Cardiac twitch properties simulated by three-states model.

We examined whether the three states model can explain the systolic and relaxation properties of cardiac muscle to clarify what factors affect these properties. Changing the values of the parameters describing the calcium transient and calcium sensitivity, we estimated the effects of these parameters on the systolic and relaxation properties of twitch contraction. The simulations showed the following four features: 1) An increase in the maximum calcium concentration and calcium sensitivity, and a prolongation of the calcium transient led to an increase in peak tension associated with an increase in the time to peak tension. 2) An increase in myosin ATPase activity led to an increase in peak tension associated with a decrease in the time to peak tension. 3) An increase of peak tension was accompanied by a prolongation of the late systolic period. 4) The constant of the late tension relaxation from 25% to 10% of the peak tension was altered when the crossbridge cycling rate, the resting calcium concentration or the late decline of the calcium transient was changed. The simulation were not contradictory to the experimental results and showed that three state muscle model can provide qualitative descriptions on the systolic and relaxation characteristics of cardiac muscle.

Myocardial rapid velocity distribution.

Myocardial motion exhibits frequency components of up to 100 Hz, as found by a phased tracking method. To simultaneously measure the rapid and minute velocity signals at multiple points along the surface of the left ventricle (LV), in this study, conventional ultrasonic diagnosis equipment was modified to allow 10 scan lines from a sector scanner to be arbitrarily selected in real-time for analysis. By considering the maximum value of the velocity in the heart wall and the maximum depth from the chest surface, the number of transmission directions of the ultrasonic pulses should be carefully confirmed to be 10 to avoid aliasing, which is much less than the number employed in conventional tissue Doppler imaging (TDI). By applying the system, the velocity signals at about 240 points in the heart walls were simultaneously measured for three healthy volunteers. During a short period of 35 ms around end-diastole, the velocity signals varied spatially in the heart wall. At the end of systole, in the wavelets near the base of the interventricular septum (IVS), the slow pulse continued for about 30 ms, just before the radiation timing of the second heart sound. Then, a steep pulse occurred just at the timing of the closure of the aortic valve. The steep pulse at the base preceded that at the apex by several ms. By Fourier transforming each wavelet, the spatial distribution of the phase of the steep pulse components were clearly displayed. By applying the measurement method to two patients with aortic stenosis (AS), irregular vibration signals, which correspond to the murmur of the heart sound, could be directly detected during the ejection period. In conventional TDI, only the large slow movements due to the heartbeat are displayed, but these rapid and minute velocity components cannot be displayed. In this study, moreover, the phase components were detected for the first time from each of the velocity signals simultaneously measured at multiple points along the 10 scan lines. This measurement and method of analysis offer potential for new diagnostic techniques in cardiac dysfunction.

Real-time velocimetry for evaluation of change in thickness of arterial wall.

We previously developed a new method, namely, the phased tracking method, for accurately tracking the movement of the heart wall and arterial wall based on both the phase and magnitude of the demodulated signals to determine the instantaneous position of an object. By this method, the local change in wall thickness during one heartbeat can be determined. We have now developed a real-time system for measuring change in thickness of the myocardium and arterial wall. In this system, four high-speed digital signal processing (DSP) chips are employed for obtaining the initially developed method in real time. The tracking results for both sides of the wall are superimposed on the M (motion)-mode image in the workstation, and the thickness changes of the arterial wall are displayed in real time. Using this system, reported herein, velocity signals of the arterial wall with amplitudes less than several micrometers can be successfully detected in real time with sufficient reproducibility. The elasticity of the arterial wall is evaluated by referring to the blood pressure. In in vivo experiments, the rapid response of the change in wall thickness of the carotid artery to the dose of nitroglycerine (NTG) is evaluated for a young healthy subject and a young smoker. This new real-time system offers potential for quantitative diagnosis of early-stage atherosclerosis by the transient evaluation of the rapid response of the cardiovascular system to physiological stress.

Onset of pulsatile waves in the heart walls at end-systole.

We have previously developed a novel ultrasonic method, namely, the phased tracking method, for accurately tracking the movement of the heart wall based on both the phase and magnitude of the demodulated signals to determine the instantaneous position of an object. With this method, it is possible to accurately detect small-amplitude velocity signals of less than a few micrometers of the heart wall that are superimposed on the motion of the heart wall due to the heart beat. There are several remarkable pulsatile waves during one cardiac cycle in the resultant velocity signals, some of them being commonly obtained for both healthy subjects and patients. These pulsatile waves cannot be recognized in standard echocardiography M-mode images. In this paper, by focusing on one pulsatile wave that occurs around the end-systole, the physiological meaning of these is considered based on various in-vivo experiments. The pulsatile wave measured by this novel ultrasonic method will offer potential for a quantitative assessment of myocardial viability.

Real-time measurements of local myocardium motion and arterial wall thickening.

We have already developed a new method, namely, the phased tracking method, to track the movement of the heart wall and arterial wall accurately based on both the phase and magnitude of the demodulated signals to determine the instantaneous position of an object. This method has been realized by an off-line measurement system, which cannot be applied to transient evaluation of rapid response of the cardiovascular system to physiological stress. In this paper, therefore, a real-time system to measure change in the thickness of the myocardium and the arterial wall is presented. In this system, an analytic signal from standard ultrasonic diagnostic equipment is analogue-to-digital (A/D) converted at a sampling frequency of 1 MHz. By pipelining and parallel processing using four high-speed digital signal processing (DSP) chips, the method described is realized in real time. The tracking results for both sides of the heart and/or arterial wall are superimposed on the M (motion)-mode image in the work station (WS), and the thickness changes of the heart and/or arterial wall are also displayed and digital-to-analogue (D/A) converted in real time. From the regional change in thickness of the heart wall, spatial distribution of myocardial motility and contractility can be evaluated. For the arterial wall, its local elasticity can be evaluated by referring to the blood pressure. In in vivo experiments, the rapid response of the change in wall thickness of the carotid artery to the dose of the nitroglycerine (NTG) is evaluated. This new real-time system offers potential for quantitative diagnosis of myocardial motility, early stage atherosclerosis, and the transient evaluation of the rapid response of the cardiovascular system to physiological stress.

Non-invasive estimation of human left ventricular end-diastolic pressure.

Sato et al. (Electronic Letters 32, 949-950, 1996) reported that one can obtain a non-invasive estimate of left ventricular (LV) pressure at around end-diastole in an isolated canine preparation. In this study we examined whether this method can be applied to humans. Using the method proposed by Kanai et al. (IEEE. Trans. UFFC, 43, 791-810,1996), we detected small amplitude LV vibration from an ultrasonic pulse Doppler signal reflected from the interventricular septum in five patients (44-63 y.o., male;4, female;1). We measured the oscillation frequency of the LV wall through the wavelet transform of small amplitude LV vibration, and calculated LV pressure at around end-diastole from the values of oscillation frequency, internal radius and wall thickness using Mirsky's equation. The estimated LV pressures at around end-diastole were similar to end-diastolic pressure measured directly by cardiac catheterization. These results show the possibility that this method allows for the non-invasive estimate of LV pressure at around end-diastole, and furthermore provides the basis for future clinical applicability of this technique.

The effect of applied mechanical vibration on two different phases of rat papillary muscle relaxation.

Applying external mechanical vibration during the relaxation phase of rat papillary muscle decreases the duration of the first part of the relaxation phase. To elucidate the basic mechanism responsible for this shortening of the relaxation period, we applied a controlled vibration to isolated twitching rat papillary muscles during various phases in the relaxation of a twitch. The first part of the relaxation phase was accelerated when length perturbations were applied in the first part of the relaxation of a twitch, dependent on both amplitude and frequency of the perturbation. When vibrations were applied in the first half of the relaxation, the second phase of relaxation was slightly slower (about 20%), but when no vibrations were applied in the first phase, relaxation could be accelerated by applying vibration in the latter half of the relaxation phase. Thus, in the latter half of relaxation, the acceleration of relaxation depended upon perturbation events earlier during that twitch. This study indicates that vibration-induced acceleration of relaxation is due (at least in part) to an apparent increase in detachment rate of attached cross-bridges from the thin filament without substantial reattachment.

Modification of human left ventricular relaxation by small-amplitude, phase-controlled mechanical vibration on the chest wall.

BACKGROUND: Direct clinical manipulation to improve an impairment of left ventricular (LV) relaxation has not been reported. We investigated whether the LV relaxation rate in humans could be modulated by phase-controlled mechanical vibration applied to the patient's anterior chest wall and whether there are some quantitative differences in the responses of normal (N), hypertrophied (H), and failing (F) ventricle. METHODS AND RESULTS: In 46 patients (N, 10; H, 18 [hypertrophic cardiomyopathy]; F, 18 [heart failure]), the vibrator was attached to the precordium and a 50-Hz, 2-mm sinusoidal mechanical vibration was applied, with the timing restricted from the onset of isovolumic relaxation to end-diastole during cardiac catheterization. Heart rate and peak LV pressure showed no difference with vibration. However, in all patients, precordial vibration caused an acceleration of the LV pressure fall. The magnitude of the induced reduction of the time constant of LV pressure decay (delta T) was larger (P < .01) in H and F than in N (4.6 +/- 2.3, 4.0 +/- 1.6, and 0.6 +/- 1.5 ms for H, F, and N, respectively). Delta T correlated strongly with the magnitude of impaired relaxation and the magnitude of transmitted vibration to the ventricle. CONCLUSIONS: Phase-controlled, small-amplitude vibration on the chest wall can directly modulate LV relaxation rate, especially in those with hypertrophy or failing ventricle.

Cross-bridge movement in rat slow skeletal muscle as a function of calcium concentration.

A single fibre bundle from rat soleus muscle was chemically skinned with saponin and the transfer of myosin heads from the thick filaments to the thin filaments at a sarcomere length of 2.4 microm was measured as a function of Ca2+ concentration using an x-ray diffraction method at 4-7 degrees C. In the relaxed state, the 1,0 spacing was 42.08 nm. The spacing showed no significant decrease when the Ca2+ concentration was below the threshold (-log10 [Ca2+] or pCa 5.8). No significant transfer of the myosin heads occurred when the Ca2+concentration was below the threshold (pCa 5.8). When the muscle was maximally activated at pCa 4.4, the spacing decreased to 40.35 nm. During the maximum isometric contraction at pCa 4.4, 54. 9 +/- 6.5% (+/-SE of the mean) of the myosin heads were transferred to the thin filaments. The transfer of the myosin heads was approximately proportional to relative tension. These results suggest that myosin heads of both fast-twitch and slow-twitch skeletal muscles transferred on the common movement as a function of Ca2+ concentration.

The effect of diastolic vibration on the relaxation of rat papillary muscle.

OBJECTIVE: It has been demonstrated that the application of an external mechanical vibration during the ventricular relaxation phase of the heart (diastolic vibration) decreases the time needed for myocardial relaxation. The objective of this study is to see whether this vibration-induced decrease in relaxation time is an intrinsic property of the contractile proteins. We hypothesize that this decrease in duration of the late systolic phase by diastolic vibration is likely to be due to a forced detachment of crossbridges from the actin filament. This would then result in a decrease in the relaxation time of myocardial tissue. METHODS: A controlled vibration of variable amplitude and frequency was applied to isolated twitching rat papillary muscles. Vibration was initiated from directly after peak tension development and ended when tension had returned to baseline. Effects of applied vibration were expressed as changes in the time interval from 90% rising- to 50% falling-force level, which was termed the 'late systolic phase'. RESULTS: The data showed that in general diastolic vibration decreased the duration of this late systolic phase. A vibration of 1.0% of Lmax at 50 Hz in the late systolic phase shortened this period by 27 ms (20-30%) on average. At increasing amplitude of vibration the increase in the rate of relaxation was even more pronounced. Shortening of this duration was slightly less at frequencies of vibration below 40 Hz than at higher frequencies of vibration. Changes in the resting muscle length did not result in significant changes in shortening of the studied relaxation period. CONCLUSION: The results show that relaxation is accelerated during application of an external vibration during the period of tension fall of an isolated cardiac muscle preparation. Therefore, we can conclude that the acceleration of relaxation due to vibration is primarily due to properties of the myocytes themselves rather than to the complex geometric structure of the heart. Tension in the relaxation phase was reduced during diastolic vibration, which suggests that the number of crossbridges bound to the actin filament was reduced by the length perturbation.

Changes in viscoelasticity of the myocardium during cardioplegic arrest.

To evaluate the efficacy of myocardial preservation during open heart surgery, we measured the viscoelasticity of the canine myocardium during cardioplegic arrest. A transfer function method was used for the measurement with a monitoring system consisting of a vibrator, a function generator, accerometers and a signal processor. Six mongrel dogs were put on cardiopulmonary bypass and after measurement of control hemodynamics, they were subjected to cardioplegic arrest at myocardial temperatures ranging from 4 to 32 degrees C. Viscoelasticity was measured at every 15 min and the cardioplegic solution was added every 30 min. After two hr of cardioplegic arrest, the myocardium was reperfused and postischemic hemodynamics were measured after 30 min of non-working beating. Satisfactory myocardial function returned in 3 hearts with the myocardial temperatures below 24 degrees C with myocardial viscoelasticity within the control range. Moderately decreased myocardial contractility was noted in a heart kept at temperature of 27 degrees C and its viscoelasticity remained in the control range of 90 min of ischemia and then began to decrease. In 2 hearts kept at temperatures higher than 29 degrees C, severely depressed myocardial contractility was noted, and viscoelasticity decreased transiently at 45 to 60 min and then returned to control levels. These results suggested usefulness of continuous monitoring of the viscoelasticity in early detection of its degenerative alterations due to impaired myocardial preservation during open heart surgery.

Theoretical treatment of striated muscle: Dynamic extension of four-state model.

We constructed a muscle model, based on the model first proposed by Gray and Gonda [6,7), that simulates the twitch contraction of striated muscle. Their original model postulated four basic states in the contraction cycle and predicted the properties of steady state contraction in striated muscle. Using the relationship between steady state tension and calcium concentration, we described several rate constants as functions of calcium concentration and calculated the number of attached crossbridges at various calcium concentration values. The results for both skeletal and cardiac muscle were approximately consistent with those of X-ray studies. Assuming that rate constants change immediately with the phasic alteration of intracellular calcium concentration, we estimated the time course of crossbridge distribution during twitch contraction; these findings were also consistent with those of X-ray studies. We also simulated the effects of calcium concentration and sarcomere length on the magnitude of twitch tension. These simulations suggest that the major determinants of crossbridge distribution during twitch contraction are the time courses of calcium transients and the rate constants of crossbridge kinetics. Our findings suggest that the model used in this study provides a theoretical basis for interpreting the characteristics of cardiac muscle encountered in the clinical setting.

Increased regional systolic myocardial stiffness of the left ventricle during coronary artery occlusion in a dog: analysis of the finite element model.

(1) We measured the instantaneous systolic transfer function of an isolated canine left ventricle (LV) before and after the ligation of the left anterior descending coronary artery (LAD). The instantaneous transfer function before the ligation of the LAD showed a resonance curve whose peak frequency was 30 to 70 Hz. On the other hand, the transfer function 40 min after the ligation of the LAD showed a divided peak in the resonance curve. (2) We constructed a finite element model of a thick-walled spherical shell with a non-uniform structure. In this model, the myocardial elasticity and viscosity of the ischemic region are different from those of non-ischemic regions. One can calculate the theoretical transfer function using modal analysis and also estimate the elasticity and the viscous coefficient of both non-ischemic and ischemic myocardium by fitting the theoretical transfer function to the experimental one. (3) The estimated elasticity of the ischemic myocardium was three to five times larger than that of the non-ischemic myocardium. The estimated viscous coefficient of the ischemic myocardium was about half that of the non-ischemic myocardium. These results showed that ischemia alters the viscoelastic properties of the myocardium during systole as well as during diastole.

Mathematical model of the effects of mechanical vibration on crossbridge kinetics in cardiac muscle.

We previously reported that the application of an external mechanical vibration to the epicardial surface caused a vibration-induced-depression (VID) of left ventricular (LV) function. The magnitude of the VID of peak LV pressure increased as either the amplitude or the frequency of the vibration increased. When LV contractility was altered by the administration of propranolol or by continuous infusion of dobutamine, the magnitude of the VID of peak LV pressure was inversely correlated with LV contractility. These characteristics were observed in open-chest and isolated canine preparations. In the present study, we constructed a muscle model to obtain a theoretical explanation for these effects. This model was first proposed by Gray, Gonda and Cheung, and has been extended in this report to explain twitch tension. This new, improved model is able to explain twitch tension and the effects of external vibration on twitch contraction semi-quantitatively. The successful predictions of the this model support the idea that external vibration directly affects contractile protein and modulates crossbridge kinetics.

Noninvasive measurement of left ventricular myocardial elasticity.

We examined Advani and Lee's equation (ALeq) and a dimension analysis-derived equation (DAeq), both of which treat vibration of the elastic spherical shell and are able to estimate elasticity of the shell noninvasively when the sizes and eigen-frequency are provided. We confirmed that ALeq was numerically identical to DAeq and that both equations gave the precise elasticity of the silicone shell. Then we estimated left ventricular (LV) myocardial elasticity noninvasively at the moment of the first heart sound emission (1HS) in 25 healthy subjects and 14 hypertrophic cardiomyopathy (HCM) patients, based on the LV eigen-frequency detected by an intraesophageal miniature vibration sensor. HCM patients had a higher mean value of LV myocardial elasticity at 1HS than healthy subjects [102.3 +/- 33.4 vs. 70.7 +/- 24.4 kPa, P < 0.01 (Pa = N/m2 = 10 dyn/cm2)]. We thereby demonstrated the possibility of a noninvasive estimate of myocardial elasticity.

Simulation study on heart failure: effects of contractility on cardiac function.

Using the model proposed by Beyar and Sideman, the effect of maximum isometric active stress at optimal sarcomere length (sigma 0) on left ventricular (LV) function was examined. Comparing the results of calculated LV function with those of reported experiments, sigma 0 was shown to be a potential indicator of myocardial contractility, and the model of Beyar and Sideman successfully predicted LV function with various myocardial contractilities. The LVP compensation curve, which describes the relationship between sigma 0 and maximum LV pressure, was then hypothesized. The combination of the Beyar-Sideman model and the LVP compensation curve enabled the prediction and approximation of the actual process of deterioration in heart failure. These models represent a step towards a fundamentally new concept in the current clinical situation of compensated heart failure and also in evaluating the process of heart failure.

Simulation study on the effect of external vibration on left ventricular function: potential indicator of LV tolerance to the sudden reduction of myocardial contractility.

In a previous study the authors reported that external mechanical vibration applied to the left ventricular (LV) epicardium induces contractility-dependent depression in LV pressure, stroke volume and stroke work. It was suggested that this depression may be caused by the direct effect of external vibration on contractile protein. In another paper in this issue, it is proved that LV function with various myocardial contractilities and the actual process of deterioration in heart failure are well simulated in the model proposed by Beyar and Sideman, after some modifications have been made. In the study reported here it is assumed that an external mechanical vibration induces sudden reduction in myocardial active stress in the model of Beyar and Sideman; in this way the contractility-dependent effect of external vibration on LV function has been simulated. The results of this simulation support the suggestion that external mechanical vibration directly affects contractile protein and reduces LV function, and it is further suggested that the reduction of LV function induced by external vibration reflects the reserve or tolerance capacity of LV to a sudden reduction of myocardial contractility.

Estimation of left ventricular myocardial elasticity and viscosity by a thick-walled spherical model.

The authors measured the transfer function (TF) of the left ventricle (LV) in an isolated canine preparation. Here TF indicates the ratio of induced vibration in LV to input vibration when an external mechanical oscillation is applied. TF had a single peak the frequency of which changed from 40 Hz to 80 Hz when LV pressure (LVP) increased from 6 mm Hg to 96 mm Hg. A mathematical model was formulated to estimate the viscoelasticity of the spherical shell. This model was constructed of the material points, elastic components which connected all the material points, and viscous components placed in series with elastic components. Theoretical TF can be computed if the viscoelastic values are given. The value of viscoelasticity at which the theoretical TF best fitted the experimental TF was considered to be the viscoelasticity of the model. The validity of this approach was verified using a silicone spherical shell. The estimated myocardial elasticity was 40 kPa when LVP was 6 mm Hg, 160-170 kPa when LVP was 96 mm Hg and was approximately proportional to LVP, whereas viscosity showed small change. The inclination of elasticity was consistent with previous reports. These results proved that myocardial elasticity can be estimated by analysing the transfer function of the left ventricle.

Effects of arterial distensibility on left ventricular ejection in the depressed contractile state.

OBJECTIVE: The aim was to evaluate the effects of arterial distensibility on ventricular ejection in various ventricular contractile states: (1) control; (2) a regionally depressed contractile state due to left circumflex coronary artery occlusion (ligation); (3) a globally depressed contractile state induced by lignocaine (lignocaine); and (4) a globally augmented contractile state due to dobutamine infusion (dobutamine). METHODS: Arterial compliance was decreased from 2.3 x 10(-4) dyne-1.cm5 (C2.3) to 0.4 x 10(-4) dyne-1.cm5 (C0.4), maintaining other afterload components and left ventricular end diastolic pressure constant. Nine excised perfused and paced canine hearts, supported from donor dogs, were used. RESULTS: In control, ligation, lignocaine, and dobutamine groups, the difference in cardiac output between the compliance values of C0.4 and C2.3 was 124(SEM 32), 204(36), 163(33), and 130(24) ml, respectively. Thus cardiac output at C0.4, as a percentage of that at C2.3, was 88(2.8)% (control), 75(2.9)% (ligation), 82(2.9)% (lignocaine), and 88(2.4)% (dobutamine), respectively: control v ligation, and lignocaine v ligation, p < 0.001; control v lignocaine, and dobutamine v ligation, p < 0.01. Stroke work at C0.4 decreased in the ligation group (63%, p < 0.001) and in the lignocaine group (70%, p < 0.001). CONCLUSIONS: When cardiac dysfunction is already present, decreased arterial distensibility has a further deleterious effect on cardiac output. This may be due to the fact that the pressure at the end of ejection is higher and as a result the change in dimension during ejection is considerably reduced, especially in cases with depressed cardiac function caused by afterload dependency.

Diastolic vibration improves systolic function in cases of incomplete relaxation.

BACKGROUND: Incomplete relaxation of the left ventricle (LV) affects LV filling, but the subsequent effect on LV systolic function remains unclear. We attempted to improve relaxation by applying oscillatory mechanical perturbation during diastole (diastolic vibration) and examined the extent to which systolic function improved. METHODS AND RESULTS: Using 10 open-chest canine preparations, pacing tachycardia and administration of propranolol were imposed to induce various levels of incomplete relaxation. Myocardial length perturbation was induced with an oscillator attached to the LV surface (50 Hz, 1-mm amplitude) and was restricted to the period from the beginning of isovolumic relaxation to end diastole. At resting heart rates, diastolic vibration caused an immediate decrease in the time constant (T) of LV pressure fall without any influence on heart rate, LV peak systolic pressure (peak LVP), stroke volume (SV), LV peak positive dP/dt, and total systemic vascular resistance. With pacing tachycardia, diastolic vibration increased both peak LVP and SV at 160 beats per minute (before) and 120 beats per minute (after propranolol), simultaneously decreasing both T and LV diastolic pressures and increasing end-diastolic segment length. The increase in peak LVP and SV caused by diastolic vibration correlated with the T/diastolic interval (r = 0.82), the assumed index of severity of incomplete relaxation. CONCLUSIONS: These results suggest that diastolic vibration accelerates the LV relaxation rate and that this increased relaxation improves systolic function through the Frank-Starling mechanism.