. To place a constrictor in the animal, the dog was again anesthetized with the same amount of nernbutal as in the first experirrent and an incisiQn was made through a left intercostal space just above the diaphragm. (Fig. 5). Two types of constrictors were used The first constrictor consisted of a plastic cuff Fig. 5 Photograph of the Two Types of Constrictors Used on the Descending Aorta 22 approximately five centimeters long Inside this plastic cuff was a 0 small rubber balloon which when inflated would canpress the aorta against the opposite side of the cuff 0 This type of calstrictor was unsatisfactory for two reasons: first t the five centimeter plastic cuff was heavy and rigid and caused a great deal of stress on the aorta even to the point of rupture; second, as the balloon was inflated there was a tendency for the balloon to pop out between the cuff and the aorta and when the pressure was released this part of the balloon would not deflate!) A more satisfactory constrictor was made from a piece of cloth onto which a balloon was sewed o This cloth was then wrapped arotmd the aorta and tied snugly, with care being taken not to compress the aorta() Since the cloth would not distend, injection of air into the balloon compressed the aorta and increased the resistance to blood flow With either type of constrictor the tube which provided air passage to the balloon was brought out through the chest wall and skin in the vicinity of the flowmeter leads and the incision was closed e Since the pressure was to be measured by a cannula in the carotid sinus or the renal artery, these operations were perfonned while the dog was still anesthetizedo After implantation of the constrictor and pressure cannula the dog was allowed to recover for about seven days 0 The condition of the dog was determined as in the first series of experiments and if recovery was satisfactory, fla.v and pressure signals were fed to the analog computer and magnetic tape recorder, the constrictor was also <) 23 connected to a controlled air source, and a voltage from the analog computer was recorded to indicate when control on the constrictor was activated. The mechanism which controls the constrictor is shown in Fig. 6. The analog computer calculates beat by beat heart rate, stroke volume, resistance, mean pressure, cardiac output fron the flaIl f(t) and pressure p(t) as has been discussed and provides summers for com- paring reference resistance to the beat by beat resistance. The PRESSURE ANALOG COMPUTER REF-R FLOW BALLOON Fig. 6 Diagram Shov.1ing the Metl-tod of Controlling Resistance in the Dog 24 comparator circuitry and the mechanism of the controller are shC'1NIl in Fig. 7. The calculated resistance was one input into the two comparators and a constant which was equal to the value of resistance when the dog was standing quietly on the treadmill was another input. Since the value of calculated resistance was sampled and held and another sample was not taken until the present heart cycle was completed tit was Resistance Fig. 7 Detailed Schematic of the Comparator and Controller Mechanism 25 necessary to make same correction in resistance with a voltage whiCh was proportional to the amount of error 0 This was because the correc- tion made by the constrictor would be too great if allCMed to continue until it could be detected at the next heart beat 0 The third input was then a ramp obtained by integrating a constant and resetting the integrator with every heart cycleo Assuming no sign inversion through the amplifiers since noninverting units were used, it is seen that the output of the top amplifier remains zero until the value of calculated resistance is greater than the constanta At this time the amplifier goes into saturation and the solenoid is opened allCMing air to escape from the It will remain open until the ramp function, which has been balloon 0 negated, causes the sum of the input voltages to again become negativeo The bottom amplifier operates in the same manner except that the solenoid opens when the calculated resistance becanes less than the constant This allows infusion of air into the balloon and increases the constriction around the aorta causing an increase in the effective peripheral _resistance 0 Even with the solenoids open for a very short period of tirre, it was difficult to obtain very accurate control without proper adjustment of the pressures, both the infusion pressure and the release pressure 0 This was true because very small amounts of air had to be moved in order to change the resistance in the aorta by a significant amount 0 1m infusion pressure of 280 mmHg and a release pressure of 140 mnHg were found experimentally to provide the best response 0 The time 0 26 constant of the error correction ramp function was also critical. If these adjustments were not properly made both in pressure and in the time constant of the ramp, oscillations were set up and the data obtained becarre maaningless. Because of the critical adjustment of this system and also because of the noise introduced on the physiological data by the opening and closing of the solenoids and relays , it was desired to find a more effective way of controlling the resistance. A new system was devised using an electropneumatic controller in place of the solenoids. This controller maintains a constant pressure on its output with a given voltage on the input. Using the recammenda- tion of the manufacturer, integral control was used making the voltage K E. >----i S 1+ 2 ~. 5 S + I-----;.p-- In 356 Pres sure Control Integral Control Calculating Resistance Fig. 8 A Diagram of the Simplified System Used in the Analysis of the Electropneumatic Resistance Control System 27 applied to the input of the controller a functicn of the integral of the e:t"'ror voltage plus the error voltage itself., steady state position error would becoma zeroC) This guaranteed that the While this type of con- trol provides zero error in steady state response, it is knam that it makes a transient response more oscillatoryo26 One purpose in using this system was to reduce the effect of oscillations Q Therefore, to gain insight into this system and to determine its area of stability, a pole zero plot of the simplified system, Figo 8, was made" To derive the transfer function for the controller a frequency response curve, Fig a 9, was obtained 0 The ampli tude of the input used to obtain this curve was two volts peak to peak biased at a three volt DeCo level to 7 8 paio 0 0 This gave an output pressure which varied fran 4 9 psi 0 From this curve, applying the mathods of Bode,23 the trans- fer function for the controller was found to be a second order equation with a natural frequency ficient l; of 0 70 0 un of 18 9 radians/second and a damping coef..., 0 This gave the following equation for the controller: P K E :: S2 + 26 5S + 356 0 Equation A This expression is only valid for positive signals on the input since the controller does not respond to negative voltageso From the integral control section of the system the following relationships were obtainedg E :: EE + El El :: ~ EE 28 E = EE E S ~= (1 + ~) +A S Equation B A m p 1 i t u d e 1 0 10 0 Frequency Fig~ 9 Frequency Response of Electropneumatic Controller Combining Equation A and Equation B it is possible to derive the open loop transfer p function~ 9S = S(S2 (S + A)K + 26 e 5S + 356) Equation C If it is assumed that the relationship between the output pressure of the controller and the actual calculated peripheral resistance of the 29 Kl~ dog is a gain coefficient then the closed loop transfer function is the follooing ~ p _ Ein - S(~2 + 26 0 (S + A)K 5S + 356) + KKltS + AJ Equation D In actuality, the calculated resistance is a sampled variable being sampled with every heart beat and the pressure=volume relationship in the balloon cuff is nonoovlinearo However" it was felt that this sim"", plified approach would give an approximation to the actual response of the control system and the parameters for a stable system could be approximated 0 The root locus plot obtained from Equation D is shown in Figa 100 Z.-/' The solid line is the root locus plot when the gain of the Increase Gain Stable Incre9ie Gain - --1- - - - - - -1- - - -+-----3K. x y rig 10 0 A Root Locus of the Simplified Control System Obtained from Equation D Unstable 30 integrator, A, is equal to X and the dotted line is the root locus when A is equal to Y. From this plot we see that as long as A, which is the effective gain of the integrator, is less than 26.6, the system will remain stable for all values of gain. As A becomes greater than 26.6 the complex pair of poles may move into the right hand side of the complex plane. This is evident because there are two more finite poles than there are zeros, and the sum of the poles must remain constant independent of gain. To make sure that the system remained stable, and because the non-lineari ties ignored would tend to make the system more unstable, a value of A much less than 26.6 was used. 0.5. This value was approx:i.m..=ttely The resulting system using the electropneumatic controller is shown in Fig. 11. J\- FLOW ANALOG ...---P---R--ES--S--=UR,.--:E------t COMPUTER ~ GRAPH RECORDER REFERENCE VOLTAGE PNEUMATIC CONTROLLER Fig. 11 Diagram Shewing the Control of Resistance Using an Electropneumatic Controller 31 During each experiment of this series a normal response to exercise was obtained and then exercise runs· were made with the con- Fig. 12 shows a typical exercise response with the troller activated. per hour and an incline of 10 treadmill at four miles 0 • The top record ShONS the nonnal response and the bottom record shoos the response with the controller activated. The nonnalized scales ShCMn apply to both tracings. WITHOUT COMPUTER CONTROL OF RESISTANCE 15 ."..-----1~:-:~~~~~:~·---·~-'·----·--~~·---"-·-·~--------------05 1.5 R . ,> (!SIstanee • - O~ w a. ~-_ - _- _-- __ ... __ _ . . . . _ ""_",..:.0_.. ...".....................=-_.-..._.':I'. :~. . ._._~:~. . :.;..,;:,.. ~___-_-_~. .-. 0.5 1.5 Cafdiae~-;--" '.~ .•_ ••-'" '. ' : :•• ' •• _.-. - .............,-"" _Outpuf _ • .' 4 II - - ,_ _ -;> -_ - -- -:.: •••-~ _ rfladmilJ Splod a - - - '. ./'" - ........ _ - ... - .......,: .. _; _ --.... : Healt Rate ~. - -_ 05 _.' .......- .-t.--------- i.~,-----..-- -~ .-- ..........- . - ~ -;' "'-..,1.5 - --.-:-.--- .s-- ~ 4 WITH COMPUTER CONTROL OF RESISTANCE Mean Aartie Pressure V\ \.... - ---- _ ---..------------ " ... . 0 - _.......- - - - - - - Resistance -..~- ...._ _ _ _ - - ---- -.-- '-- - - --.- -- -- - - - -.- -- -..- --. _.'. _H~~:.~:_~:~_~~_ ~:~~-.B~.".---.------- ____ .-.--_-.~.-.--~-. -~ ___ Cardiac Output _ -:.--~ __ -. 1 Second H Fig. 12 Typical Exercise Response Before and During the Control of Effective Peripheral Resistance 32 First, considering the normal response of the dog without any control, the heart rate rose 120 percent above the resting value within five seconds after the treadmill was turned ona TIle cardiac output in- creased 70 percent of its nasting value and peripheral resistance fell 45 percent of its resting value o The rrean aortic pressure had a small dip of 12 percent after which it rose 20 percent above its resting value, The dog was exercised again at the same treadmill speed three minutes after the completion of the nonnal exercise rtm 0 This time, hCMever, just prior to the turning on of the treadmill, the controller was turned a1 and resistance was maintained at a value equal to the nonnal nasting resistance 0 Here, there is no marked increase of heart rate with the onset of exercise although there is a slight increase as exercise continuedo value 0 This amounts to about 20 percent increase over the resting There is the same slight increase in cardiac output as observed in heart rate o The arterial pressure seems to increase the same amotmt in both cases although not as rapidly in the latter case Q From these results it appears that the drop in peripheral resistance is important in changing the heart rate and cardiac output at the onset of exercise G If peripheral resistance is not allowed to drop, the marked changes in heart rate and cardiac output of exercise do not occurc In Figo 13 we see the effect of turning the controller on and off during exercise o TIle controller was first applied prior to turning the treadmill ono Here again, as has just been described, wi th resistance held at nonnal levels, there is a small increase in 33 cardiac output and in heart rate. When the controller is turned off while the dog is exercising, there is a sudden drop in resistance and pressure and an increase in heart rate from 180 to 235 beats/minute. The peak of the increased heart rate is greater than heart rate would be if the controller had not been ~pplied and the dog was just exer- cising on the treadmill. 1) This may be caused by two factors: A reactive hyperemia effect in which the lack of blood flOW' has caused 10W'er resistance than would normally occur during exercise. 2) The sudden change in arterial pressure. Since the frequency of firing of the baroreceptor is proportional to the pressure and the deri vati ve of pressure, 13 the rapid change caused by the sudden releasing of the constrictor could cause a greater baroreceptor reflex response. Fig. 13 Effect of Clanging Resistance During Exercise 34 When the controller is applied again, raising the resistance back to its resting value, there is a rise in pressure, a drop in heart rate to 140 beats/minute, and also a drop in cardiac output 0 Turning the controller off once again the pressure and the peripheral resistance drop, the heart rate increases to 250 beats/minute, and the cardiac output increases 0 The treadmill is turned off and a rather rapid decrease in heart rate to 220 beats/minute is observed as was shown in the first series of experimentso There appears to be two major effects on the animal brought about by the onset of exercise 0 One of these is an oveI"-all arousal of the animal t apparently initiated in the central nervous system 0 This arousal may reset the reference pressure level and thus account for the increase in pressure that was seen in Fig o 12 under normal conditionso This effect can be demonstrated by the experimenter merely reaching to tum on the treadmill and while no actual exercise takes place, an increase in heart rate appearso This type of response could also ac- count for the overshoot that is observed in Figo 12 in the heart rate Q The other effect is essentially a vasodilitation in the skeletal muscle causing a drop in peripheral resistance and allowing more blood to flow through the exercising muscle a The mechanism which brings about this vasodilitation is not completely understood but it is thought to be the effect of local metabolism changes on the chemical environmental With these ideas in mind and from the results of the experimental data, the model which is diagramed in Figo 14 was proposed 0 Since arterial pressure is a product of cardiac output and peripheral resistance, 35 i it is seen that if cardiac output remains at a constant value the drop in peripheral resistance will cause a drop in arterial pressure. This drop in pressure is detected by the baroreceptors in the aortic arch and in the carotid sinus area and a decrease in activity on the efferent nerves fron this area is sensed by the cardiovascular control center in the medulla. When this change in frequency is canpared to some refer- ence level, an increase in frequency of firing in the sympathetics and a decrease in frequency of firing of the vagus nerve results. This in- crease in acti vi ty on the sympathetics increases heart rate and may EXERCISE + ( S.fIllpIJIII,lIc) Enyironment " ' - -_ _----J Arteria I Arterial Pressure Fig. 14 Diagram of Proposed Model for the Control of Cardiac Output 36 affect stroke volume but in normal exercising animals small changes in stroke volume have been observed while heart rate has increased markedlyo Since cardiac output is the product of stroke volume and heart rate tit is increased proportionally to heart rate o The arterial pressure re- turns to a near normal value as cardiac output is increased o It is obvious that it is necessary for the central blood pressure to remain near normal in order to increase the flow through the muscle 0 If the resistance drops and the pressure also drops then the flCM through the tissue will not increase and the purpose for the vaso- dili tat ion will not be realized, The increased firing of the sympathe- tics also tends to cause a vasoconstriction but the local chemical changes due to the increased metabolism seem to be strong enough to keep the vessels dilated 0 One part of this mcxiel which is obscure and difficult to l.IDdeI'stand is what takes place in the central nervous system when an error is detected through the baroreceptors 0 In an effort to obtain a better tmderstanding of the involvement of the baroreceptors and the central nervous system in the control of cardiac output, a third series of experiments was perfonned o Experiment III -- Constriction of the Brachiocephalic Artery In this set of experiments a more exact effect of the barereceptors was considered by first denervating the aortic arch and then controlling the pressure in the carotid sinus by means of a constrictor on the brachiocephalic artery, Fig" 15 0 The pressure sensed by the 37 intact baroreceptors then could be controlled by the constrictor. This maneuver, as in the preceding experiment, opens a reflex loop in the intact animal and the direct effect of carotid sinus baroreceptor stimulation can be observed. The dogs were again anesthetized with nembutal and an incision ftlas made into the second interspace. All adventitia along the aortic arch was dissected away to destroy the baroreceptor afferent nerves and a fl~ter was placed around the ascending aorta. The same cloth con- strictor which was used on the descending aorta was placed around the , - - - - - - H. R. , - - - - - S.V. Pes (t) ~--~ CONTROLLER Fig. 15 Diagram Showing the Method of Brachiocephalic I\rtery Constriction 38 brachiocephalic artery and the air tube for the constrictor along with the two fla-nneter leads were brought to the surface of the skin on the back of the dog 0 The incision was closed and a small incision was made in the neck: to insert a small cannula into the thyroid artery to measure the pressure PcsCt) in the vessels above the brachiocephalic constrictoro The pressure in the aortic arch was usually obtained by removal of a kidney and insertion of a cannula through the renal artery 0 The dog was allowed to recover for three to four days before experimentation Il With the outputs from the flOW' transducer fCt) and pressure transducers pcsCt) and pet) connected to the analog computer and to the magnetic tape recoroer and with the dog standing quietly on the treadmill t a step voltage of about three volts was applied to the electropneumatic controller o This increased the pressure in the balloon to six psi and canpletely constricted the brachiocephalic artery of this constriction are shown in rigo 16 0 were calculated using the digital camputero 0 The results The values in this figure This method of calculation will be explained in the next sectiono When the constrictor was applied the carotid sinus pressure dropped to about 50 percent of its unconstricted value, and while in this record the pressure remained at this level, sane dogs showed a gradual return to a value 25 percent bela.t the unconstricted valueo '!his gradual return was probably brought about by the collateral circulation from the left vertebral artery 0 From this change in carotid sinus pressure the expected increase in heart rate occurred but cardiac output remained essentia] ly constant 0 A rise of 80 percent in mean 39 Fig. 16 Effects of Constricting the Brachiocephalic Artery with the Aortic Arch Denervated and the Ibg at Rest aortic pressure was also observed. This change in pressure has a time constant four times longer than the time constant of the drop in carotid sinus pressure, indicating that the increase in pressure is due primarily to reflex sympathetic vasoconstriction and not to the occlusion of the brachiocephalic artery which is one of the major vessels. Release of the constrictor allowed the increased pressure to be sensed by the baroreceptors and a strang inhibitory reaction resulted. 40 The heart rate dropped imnediately and the aortic pressure returned rapidly to the unconstricted value o The dog was then exercised on the treadmill at four miles per hour and the constrictor was turned on and off during the exercise runa Table II gives the values obtained from one dog which shCM'ed a typical respoose o The values of stroke volume, heart rate, cardiac output, mean pressure and resistance are mean steady state values reached during each condition mentioned" All parameters have a value of 1 00 with the dog 0 standing quietly on the treadmill G Table II Variable Values Obtained with Brachiocephalic Constriction at Rest and During Exercise Condition ' Stroke Volume Heart Fate 1 0 00 Normal, Resting Constriction, Resting Normal, Exercise Constriction, Exercise Cardiac Output Mean Pressure Resistance 1 0 00 1 0 00 1000 1 00 075 1 64 1024 1 0 92 1055 1017 L , 36 1~60 1029 080 092 1 0 93 1 080 201 1017 0 I 0 In this dog there is a 17 percent increase in stroke volume and a 36 percent increase in heart rate during exercise Q This gives a 60 percent increase in cardiac output, two-thiros of which appears to be due to heart rate e However, when the constrictor is applied during exercise. an additional increase in heart rate of 57 percent is obtained, 41 but because the resistance is also increased due to the strong vasoconstriction action of the sympathetics, the stroke volume decreases 25 percent causing the cardiac output to increase only 20 percent. Th.us, unless resistance is allcwed to decrease or at least remain at the same value, the increase in heart rate has a small effect on cardiac output. A typical response of heart rate t cardiac output and carotid sinus pres- sure to brachiocephalic coostriction during exercise is shewn in Fig. 17. Notice the -~~~ ~ a~nt with the above explanation. ~------~ ,.. -------) . ' . - ; MEAN PRESSURE (C.s. ! q"".,_ •. "-"':--'.oP :..J'W l"7"""'!. :".' ~'.~, .~.m .• "~.7.:. •• ......, .... , ", ' , i ""~" I'I·I'~"··'·· .. ~.'_ - ru~ lj't.~ , ;r:TTl:c:J:,"".......:" " .". 'ffffir. ' . . ;~ ~~=_~,: _~. ..~!".. ..~.\·-=~.:*'f.;;!I-J·:Y~!,!"'lI'l"':df."" . .~'~r-------------- .: ~: - O· C.o.:·· - 0 p. :. .;:-I"' r r-~~-- -,~_~'-=--~: 'fI~~~~' ~~~ - :_.-'-~-'-~""';.~_-~:-~'-'- - - - - - - - - - - - - : -~~~-,' -. ~!l! ' . - ........ J'!"I •• "' .. !I!. ,. " .. ' -~--.'.-,:-':'-~--'--*-CO-NS-'-r-:R-IC-:T-~-."""-""""IIIIiiiiIIIiII""'-------------- Fig. 17 Effect of Constriction of the Bradhiocephalic Artery with the I::bg Exercising at Four Miles Per Hour 42 It appears that there are wo ways to increase cardiac output during exercise, both of which are resistance dependent. Heart rate may increase because of the baroreceptor reflex and stroke volume may change because of the resistance changes which occur and are reflected by the aortic pressure. From the above explanation, the stroke volume mechanism appears to have dominating control. With this additional information, the model of cardiac output control as described in the preceding section must be modified to include the mechanical effect of aortic pressure changes which are a function of EXCERCISE (SYMPATHETIC) + C N S LOCAL TISSUE ENVIRONMENT (VAGUS) ARTERIAL BARORECPTORS CO ARTERIAL r---------~~--~ PRESSURE Fig. 18 Diagram of the New Model of Cardiac Control with the Effect of Arterial Pressure on Stroke Volume Included 43 peripheral resistance" This is shavn by the line from arterial pressure to stroke volume (Figo 18)0 ANAlDG COMPUTER MODEL To further justify the validity of the rodel of Fig. 18 and to detennine quantitatively the parameters involved in the system, the model was progranmed for the analog computer. A descriptim of the equations and considerations involved in the -analog computer set-up can .best be obtained by considering the schematic diagram in Fig. 19. Little is knCMll of the JI¥:!thod in which the central nervous system detects the change in frequency of firing of the baroreceptor Fig. 19 Analog Canputer Schema.tic for the Sinn.tlation of the Control of Cardiac Output 45 nerves t but exper:iments seem to sho;.;r some type of comparator exists. For this reason, a summer was used, amplifier 1, and comparison was made between a reference level and pressure. sent on the baroreceptor nerves whiQ~ Hhile it is the frequency pre- the central nervous system receives, experiments in this laboratory have shaNn that in the normal physiological range the average frequenC'j of firing is directly proportional to the pressure (Fig. 20). Therefore, pressure was fed back directly to the central nervous system summer, amplifier 1. Also, since exercise appears to have a direct effect on the centrel nervous system and may modify the reference level t a signal proportional to exercise was added. 120 Average 100 Frequency Of Action Potentials (Seconds-I) 40 20 0 100 P I Mean Arterial Pressure (mmHg) Fig. 20 The Relationship of Arterial Pressure to the Frequency of the Action Potentials on the Baroreceptors The output of amplifier 1 is then the frequency present on the sympathetic (fl ) and vagus system (f 2 ) with fl being proportional to the output and f2 inversely proportiooal to the output. The equations and computer set-up which describe the relationship of fl and f2 to heart rate are those which Warner reported in 19620 26 The total effect of these nerves on the heart rate was assumed to be the Stml of the individual effectso From Warner's paper it is known that this is only a loose approxi- ma.tioo but it was used because the function describing the interaction of fl and f2 is not knowno Stroke voltmle is calculated fran a constant no load stroke volume which is modified by the mean arterial pressure and sympathetic activityo Since the relationship between stroke voll..lJIe and frequency of firing of the sympathetics is not described, it was assumed that the same diffusion process of norepinephrine as was used in the calculation of heart rate was present 0 The time constants may be dif- ferent but they also were assumed to be the same in order to reduce the number of variables used in the rnode1 0 Little quantitative infonnation is known about the mechanism which causes vasodilitation during exercise so the time course of resistance during an exercise run was used as a guide in deriving an equation to be used in the analog model Q This time course of resistance shooed a rapid drop in resistance, ten seconds, with the onset of exercise and a slOVl return at the end of exercise of about 40 seconds 0 The accepted opinion for the cause of vasodilitation is a build-up of a metabolite having a local effect with no change being mediated through the nervous system Cl Accepting this concept, the 47 follONlng derivation was made c The concentration, S, of a metabolite is related to resistance, R = RI - Kl3 S where RI is the nonnal resting value of resistance and includes the effect of sympathetic actionQ The change in S is proportional to the fornation of the me tabo Iite and the rate at which it is destroyed, where M is the metabolism of the retaboli te and consists of two parts, resting metabolism Mr and working metabolism ~o KI is much larger than K2 because of the fast drop and slow return of resistanceo Since resis- tance reaches a minimum value and decreases no further, it was assumed that only a certain concentration of the metabolite, Smax' could be reached. KI is, therefore, a function of affecting K2 (Smax .., S) G) One of the factors would be the wash-out of the metabolite and would depend an cardiac outputo Considering these factors, the equation for the change of S with respect to time becanes the following: A oamplete list of all equations used in the model and a definition of their parameters is given in Appendix Ao In order to match the output of the analog model to the actual data a different method of calculating stroke volume, heart rate, mean 48 pressure. cardiac output and resistance from f(t) and p(t) was used o The raw data which consisted of the flow curve, pressure curve and a voltage proportional treadmill speed were fed into three channels of an analog to digital convertor which sampled each channel simultaneously 100 tines per secondo The digitized data was received by a Control Data 3200 computer and after 120 points were received, the magnitude of each point was scanned and the maximum of two adjacent fla.v pulses foundo The number of samples between these two values was determined and because a constant rate of sampling was used, the period between heart beats was easily determinedC1J Heart rate, of course, is the reciprocal of this value 0 A pattern recognition procedure was used to determine systole and diastole of the flow CUNeo The points during diastole were averaged to obtain a base line value which was subtracted from all points because the flow t recoroed from the ascending aorta, is zero during diastole (I The integral over one heart cycle of the flow curve was obtained to give stroke volume the ~ressure IJ Also over the same ntmlber of samples, the integral of was obtained as was an average over the samples from tread- mill speed to give one value for each heart beato The speed and interrupt feature of the 3200 allCMs for calculations to be made at the same time the data is being sampled o There- fore, sampling was done continuously and by analyzing the sampled points and determining each maximum, a beat by beat calculation of stroke volume t mean pressure and heart rate using the above method was obtained 0 Also t the one averaged value of treadmill speed was stored for each beat e 49 The calculation of cardiac output and resistance was easily obtained from these variables o When 400 values of each variable had been ob- tained, the sarrpling stopped and the values were stored on digital tape along with a file number which defined the :recont. This canputer pro- gram also allowed for another pressure and a voltage proportional to constriction to be analyzed and averagedo With this data on tape, a second program was used to read the tape and display the data on the scope of the analog computer <II This program included the facility of calling any file number, changing the mul tiple .of real time the data would be displayed and choosing on which channel of the digital to analog convertor each variable would be sent (I The read-out scheme was synchronized with the analog scope display by using the interrupt control feature of the digital computer(l To begin the model matching, the baroreceptor reflex was considered first by interrupting the feedback from the pressure multiplier Mp, Fig {I 19, and driving the rrodel with a carotid sinus pressure obtained during one of the brachiocephalic constriction experiments o The para- meters of the model were adj usted until a match between the theoretical and experimental aortic pressure was obtainedo Next, heart rate was considered and a good match was obtained except for the response when the constrictor was turned off 0 The sudden drop in heart rate was not matched because the vagus response is much greater than can be obtained by sunming the sympathetic and vagus frequencies e If the vagus sensi- tivity was increased enough to match the off response, then the on response was too fast and too large o This was expected because it has 50 been shown 26 that a mild vagal stimulus almost completely destroys any Sj1llpathetic action o Stroke volume was matched next and cardiac output and resistance were then determined o Wi th the pararreters of the model approximately determined, the pressure multiplier output was reconnected and treadmill speed was used to drive the model since it was assumed to be proportional to exerciseo A match for resistance was obtained first as it was the least sensitive to adj ustrnent of parameters in other parts of the model and seemed to be dependent on the time course and amplitude of the forcing function. match for heart rate was then obtained followed by stroke volume 0 A Wi th the mdel predicting these three variables, cardiac output and mean press~ were automatically detenninedg Using this procedure, the abili ty of the model to predict the experimental data is shown in Fig 0 21~ First consideration of this figure seems to indicate that the most obvious error in the m:::del' s predictioo is in the change of pressure at the end of exercise" It is possible that this er:ror is caused by the heart rate failing to respond fast enough and also resistance may start to rise too soono At the start of exercise the time course prediction of all variables is good with the exception of stroke volume which appears to rise too fasto In Appendix B a complete list of the constants used to obtain the solution shown in Figo 21 is givenQ These constants are relative to each other and the actual values would have to be obtained by calibration of heart rate t pressure and stroke volume instead of considering relative change onlyo It is interesting to note the following facts, however: 51 Fig. 21 The Prediction of .Mean Pressure, Heart Rate" Stroke Volume, Resistance and Cardiac Output During Exercise by the Analog Computer Superimposed on the Values Obtained from Experiment 1. To obtain the rise in pressure above its control value, the arousal due to exercise, EA' must be equal in amplitude to the function, drives the model through resistance. ~, which By increas- ing EA, an overshoot in heart rete with the onset of exercise could also be obtained. 52 20 The S-A Node seems to be m::>re sensitive to the Cal- centration of acetylocholine than the substance AB which is asstuned to exist during sympathetic stimulationCl This canes from the relati va magnitude of constants Kl2 3(1 ~an = 52 and KS = 0520 aortic pressure and sympathetic efferent activity both have a significant influence on strake volume during exercise" 4 Q The constants involved in the sympathetic system are larger than those in the vagus system Q This indi- cates the sympathetic is a slower responding system 50 0 With increasing treadmill speed t the change in cardiac output is smaller for a given change in exercise ~o This thesis concludes with an analog model which has limitations but provides a solution to the control of canliac output o This solution is not unique and as the model is used to predict the response to different types of stimulation, changes will be made (8 HONever, a basic model has been presented based on the just described experiments which show that peripheral resistance is a very important factor in controlling cardiac output, both by its effect on the baroreceptor reflex and its direct mechanical effect on stroke volume In At this stage of experimentation the most important role of the model has not been to explicitly give numerical values to parameters of the the type of research that must be sys~em carr~ed but to give insight into out to fully describe this 53 cootrol system as well as insight into the possible nature of relation"", ships not yet knowne REFERENCES 1) Bard t Pm Medical Physiology, 11th Edo, wuis, 1961 0 Co Vo Mosby, Coo, Sto 2) Dickinson, Richardso "Discussion of Starling!s I.a.w of the Heart," Physiological Review, 35~156, 1955 0 3) Gauer, Otto Ho "Volume Changes of the left Ventricle During Blood Pooling and Exercise in the Intact Anima.l o Their Effects on left Ventricular Performance," Physiological Review, 35~143, 1955 0 4) Gregg, Do Eo, Sabiston, Do Co and Theilen, Eli 0 "Perfonnance of the Heart: Changes in left Ventricular End-Diastolic Pressure and Stroke Work During Infusion and Following Exercise." Physiological Review, 35~130t 1955 0 5) Guyton, Ao Co "Determination of Cardiac Output by Equating Venous Return Curves with Cardiac Response Curves," Physiological Review, 35:123, 1955 0 0 6) Hamilton, W0 F 0 8g527. 1953 0 7) Hamilton, Wo Fo "Role of the Starling Concept in Regulation of the Normal Circulation," Physiological Review, 35~161, 1955 0 8) Katz, La No "Analysis of the Several Factors Regulating the PeI"-= fonnance of the Heart," Physiological Review, 35~91, 1955 9) Kolin" Ao 1959 0 10) 11) "The Physiology of the Cardiac Output t" Circulation, "Electromagnetic Blood Flowmeters 9 " Science, 130~l088, Kolin, Ao and Kado!l Ro To uMiniaturization of the Electromagnetic Blood Flowmeter and Its Use for the Recording of Circulatory Responses of Conscious Animals to Sensory Stimuli," Proceedings of the National Academy of Sciences~ 45:1312, 1959 0 Laber t V0 "Regulation of Energy Liberation in the Isolated Heart," Review, 35 ~123, 1955() Physiolo~cal 12) Piper, He and Starling, Ho "The Regulation of the Heart Beat," Journal of PhysioloSlt 45:465, 1914 0 13) Ridges, J o Do, Topham~ Wo So and Warner, Ho Ro "The Transfer Function of Arterial Pressure Receptors," Physiologist, 5~202, 1962 (abstract)o 55 14) Rushmer, Ro F0 "Effects of Nerve Stimulation and Hormones on the Heart; the Role of the Heart in General Circulatoty Regulation," In Handbook, of Ph.¥siology, vole 1, sec" 2 Circulation, Waverly Press, Incc- t Baltl.mO:re t 1962. 15) Rushmer. RO- Fa Cardiac Dia.gl}osis, Chapto 6,Wo BoSaunders" Philadelphia., 1955 0 16) Rushmer, R, Fo "Applicability of Starlingl?s Law of the Heart to Intact, Unanesthetized Animalsi)" Physiological Review, 35~138. 1955 17) Rushmer, Ro Fo "Continuous Measurements of Left Ventricular Dimensions in Intact, Unanesthetized Dogs," Circulation Research, 2~14, 1954 0 18) Rushmer, Ro F t Smith, 01) and Franklin" Do "Mechanisms of Cardiac Control in Exercise," CirculationResearoh~ 7~602, 1959 0 (j 0 19) Sarnoff, S" J e "Myocardial Contractility as Described by Ventricular Function Curve; Observations on Starling 9 s Law of the Heart," Physiological Review, 35g107, 1955 0 20) Sarnoff, So J 0, Case, Ro Bo, Berglund, Eo and Sarnoff, La "Ventricular Function Io Starling j s Law of the Heart Studied by Means of Simultaneous Right and left Ventricular Ftmction Curves," Circula~, 9g706, 1954~ 21) Sarnoff t So J 0 , Gilmore, J 0 Po, Brockman, Sq K o , Mitchell and Linden, Ro J "Regulation of Ventricular Contraction by the Carotid Sinus: Its Effect on Atrial and Ventricular Dynamics," Circulation, 8g1123, 1960" 0 22) 23) Sarnoff, So Jo and Mitchell, J<!J Ho "The Regulation of the Performance of the Heartj)" American Journal of Medicine, 30:747, 1961 Smith, Go W41, Wood, Rv Co Hill, New York, 1959 Principles of Analog Canputation, McGraw- 0 24) Starling tEo H "The Linac:re Lecture on the Law of the Heart, ff (given at Cambridge, 1915), Longmans, Green, London, 1819 <) 0 25) 0 Starling, Eo Ho Princitles of Human Physiology, 5th Ed$' lea & Febiger, Philadelphia, 9 30 0 26) Thaler, Co J o and Brown, Ro Co Hill! 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Jo 4:485, 19510 "Detenninants of Cardiac Performance,n Circulation, APPENDIX A EQUATIONS FOR ANALOG MODEL Central Nervous System SUJ'JJIer fl = KR f2 = Kf - fl + EA - 15' Heart Rate Sympathetic dA2 crt: = K3 (AI - A2 ) - K4 (A2)(B) - KS AB c;:: = K4 (~) (B) B = KB - KS AS - AS Vagus dC2 at HR = KS = Kg AS + Nf2 - KIO C2 Kl~ Po + 11 C2 Stroke Volume SV = KSV - K13 Cardiac Output CO = SV Resistance x HR P + K19 AB 58 R = Ro + Rs - ~ = K17 K16 S fl - KIa Rs Mean Pressure P=RxCO DEFINITIONS Ao - Al .... Concentration of norepinephrine at the nerve ending(j ~ - Concentration of norepinephrine at the active site of the S-A Concentration of norepinephrine in the blood o Node 0 - Substance which must B ~act the norepinephrine in order for it to produce a change in heart rate o - Concentration of acetylcholine at the active site in the S-A C2 Node," Output~ CO - Cardiac EA - Arousal due to exercise o fl .., Frequency of sympathetic neIVe firing(l f2 .., Frequency of vagus nerve firing" HR - Heart Rate Kl 0 (l 0 0 K19 - Rate and gain constants 0 KB ~ Total amount of B presento Kf = Tonic frequency of vagus nerveo KR - Reference constant in central nervous system0 Ksv .., M No after load or innervated stroke volume o - Average number of vesicles at each nerve ending Charged with acetylcholine 0 59 ~ ... Maximum number of charged vesicles o ~ - Resting metabolism of metabolite o Mw - Metabolism of metabolite during exeroise o P - Mean aortic pressure averaged over ale heart beat Po OK> 0 Nonnal period of heart cycle before vagal stimulation. R -. Resistancee RO - Resting value of resistance without nervous or metabolite changes 0 RS .... Resistance due to sympathetic stimulation S ... Concentration of a metabolite which causes vasodilitation o SV - Stroke Volume~ Smax -' Maximum of S that can exist 0 0 APPENDIX B CONSTANTS FROM ANALOG MODEL Aa = 0036 EA =tt Ka = 2000 Kr :: 27 KR :: Ksv = 22 Kl :: K2 = ljl6l K3 :: K4 K5 = 0005 = 0040 K6 = 052 K7 :: 0350 K8 :: 0023 = (20 during exercise (0 33 0672 1 05 0 = 0003 KIO = 0678 Kg Kll = Q K12 :: 52 K13 = 057 K14 :: 2 00 x 10- 4 K1 5 :: 5 O x 10- 5 K16 :: 2.00 700 Q at rest 61 K17 = 0001 K18 = 0002 K19 = 040 ~ =2 Mr :: 02 Po = 11 Ra :: 47 Smax :: 20