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Flow in stenosed epicardial arteries as predicted by a mathematical model of the coronary circulation and compared to canine experiments
13 THE STEADY-STATE
AND TRANSIENT RESPONSES TO IMPOSED ALTERNATIONS IN FILLING VOLUMES: MODULATION BY THE FRANK-STARLING MECHANISM AND BY VARIATIONS IN AFTERLOAD. Avner Veler, David Adler, Yona Mahler, Department of Biomedical Engineering, Hadassah University Hospital, Jerusalem, ISRAEL Quantitative discrete analysis of sustained mechanical alternans (SNA) initiated by alternations in filling volumes (FV) shows that the response depends on: (1) volumes prior to the strong and weak e-FV,/FV,, where Fv, and FV, are the filling beats, respectively; (2) SV-y(EDV-EDVD), where 1 is the slope of the SV-EDV relation and EDVD is the threshold EDV for which there is no SV; (3) X-d, where cr-AP(j+l)/ASV(j) and L-ASV(j+l)/AP(j+l). Note, ASV(j)-SV(j)-SV,, (SS-steady state), P is the opening aortic pressure. X is the 'afterload factor' since AP(j)-P(j)-P,,. it reflects the resultant effect of P on SV. A second order difference equation of the type (4) SV(n)-f[SV(n-l),SV(n-2)] is obtained from equations (l-3). The solution of (4) implies the following SS and transient responses. In SS p- (l-x)(1+0)-~ / (lp-SVs/SVw. The condition for two non-zero SV's is A-cl-[Br/(l+B)]. A) (l+e)-re , where The transient response depends on 7 and X. When Xl-y, a transient increase in both the weak and the strong beats occurs until a SS is obtained. When Xtl-7, a transient decrease in the weak beats and a transient increase in the strong beats occurs prior to the SS. In conclusion SMA initiated by FV alternations is characterized by the means of three measurable parameters: 7,0,X.
14 OPTIMAL
OPERATION OF IABP Ofer Barneal, Brian Smith*, Stephen Dubi$, Thomas W. Moores, Dov Jarons. IBiomedical Engineering Program, Tel Aviv University, Israel, and sBiomedica1 Engineering and Science Institute, Drexel University, Philadelphia, PA 19104 USA. The in&a-aortic balloon pump (IABP), a temporary cardiac assist device, is inflated and deflated in the descending thoracic aorta to increase diastolic pressure and decrease systolic pressure. These hemodynamic effects are expected to increase coronary flow thereby increasing cardiac oxygen supply, and to decrease the afterload thereby decreasing cardiac oxygen consumption. Based on these objectives, a performance index has been formulated: I(A,)= K,MDPK,P.SP. The index reflects. cardiac oxygen balance and is calculated from clinically available hemodynamic variables. !mplemented m an opti+mal control.system together with an optimization algorithm, the performance index IS contmuously maxnmxed by varmtions of the balloon’s deflation time which is sensitive to changes in cardiovascular system. The variable which is controlled is Ad, the difference between the next R-wave and the deflation time rather than time from the previous R-wave. This provides an almost instantaneous response to changes in heart rate. Each iteration m the optimization algorithm is composed of two phases: search and quadratic estimation. The constraints under which the search operates are maximum and minimum step sizes and Ad values. Optimal values for the constraints, dynamics of the control system, importance of weights (K1 and Kz) selection, and sensitivity of the performance index to changes in Ad were assessed in animal experiments. The results show that excellent tracking of optimal timing can be obtained while observing physiologically Imposed constramts. Selection of weights was not found to significantly affect the optimal timing.
15 FLOW IN STENOSED EPICARDIAL
ARTERIES AS PREDICTED BY A MATHEMATICAL MODEL OF THE CORONARY CIRCULATION AND COMPARED TO CANINE EXPERIMENTS. D. Manor, A. Meirowitz, R. Shofti, S. Sideman, U. Dinnar, and R. Beyar. Cardiac System Research Center, Biomedical Engineering, Technion, Haifa, The phasic flows in the epicardial and myocardial vessels was explored at increasing stenosis level using a mathematical model and compared to experimental studies in dogs. The epicardial tree is simulated from realistic coronary circulation which is geometry. The myocardial subjected to the cyclic intramyocardial pressures is divided into 3 compartments (arterial vessels, microcirculation and venous vessels) represented each by a resistance and a capacitance that change with time as a function of the vessel cross sectional area. The results show that while the epicardial arterial flow is mostly diastolic and the venous flow is mostly systolic the normal average transmural flow is continuous. The phasic nature of the epicardial arterial flow is modified during critical coronary stenosis so that its systolic to diastolic ratio is increased. The model predictions regarding arterial phasic flow were verified by measurements in dogs of phasic coronary flow in normal and experimental LAD stenosis. Utilizing such a model in parallel to experimental studies provides a tool in understanding the mechanisms of interaction between cardiac contraction and coronary flow in the normal and ischemic heart. VI
AND TRANSIENT RESPONSES TO IMPOSED ALTERNATIONS IN FILLING VOLUMES: MODULATION BY THE FRANK-STARLING MECHANISM AND BY VARIATIONS IN AFTERLOAD. Avner Veler, David Adler, Yona Mahler, Department of Biomedical Engineering, Hadassah University Hospital, Jerusalem, ISRAEL Quantitative discrete analysis of sustained mechanical alternans (SNA) initiated by alternations in filling volumes (FV) shows that the response depends on: (1) volumes prior to the strong and weak e-FV,/FV,, where Fv, and FV, are the filling beats, respectively; (2) SV-y(EDV-EDVD), where 1 is the slope of the SV-EDV relation and EDVD is the threshold EDV for which there is no SV; (3) X-d, where cr-AP(j+l)/ASV(j) and L-ASV(j+l)/AP(j+l). Note, ASV(j)-SV(j)-SV,, (SS-steady state), P is the opening aortic pressure. X is the 'afterload factor' since AP(j)-P(j)-P,,. it reflects the resultant effect of P on SV. A second order difference equation of the type (4) SV(n)-f[SV(n-l),SV(n-2)] is obtained from equations (l-3). The solution of (4) implies the following SS and transient responses. In SS p- (l-x)(1+0)-~ / (lp-SVs/SVw. The condition for two non-zero SV's is A-cl-[Br/(l+B)]. A) (l+e)-re , where The transient response depends on 7 and X. When Xl-y, a transient increase in both the weak and the strong beats occurs until a SS is obtained. When Xtl-7, a transient decrease in the weak beats and a transient increase in the strong beats occurs prior to the SS. In conclusion SMA initiated by FV alternations is characterized by the means of three measurable parameters: 7,0,X.
14 OPTIMAL
OPERATION OF IABP Ofer Barneal, Brian Smith*, Stephen Dubi$, Thomas W. Moores, Dov Jarons. IBiomedical Engineering Program, Tel Aviv University, Israel, and sBiomedica1 Engineering and Science Institute, Drexel University, Philadelphia, PA 19104 USA. The in&a-aortic balloon pump (IABP), a temporary cardiac assist device, is inflated and deflated in the descending thoracic aorta to increase diastolic pressure and decrease systolic pressure. These hemodynamic effects are expected to increase coronary flow thereby increasing cardiac oxygen supply, and to decrease the afterload thereby decreasing cardiac oxygen consumption. Based on these objectives, a performance index has been formulated: I(A,)= K,MDPK,P.SP. The index reflects. cardiac oxygen balance and is calculated from clinically available hemodynamic variables. !mplemented m an opti+mal control.system together with an optimization algorithm, the performance index IS contmuously maxnmxed by varmtions of the balloon’s deflation time which is sensitive to changes in cardiovascular system. The variable which is controlled is Ad, the difference between the next R-wave and the deflation time rather than time from the previous R-wave. This provides an almost instantaneous response to changes in heart rate. Each iteration m the optimization algorithm is composed of two phases: search and quadratic estimation. The constraints under which the search operates are maximum and minimum step sizes and Ad values. Optimal values for the constraints, dynamics of the control system, importance of weights (K1 and Kz) selection, and sensitivity of the performance index to changes in Ad were assessed in animal experiments. The results show that excellent tracking of optimal timing can be obtained while observing physiologically Imposed constramts. Selection of weights was not found to significantly affect the optimal timing.
15 FLOW IN STENOSED EPICARDIAL
ARTERIES AS PREDICTED BY A MATHEMATICAL MODEL OF THE CORONARY CIRCULATION AND COMPARED TO CANINE EXPERIMENTS. D. Manor, A. Meirowitz, R. Shofti, S. Sideman, U. Dinnar, and R. Beyar. Cardiac System Research Center, Biomedical Engineering, Technion, Haifa, The phasic flows in the epicardial and myocardial vessels was explored at increasing stenosis level using a mathematical model and compared to experimental studies in dogs. The epicardial tree is simulated from realistic coronary circulation which is geometry. The myocardial subjected to the cyclic intramyocardial pressures is divided into 3 compartments (arterial vessels, microcirculation and venous vessels) represented each by a resistance and a capacitance that change with time as a function of the vessel cross sectional area. The results show that while the epicardial arterial flow is mostly diastolic and the venous flow is mostly systolic the normal average transmural flow is continuous. The phasic nature of the epicardial arterial flow is modified during critical coronary stenosis so that its systolic to diastolic ratio is increased. The model predictions regarding arterial phasic flow were verified by measurements in dogs of phasic coronary flow in normal and experimental LAD stenosis. Utilizing such a model in parallel to experimental studies provides a tool in understanding the mechanisms of interaction between cardiac contraction and coronary flow in the normal and ischemic heart. VI