Importance of Atral Complance n Cardac Performance By Hroyuk Suga ABSTRACT Effects of changes n atral complance on cardac performance were analyzed usng a crculatory analog model. The atrum was assumed to be a noncontractng chamber wth a constant complance. It connected the venous return system, whch was represented by mean crculatory fllng pressure and a venous return resstance n accordance wth Guyton's concept, wth the ventrcle, whch was characterzed by a tme-varyng elastcty. Atral complance was ncreased from near zero to a value at whch atral volume was twce ventrcular stroke volume, whle the parameters of ventrcular contractlty were kept unchanged. Cardac output ncreased from,400 to 3,40 ml/mn wth ncreases n atral complance from to 0 ml/mm Hg (venous return resstance mm Hg sec/ml), whereas mean atral pressure smultaneously decreased from 3.0 to. mm Hg. Ths result ndcates that cardac performance n terms of the cardac output-mean atral pressure relatonshp was markedly mproved by ncreases n atral complance n spte of constant ventrcular contractlty. The analyss of the model strongly suggests that natural atral complance n stu, by poolng venous return flow durng systole and supplyng t to the ventrcle durng dastole, facltates the transformaton of the contnuous venous return flow nto the ntermttent ventrcular fllng flow. KEY WORDS ventrcular fllng cardac output Starlng's law of the heart crculatory analog model venous return atral functon atral sze Downloaded from http://ahajournals.org by on November 4, 018 The physologcal sgnfcance of atral complance s not well understood, but some ndrect evdence does suggest that t s mportant n hemodynamcs. Brghton et al. (1) and Peters et al. (4th Annual Meetng of the Bomedcal Engneerng Socety, 1973) have observed that the addton of a flexble atrum to the nlet of an artfcal heart substantally mproves the heart's output. However, performance of an artfcal heart s not equal to that of the natural ventrcle, and doubt stll exsts about the physologcal sgnfcance of atral complance. The purpose of the present analyss was to evaluate quanttatvely the mportance of atral complance n natural cardac performance. In anmal experments, t s dffcult to change atral complance alone wthout affectng venous return resstance, and slght changes n venous return resstance senstvely affect cardac output (). Therefore, a reasonable analog model of the cardovascular system based on physologcal fndngs n the lterature was used n the present study. Atral complance was vared n the model whle the other parameters of the venous return system ventrcular contractle state, valve characters- From the Department of Physology, Faculty of Medcne, Unversty of Tokyo, Japan. Receved January, 1974. Accepted for publcaton March 19, 1974. tcs, and arteral pressure were kept constant. The results of ths analyss suggest that an atrum wth an approprate complance can ncrease cardac output 35-%. Methods Fgure 1 shows the electrc analog model of the crculatory system used n the present study; the rght heart and the pulmonary crculaton were purposely elmnated from the model to smplfy the analyss. Arteral pressure (Pa) was modeled as f t were held constant and therefore represented by a constant-voltage battery. The venous return system was modeled n accordance wth Guyton's concept () as a venous return source pressure (Pv), whch represents mean crculatory fllng pressure, and a venous return resstance (Rv). The ventrcle was represented by a tme-varyng elastcty (E[t] ) (the nstantaneous pressure-volume rato) n accordance wth prevous expermental fndngs on the ventrcular pressure-volume relatonshp (3-5); a ventrcular model of ths type has conventonally been used by others (6-9). The tme-varyng elastcty of the ventrcle ncreases durng systole and reaches ts peak value (Emax) at the end of systole (3-5). My prevous mathematcal analyss (3) has shown that the peak value of elastcty determnes end-systolc ntraventrcular volume and hence stroke volume when the end-dastolc volume s gven and that the tme course per se of tmevaryng elastcty s not a prmary determnant of ether end-systolc or stroke volume. Therefore, n the present analyss, a smple tme course was assgned to tmevaryng elastcty as a reasonable approxmaton of the physologcally observed tme course. Elastcty was Crculaton Ra earth. Vol. 35, July 1974 39
40 SUGA SF-Illab- VEIN ATRIUM VENTRICLE ARTERY FIGURE 1 Analog model of the crculatory system. Pa = arteral pressure, Pv = venous return source pressure (mean crculatory fllng pressure), Pat = atral pressure. Vat - atral volume, Vvt = ventrcular volume, Fv = venous return flow, Rv = venous return resstance, Rat, = atroventrcular valvular resstance, Rvt = aortc valvular resstance, Cat = atral complance, and E(t) = ventrcular tmevaryng elastcty (nstantaneous ventrcular pressure-volume rato). See text for further dscusson. Downloaded from http://ahajournals.org by on November 4, 018 consdered to be zero durng dastole, mplyng that dastolc ventrcular complance was nfnte. Peak elastcty was consdered to be constant durng systole; ths condton s smlar to Warner's (6) assumpton. Furthermore, n the model, the ventrcle was connected to the artery va an aortc valve wth a small resstance (Rvt). The atrum, whch was represented by a lnear complance (Cat), was connected to the ventrcle va a valve wth a small resstance (Rat). It was also connected drectly to the venous return resstance. The parameters of the model elements were: Pa = mm Hg, Pv = 5 mm Hg, Emax = 4.5 mm Hg/ ml, Rvt = 0.01 mm Hg sec/ml, Rat = 0.01 mm Hg sec/ ml, Rv = or 0. mm Hg sec/ml, and Cat = -0 ml/mm Hg. These values seem reasonable for a 0-kg dog at rest. The performance of the model was analyzed wth an analog computer (Pace, TR-10). As ndcated n Fgure 1, venous return flow (Fv) through the venous return resstance, atral pressure (Pat), atral volume (Vat), and ventrcular volume (Vvt) were measured whle the lnear complance of the atrum was changed n steps. Mean atral pressure was calculated by averagng the nstantaneous atral pressure tracng. The same varables were agan measured after venous return resstance had been changed to a second value. Heart rate was modeled as f t were constant at 10 beats/mn. Results Peak systolc and dastolc values (full excurson) of the measured varables and the calculated cardac output are lsted n Table 1. Some sample tracngs showng both a large and a small atral complance are llustrated n Fgure. As atral complance ncreased from a value close to zero, the magntude of the changes n venous return flow and atral pressure became smaller, the mean level of venous return flow ncreased, the atral volume ncreased, the mean atral pressure decreased, the ventrcular stroke volume ncreased, and the enddastolc volume ncreased; end-systolc volume, however, remaned unchanged. Hence, cardac output (stroke volume x heart rate) ncreased. Fgure 3 shows the marked ncreases n stroke volume that occurred n response to the ncreases n atral complance. The ncreases n atral complance from ml/ mm Hg to 0 ml/mm Hg ncreased cardac output logarthmcally up to 35% when venous return resstance was mm Hg sec/ml and up to % when venous return resstance was 0. mm Hg sec/ml. At an atral complance of 5 ml/mm Hg, cardac output had already ncreased sgnfcantly; any addtonal ncrease n atral complance above 5 ml/mm Hg dd not affect cardac output much. Therefore, t seems that a sgnfcant mprovement n cardac performance s attaned when the atral complance s such that atral volume s more than half of the concomtant stroke volume of the ventrcle. Fgure 4 shows the relatonshp between cardac output and mean atral pressure. Increases n atral complance caused a consderable mprovement n cardac performance n terms of the cardac output-mean atral pressure relatonshp, snce a larger cardac output was pumped from a lower mean atral pressure at a hgher atral complance. Crculaton Rttmrth, VoL 35, July 1974
ATRIAL COMPLIANCE 41 TABLE 1 Effects of Varous Levels of Atral Complance on Cardac Performance Venous return Atral complance (ml/mm Hg) oc of Qnpo rcololalllc (mmhgsec/ml) Varables Phase 0. 1 5 10 0 0. Fv (ml/sec) Vat (ml) Pat (mm Hg) Vvt (ml) CO. (ml/mn) 45 l 9.0 130 1 4.9 9.5 13.5 0.3 4.9 3 1560 5 4.6 4.6 33.0 10 15 8.5.0 4. 34.7 000 8 13.0.6 36.5 0 34 9.0 1.8 37.5 340 38 3 1.5 38.0 400 Fv (ml/sec) Vat (ml) Pat (mm Hg) Vvt (ml) CO. (ml/mn) 8 38.0 400 81 38.5 460.4 0.4 39.0 50 40.0 640 9 8.8 1.4 4.4 41.5 79 30 16.5 4.0 3.3 0.8.0 310 75 48 30.0 14.0 3.0 1.4 4 340 6 56 48.0 3.4 1.5 4 340 Fv = venous return flow, Vat - atral volume, Pat - atral pressure, Vvt - ventrcula volume, and CO. = cardac output. Downloaded from http://ahajournals.org by on November 4, 018 SF-Illab- VENOUS RETURN FLOW Fv 150 " ml/sec ol ATRIAL VOLUME VAT ml 30r 0 L 5r ATRIAL PRESSURE PAT nneg OL VENTRICULAR VOLUME VVT Wr BI ATRIAL COMPLIANCE JU QL HEART RATE - 10... VJ V VVWJ AA/W _^ A/X/VV J Jl/l/l/l / lfaaaa LARGE boats/mn FIGURE Effects of atral complance on cardodynamcs. MM SMALL The two rectlnear lnes n Fgure 4 are the theoretcally calculated venous return curves for the two venous return resstances used n the model. The pressure-axs ntercept of both lnes s the specfed venous return source pressure (Pv = 5 mm Hg), and ther slopes are the recprocals of the specfed venous return resstances. The data pont under a gven venous return resstance moves Crculaton Rtstanh. Vol. 35, July 1974 CD OH )-_ CO CD CNI p' 9- ^ ^ Rv = ^ - - Rv = 0. mmhg ml sec 0 1 3 * 5 0 ATRIAL COMPLIANCE ml/mmhg FIGURE 3 Effects of atral complance on stroke volume. Rv - venous return resstance. along the correspondng venous return curve as atral complance s vared. The effect of ncreases n atral complance on cardac output s greater wth the larger venous return resstance. Interestngly, the peak and the mean level of atral pressure durng dastole ncreased wth n-
4 SUGA Downloaded from http://ahajournals.org by on November 4, 018 c H - cs - SF-Illab- Rv = 0. CAT = o Rv = mmhg sec/ml CAT = CAT O.A 1 1 0 1 3 MEAN ATRIAL PRESSURE = 0 CAT = = ^ ml/nm FIGURE 4 Effects of atral complance on cardac performance n terms of the cardac output-mean atral pressure relatonshp. The two rectlnear lnes are the theoretcally calculated venous return curves. Rv - venous return resstance and Cat = atral complance. See text for further dscusson. creases n atral complance, although the mean level of atral pressure durng the entre cardac cycle decreased. Dscusson The results of ths analyss suggest that atral complance s an mportant determnant of the performance of the heart as a whole. The natural atrum contracts and, therefore, s not fully consstent wth the present assumpton of lnearty and constancy of atral complance. However, more than half of the ventrcular fllng process occurs durng the dastolc perod before the atral contracton (10, 11). Therefore, the present assumpton s stll a practcally reasonable approxmaton, and the resultant suggeston should hold n the natural stuaton. The apparent mprovement n cardac performance wth larger atral complances can be explaned as follows. The smaller the atral complance s n the model, the greater are the ampltude and the mean level of atral pressure. However, smultaneously, the mean level of atral pressure durng the perod of ventrcular fllng, whch serves as the effectve source pressure of ventrcular fllng, s smaller. The smaller source pressure causes less fllng and a smaller end-dastolc ventrcular volume. Moreover, venous return to the atrum decreases because of the hgher mean atral pressure. In contrast, when the atral complance s large, the atral pressure varaton s small and the mean level of atral pressure durng ventrcular fllng s mantaned at a relatvely hgh level. Thus, atral complance serves to buffer the pressure changes n the atrum durng a cardac cycle and to smooth the transformaton of the steady venous return flow nto the ntermttent ventrcular fllng flow. The fndng that a larger atral complance mproves cardac performance more when the venous return resstance s larger suggests that the natural atral complance s more advantageous when the caval vens are partally collapsed. Ths fndng corroborates the mportance of a complant atrum at the nlet of the artfcal heart ventrcle, because the artfcal heart actvely sucks blood and collapse of the caval vens would occur wthout such an atrum. The observed dssocaton of the mean atral pressure averaged over the entre cardac cycle and the end-dastolc ventrcular volume s physologcally sgnfcant. It suggests that mean atral pressure does not always serve as the source pressure of ventrcular fllng. Rather, the mean value of atral pressure averaged only over the perod of ventrcular fllng seems to be the effectve, drect source pressure of ventrcular fllng. The stuaton s smlar for ventrcular pressure. Nobody thnks that the mean ventrcular pressure averaged over the entre cardac cycle s the source pressure of aortc flow durng ejecton. Instead, the ventrcular pressure durng the ejecton perod serves as the effectve source pressure of ventrcular ejecton. References 1. BRIGHTON JA, WADE ZA, PIERCE WS, PHILLIPS WM, O'BANNON W: Effect of atral volume on the performance of a sac-type artfcal heart. Trans Am Soc Artf Intern Organs 19:567-57, 1973. GUYTON AC: Cardac Output and Its Regulaton. Phladelpha, W. B. Saunders Company, 1963, pp 163-0 3. SUGA H: Theoretcal analyss of a left ventrcular pumpng model based on the systolc tme-varyng pressure-volume rato. IEEE Trans Bomed Eng 18:47-55, 1971 4. SUGA H, SAGAWA K: Mathematcal nterrelatonshp between nstantaneous ventrcular pressure-volume rato and myocardal force-velocty relaton. Ann Bomed Eng 1:160-181, 197 Crculaton Ratarth. Vol 35. July 1B74
ATRIAL COMPLIANCE 5. SUCA H, SACAWA K, SHOUKAS AA: Load ndependence of the nstantaneous pressure-volume rato of the canne left ventrcle and effects of epnephrne and heart rate on the rato. Crc Res 3:314-3, 1973 6. WARNER HR: Control of the crculaton as studed wth analog computer technques. In Handbook of Physology, sec, vol 3, Crculaton, edted by WF Hamlton and P Dow. Washngton, D. C, Amercan Physologcal Socety, 1965, pp 185-1841 7. BENEKEN JEW, DEWIT B: Physcal approach to hemodynamc aspects of the human cardovascular system. In Physcal Bass of Crculatory Transport: Regulaton and Exchange, edted by EB Reeve and AC Guyton. Phladelpha, W. B. Saunders Company, 1967, pp 1-45 8. RIDEOUT VC: Cardovascular system smulaton n bomedcal engneerng educaton. IEEE Trans Bomed Eng 19: 101-107, 197 9. COOK AM, SIMES JG: Smple heart model desgned to demonstrate bologcal system smulaton. IEEE Trans Bomed Eng 19:97-100, 197 10. BRECHEK GA, GALLETTI PM: Functonal anatomy of cardac pumpng. In Handbook of Physology, sec, vol, Crculaton, edted by WF Hamlton and P Dow. Washngton, D. C, Amercan Physologcal Socety, 1963, pp 759-798 11. NOLAN SP, DIXON SH JR, FISHER RD, MORROW AG: Influence of atral contracton and mtral valve mechancs on ventrcular fllng: Study of nstantaneous mtral valve flow n vvo. Am Heart J 77:784-791, 1969 Downloaded from http://ahajournals.org by on November 4, 018 Crculaton Raearch. Vol. 3S, July 1974