Physical determinants of left ventricular isovolumic pressure decline: model prediction with in vivo validation

The rapid decline in pressure during isovolumic relaxation (IVR) is traditionally fit algebraically via two empiric indexes: tau, the time constant of IVR, or tau(L), a logistic time constant. Although these indexes are used for in vivo diastolic function characterization of the same physiological process, their characterization of IVR in the pressure phase plane is strikingly different, and no smooth and continuous transformation between them exists. To avoid the parametric discontinuity between tau and tau(L) and more fully characterize isovolumic relaxation in mechanistic terms, we modeled ventricular IVR kinematically, employing a traditional, lumped relaxation (resistive) and a novel elastic parameter. The model predicts IVR pressure as a function of time as the solution of d(2)P/dt(2) + (1/micro)dP/dt + E(k)P = 0, where micro (ms) is a relaxation rate (resistance) similar to tau or tau(L) and E(k) (1/s(2)) is an elastic (stiffness) parameter (per unit mass). Validation involved analysis of 310 beats (10 consecutive beats for 31 subjects). This model fit the IVR data as well as or better than tau or tau(L) in all cases (average root mean squared error for dP/dt vs. t: 29 mmHg/s for model and 35 and 65 mmHg/s for tau and tau(L), respectively). The solution naturally encompasses tau and tau(L) as parametric limits, and good correlation between tau and 1/microE(k) (tau = 1.15/microE(k) - 11.85; r(2) = 0.96) indicates that isovolumic pressure decline is determined jointly by elastic (E(k)) and resistive (1/mu) parameters. We conclude that pressure decline during IVR is incompletely characterized by resistance (i.e., tau and tau(L)) alone but is determined jointly by elastic (E(k)) and resistive (1/micro) mechanisms.     

Impaired left ventricular filling due to right-to-left ventricular interaction in patients with pulmonary arterial hypertension

The aim of this study was to investigate the contribution of direct right-to-left ventricular interaction to left ventricular filling and stroke volume in 46 patients with pulmonary arterial hypertension (PAH) and 18 control subjects. Stroke volume, right and left ventricular volumes, left ventricular filling rate, and interventricular septum curvature were measured by magnetic resonance imaging and left atrial filling by transesophageal echocardiography. Stroke volume, left ventricular end-diastolic volume, and left ventricular peak filling rate were decreased in PAH patients compared with control subjects: 28 +/- 13 vs. 41 +/- 10 ml/m(2) (P < 0.001), 46 +/- 14 vs. 61 +/- 14 ml/m(2) (P < 0.001), and 216 +/- 90 vs. 541 +/- 248 ml/s (P < 0.001), respectively. Among PAH patients, stroke volume did not correlate to right ventricular end-diastolic volume or mean pulmonary arterial pressure but did correlate to left ventricular end-diastolic volume (r = 0.62, P < 0.001). Leftward interventricular septum curvature was correlated to left ventricular filling rate (r = 0.64, P < 0.001) and left ventricular end-diastolic volume (r = 0.65, P < 0.001). In contrast, left atrial filling was normal and not correlated to left ventricular end-diastolic volume. In PAH patients, ventricular interaction mediated by the interventricular septum impairs left ventricular filling, contributing to decreased stroke volume.     

Chamber properties from transmitral flow: prediction of average and passive left ventricular diastolic stiffness.

A chamber stiffness (K(LV))-transmitral flow (E-wave) deceleration time relation has been invasively validated in dogs with the use of average stiffness [(DeltaP/DeltaV)(avg)]. K(LV) is equivalent to k(E), the (E-wave) stiffness of the parameterized diastolic filling model. Prediction and validation of 1) (DeltaP/DeltaV)(avg) in terms of k(E), 2) early rapid-filling stiffness [(DeltaP/DeltaV)(E)] in terms of k(E), and 3) passive (postdiastasis) chamber stiffness [(DeltaP/DeltaV)(PD)] from A waves in terms of the stiffness parameter for the Doppler A wave (k(A)) have not been achieved. Simultaneous micromanometric left ventricular (LV) pressure (LVP) and transmitral flow from 131 subjects were analyzed. (DeltaP)(avg) and (DeltaV)(avg) utilized the minimum LVP-LV end-diastolic pressure interval. (DeltaP/DeltaV)(E) utilized DeltaP and DeltaV from minimum LVP to E-wave termination. (DeltaP/DeltaV)(PD) utilized atrial systolic DeltaP and DeltaV. E- and A-wave analysis generated k(E) and k(A). For all subjects, noninvasive-invasive relations yielded the following equations: k(E) = 1,401. (DeltaP/DeltaV)(avg) + 59.2 (r = 0.84) and k(E) = 229.0. (DeltaP/DeltaV)(E) + 112 (r = 0.80). For subjects with diastasis (n = 113), k(A) = 1,640. (DeltaP/DeltaV)(PD) - 8.40 (r = 0.89). As predicted, k(A) showed excellent correlation with (DeltaP/DeltaV)(PD); k(E) correlated highly with (DeltaP/DeltaV)(avg). In vivo validation of average, early, and passive chamber stiffness facilitates quantitative, noninvasive diastolic function assessment from transmitral flow.     

Load-independent index of diastolic filling: model-based derivation with in vivo validation in control and diastolic dysfunction subjects.

Maximum elastance is an experimentally validated, load-independent systolic function index stemming from the time-varying elastance paradigm that decoupled extrinsic load from (intrinsic) contractility. Although Doppler echocardiography is the preferred method of diastolic function (DF) assessment, all echo-derived indexes are load dependent, and no invasive or noninvasive load-independent index of filling (LIIF) exists. In this study, we derived and experimentally validated a LIIF. We used a kinematic filling paradigm (the parameterized diastolic filling formalism) to predict and derive the (dimensionless) dynamic diastolic efficiency M, defined by the slope of the peak driving force [maximum driving force (kx(o)) proportional, variant peak atrioventricular (AV) gradient] to maximum viscoelastic resistive force [peak resistive force (cE(peak))] relation. To validate load independence, we analyzed E-waves recorded while load was varied via tilt table (head up, horizontal, and head down) in 16 healthy volunteers. For the group, linear regression of E-wave derived kx(o) vs. cE(peak) yielded kx(o) = M (cE(peak)) + B, r2 = 0.98; where M = 1.27 +/- 0.09 and B = 5.69 +/- 1.70. Effects of diastolic dysfunction (DD) on M were assessed by analysis of preexisting simultaneous cath-echo data in six DD vs. five control subjects. Average M for the DD group (M = 0.98 +/- 0.07) was significantly lower than controls (M = 1.17 +/- 0.05, P < 0.001). We conclude that M is a LIIF because it uncouples intrinsic DF (i.e., the pressure-flow relation) from extrinsic load (left ventricular end-diastolic pressure). Larger M values imply better DF in that increasing AV pressure gradient results in relatively smaller increases in peak resistive losses (cE(peak)). Conversely, lower M implies that increasing AV gradient leads to larger increases in resistive losses. Further prospective validation characterizing M in well-defined pathological states is warranted.     

Elucidation of spatially distinct compensatory mechanisms in diastole: radial compensation for impaired longitudinal filling in left ventricular hypertrophy.

Cardiac output maintenance is so fundamental that, when regional systolic function is impaired, as during ischemia, nonischemic segments compensate by becoming hypercontractile. By analogy, diastolic compensatory mechanisms that maintain filling volume must exist but remain to be fully elucidated. Viewing filling in spatially distinct (longitudinal, radial) mechanistic terms facilitates elucidation of diastolic compensatory mechanisms. Because impairment of longitudinal (long axis) diastolic function (DF) in left ventricular hypertrophy (LVH) is established, we hypothesized that to maintain filling volume, radial (short-axis) filling function would compensate. In 20 normal left ventricular ejection fraction (LVEF) subjects (10 with LVH, 10 without LVH), we analyzed longitudinal function via Doppler tissue imaging of mitral annular motion and radial function as change in short-axis endocardial dimension via M-mode. The spatial (long axis, short axis) endocardial LV dimensions and their changes allowed assignment of E-wave filling volume into (cylindrical geometry-based) longitudinal and radial components. Despite indistinguishable (P = 0.70) E-wave velocity-time integrals (E-wave filling volume surrogate), systolic stroke volumes, and end-diastolic volumes in the LVH and control groups, longitudinal volume in absolute terms and the percent of E-wave volume accommodated longitudinally were reduced in the LVH group (P < 0.05 and P < 0.01, respectively), whereas the percent of E-wave volume accommodated radially was enhanced (P < 0.01). We conclude that, in normal LVEF (decreased longitudinal volume accommodation) LVH subjects vs. controls, spatially distinct compensatory mechanisms in diastole manifest as increased radial volume accommodation per unit of E-wave filling volume. Assessment of spatially distinct diastolic compensatory mechanisms in other pathophysiological subsets is warranted.     

Anomalous origin of the left coronary artery: the effects of aortocoronary vein bypass on left ventricular function

The diagnosis, angiographic evaluation and surgical treatment by aortocoronary vein bypass are described in a 3½-year-old girl with anomalous origin of the left coronary artery from the pulmonary artery. The anomaly had resulted in cardiac dilatation, diminished left ventricular contractility, an aneurysm of the left ventricular free wall and mitral regurgitation.At the postoperative cardiac catheterization the graft was demonstrated to be patent, but a significant proportion of the flow to the left coronary artery was derived from anastomotic connections with the right coronary artery. The most striking evidence of improvement was obtained from the left ventricular volume studies which showed that the end systoiic volume had decreased from 85 to 49 ml./m.² with an increase in ejection fraction from 0.39 to 0.62, suggesting enhanced left ventricular contractility after surgery.The patient continues to do well and is free from symptoms.     

Association of the left common ostium with clinical outcome after pulmonary vein isolation in atrial fibrillation

IntroductionElectrical pulmonary vein isolation (PVI) is used for the invasive treatment of atrial fibrillation (AF). However, despite the procedure’s technical evolution, the rate of AF recurrence due to electrical reconnection of the PVs is high. The aims of this study was to assess the influence of left common pulmonary venous ostium (LCO) on clinical outcomes following PVI.MethodsRetrospective cohort of 254 patients who underwent the first procedure of PVI from the years 2013–2018 was assessed. Patients with persistent AF of long duration and extra-pulmonary focus associated with triggers for arrhythmia were excluded. Patients were stratified into two groups according to the presence of a LCO and received follow up for atrial tachyarrhythmia-free survival. The mean follow-up period was 28 ± 1.73 months.ResultsThe majority were men (68.5%), with a mean age of 54 ± 12 years. With respect to the atrial anatomy, LCO occurred in 23.6% of cases after pulmonary venous angiotomography. The arrhythmia-free survival rate was 79.5% in the follow-up period. The Cox regression model was utilized and the adjusted hazard ratio for LCO was 0.36 (95% CI 0.15–0.87; p = 0.02) in terms of age, body mass index, left atrium diameter, bi-directional blocking of the cavotricuspid isthmus, persistent AF, left ventricular ejection fraction adjusted model.ConclusionAnatomic abnormality with the presence of the LCO is present in a quarter of patients undergoing AF ablation, which is associated with a lower rate of arrhythmia recurrence in our population.     

Measurement of strain in the left ventricle during diastole with cine-MRI and deformable image registration

The assessment of regional heart wall motion (local strain) can localize ischemic myocardial disease, evaluate myocardial viability, and identify impaired cardiac function due to hypertrophic or dilated cardiomyopathies. The objectives of this research were to develop and validate a technique known as hyperelastic warping for the measurement of local strains in the left ventricle from clinical cine-magnetic resonance imaging (MRI) image datasets. The technique uses differences in image intensities between template (reference) and target (loaded) image datasets to generate a body force that deforms a finite element (FE) representation of the template so that it registers with the target image. To validate the technique, MRI image datasets representing two deformation states of a left ventricle were created such that the deformation map between the states represented in the images was known. A beginning diastolic cine-MRI image dataset from a normal human subject was defined as the template. A second image dataset (target) was created by mapping the template image using the deformation results obtained from a forward FE model of diastolic filling. Fiber stretch and strain predictions from hyperelastic warping showed good agreement with those of the forward solution (R2=0.67 stretch, R2=0.76 circumferential strain, R2=0.75 radial strain, and R2=0.70 in-plane shear). The technique had low sensitivity to changes in material parameters (deltaR2= -0.023 fiber stretch, deltaR2=-0.020 circumferential strain, deltaR2=-0.005 radial strain, and deltaR2=0.0125 shear strain with little or no change in rms error), with the exception of changes in bulk modulus of the material. The use of an isotropic hyperelastic constitutive model in the warping analyses degraded the predictions of fiber stretch. Results were unaffected by simulated noise down to a signal-to-noise ratio (SNR) of 4.0 (deltaR2= -0.032 fiber stretch, deltaR2=-0.023 circumferential strain, deltaR2=-0.04 radial strain, and deltaAR2=0.0211 shear strain with little or no increase in rms error). This study demonstrates that warping in conjunction with cine-MRI imaging can be used to determine local ventricular strains during diastole.     

山羊房颤模型中左心房与肺静脉外膜碎裂电位的动态比较

目的:比较在持续性房颤发生、发展过程中,房颤模型山羊左心房与肺静脉外膜碎裂电位(CFAEs)的变 化,以期探讨肺静脉外膜碎裂电位(CFAEs)在持续性房颤中的作用.方法:选取10只雌性山羊,使用左心房快速刺激,发送输出电压为6 V、周长为20 ms的脉冲1 s,间隔2 s后重复发放,以此方法建立持续性房颤模型(房颤持续...     

Atrioventricular plane displacement is the major contributor to left ventricular pumping in healthy adults, athletes, and patients with dilated cardiomyopathy

Previous studies using echocardiography in healthy subjects have reported conflicting data regarding the percentage of the stroke volume (SV) of the left ventricle (LV) resulting from longitudinal and radial function, respectively. Therefore, the aim was to quantify the percentage of SV explained by longitudinal atrioventricular plane displacement (AVPD) in controls, athletes, and patients with decreased LV function due to dilated cardiomyopathy (DCM). Twelve healthy subjects, 12 elite triathletes, and 12 patients with DCM and ejection fraction below 30% were examined by cine magnetic resonance imaging. AVPD and SV were measured in long- and short-axis images, respectively. The percentage of the SV explained by longitudinal function (SV(AVPD%)) was calculated as the mean epicardial area of the largest short-axis slices in end diastole multiplied by the AVPD and divided by the SV. SV was higher in athletes [140 +/- 4 ml (mean +/- SE), P = 0.009] and lower in patients (72 +/- 7 ml, P < 0.001) when compared with controls (116 +/- 6 ml). AVPD was similar in athletes (17 +/- 1 mm, P = 0.45) and lower in patients (7 +/- 1 mm, P < 0.001) when compared with controls (16 +/- 0 mm). SV(AVPD%) was similar both in athletes (57 +/- 2%, P = 0.51) and in patients (67 +/- 4%, P = 0.24) when compared with controls (60 +/- 2%). In conclusion, longitudinal AVPD is the primary contributor to LV pumping and accounts for approximately 60% of the SV. Although AVPD is less than half in patients with DCM when compared with controls and athletes, the contribution of AVPD to LV function is maintained, which can be explained by the larger short-axis area in DCM.     

Sub-clinical left ventricular diastolic dysfunction in early stage of chronic obstructive pulmonary disease

Sub-clinical cardiac dysfunction may be significantly associated with chronic obstructive pulmonary disease (COPD) with a different degree of severity. In a cross-sectional design we aimed to evaluate the frequency of left ventricular diastolic dysfunction (LVdd) and its correlation with lung function, pulmonary arterial pressure and systemic inflammation in a selected population of COPD at an early stage of their disease. Fifty-five COPD patients with no clinical signs of cardiovascular dysfunction were recruited and compared to 40 matched healthy controls. All the subjects underwent pulmonary function testing, doppler echocardiography, and interleukin-6 blood sampling. Presence of LVdd was defined according to the significant change in both the ratio between early and late diastolic transmitral flow velocity (E/A ratio), isovolumetric relaxation time (IVRT), and deceleration time (DT). The frequency of LVdd was higher in the COPD group (70.9 percent) compared to controls (27.5 percent). In these patients decreased E/A ratio, and prolonged IVRT and DT clearly pointed to left ventricular filling impairment, a condition we found to be especially severe in those patients suffering from lung static hyperinflation as expressed by inspiratory-to-total lung capacity ratio (IC/TLC) <0.25. Circulating levels of interleukin-6 were also higher among COPD patients compared to controls. The results of the present study suggest that subclinical left ventricular filling impairment is frequently found in COPD patients at the earlier stage of the disease even in the absence of any other cardiovascular dysfunction. Doppler echocardiography may help the early identification of LVdd in COPD patients.     

Effects of changes in left ventricular loading and pleural pressure on mitral flow

The cause of the fall in left ventricular (LV) stroke volume (SV) during a fall in pleural pressure (Pp1) has been in dispute for over a century. We have defined the changes in the temporal relationship between LV inflow (Qm) and outflow (Qa) in a canine preparation to test the mutually exclusive hypotheses that the fall in LVSV is caused only by changes during diastole (e.g., ventricular interdependence) or only by changes during systole (e.g., afterload). The ability of the experimental preparation to measure the results of acute changes in right heart volume or output and acute changes in LV afterload was validated in open-chest studies with and without pericardial constraint. In closed-chest studies, with a fall in Pp1 during a Mueller maneuver Qm reached both its inspiratory minimum and expiratory maximum before Qa in 80% of the Mueller maneuvers, invalidating both hypotheses, which each required that one flow lead the other in 100% of the Mueller maneuvers. Review of individual records suggested that if the rapid changes in Pp1 occurred during systole, Qa could vary in a manner independent of the preceding Qm. These studies suggest that both diastolic and systolic events may contribute to the fall in SV, while causing opposite changes in LV volumes.     

Quantification of coronary microvascular resistance using angiographic images for volumetric blood flow measurement: in vivo validation

Structural coronary microcirculation abnormalities are important prognostic determinants in clinical settings. However, an assessment of microvascular resistance (MR) requires a velocity wire. A first-pass distribution analysis technique to measure volumetric blood flow has been previously validated. The aim of this study was the in vivo validation of the MR measurement technique using first-pass distribution analysis. Twelve anesthetized swine were instrumented with a transit-time ultrasound flow probe on the proximal segment of the left anterior descending coronary artery (LAD). Microspheres were injected into the LAD to create a model of microvascular dysfunction. Adenosine (400 μg·kg(-1)·min(-1)) was used to produce maximum hyperemia. A region of interest in the LAD arterial bed was drawn to generate time-density curves using angiographic images. Volumetric blood flow measurements (Q(a)) were made using a time-density curve and the assumption that blood was momentarily replaced with contrast agent during the injection. Blood flow from the flow probe (Q(p)), coronary pressure (P(a)), and right atrium pressure (P(v)) were continuously recorded. Flow probe-based normalized MR (NMR(p)) and angiography-based normalized MR (NMR(a)) were calculated using Q(p) and Q(a), respectively. In 258 measurements, Q(a) showed a strong correlation with the gold standard Q(p) (Q(a) = 0.90 Q(p) + 6.6 ml/min, r(2) = 0.91, P < 0.0001). NMR(a) correlated linearly with NMR(p) (NMR(a) = 0.90 NMR(p) + 0.02 mmHg·ml(-1)·min(-1), r(2) = 0.91, P < 0.0001). Additionally, the Bland-Altman analysis showed a close agreement between NMR(a) and NMR(p). In conclusion, a technique based on angiographic image data for quantifying NMR was validated using a swine model. This study provides a method to measure NMR without using a velocity wire, which can potentially be used to evaluate microvascular conditions during coronary arteriography.     

Electrical connections between left superior pulmonary vein, left atrium, and ligament of Marshall: implications for mechanisms of atrial fibrillation

The importance of the ligament of Marshall (LOM) to rapid activations within the left superior pulmonary vein (LSPV) during atrial fibrillation (AF) remains poorly understood. We aimed to characterize the importance of electrical coupling between the LSPV with the left atrium (LA) and the LOM in the generation of high-frequency activations within this PV. We performed high-density mapping of the LSPV-LA-LOM junction in eight dogs, using 1,344 electrodes with a 1-mm resolution before and after posterior ostial ablation to diminish PV-LA electrical connections. A LOM potential was recordable up to 6.5 mm (SD 2.2) into the LSPV in all dogs during sinus rhythm (SR) and LA pacing. Functional LOM-LSPV electrical connections bypassing the PV-LA junction were present in five of eight dogs. Direct LOM-LSPV connections contributed to 46.5% (SD 16.0) of LSPV activations during AF, resulting in a greater propensity to develop focal activations (P < 0.05) and a higher activation rate during AF of LSPVs with direct LOM connections compared with those without (P < 0.03). Posterior LSPV ostial ablation without damaging the anterior wall or LOM slowed residual LA-PV conduction (P < 0.001). This diminished PV-LA coupling prevented the reinduction of LSPV focal activations in all dogs. However, persistent LOM focal activations in two dogs continued to activate the LSPV rapidly [cycle length 151.8 ms (SD 4.8)] via direct LOM-LSPV connections. LOM-LSPV connection forms an accessory pathway that contributes to the electrical coupling between LSPV and LA during SR and AF. This pathway may contribute to rapid activations within the LSPV during AF.     

Right and left ventricular function after chronic pulmonary artery banding in rats assessed with biventricular pressure-volume loops

In many patients with congenital heart disease, the right ventricle (RV) is subjected to abnormal loading conditions. To better understand the state of compensated RV hypertrophy, which could eventually progress to decompensation, we studied the effects of RV pressure overload in rats. In the present study, we report the biventricular adaptation to 6 wk of pulmonary artery banding (PAB). PAB resulted in an RV pressure overload to approximately 60% of systemic level and a twofold increase in RV mass (P < 0.01). Systemic hemodynamic parameters were not altered, and overt signs of heart failure were absent. Load-independent measures of ventricular function (end-systolic pressure-volume relation, preload recruitable stroke work relation, maximum first time derivative of pressure divided by end-diastolic volume), assessed by means of pressure-volume (PV) loops, demonstrated a two- to threefold increase in RV contractility under baseline conditions in PAB rats. RV contractility increased in response to dobutamine stimulation (2.5 microg.kg(-1).min(-1)) both in PAB and sham-operated rats in a similar fashion, indicating preserved RV contractile reserve in PAB rats. Left ventricular (LV) contractility at baseline was unaffected in PAB rats, although LV volume in PAB rats was slightly decreased. LV contractility increased in response to dobutamine (2.5 microg.kg(-1).min(-1)), both in PAB and sham rats, whereas the response to a higher dose of dobutamine (5 microg.kg(-1).min(-1)) was blunted in PAB rats. RV pressure overload (6 wk) in rats resulted in a state of compensated RV hypertrophy with preserved RV contractile reserve, whereas LV contractile state at baseline was not affected. Furthermore, this study demonstrates the feasibility of performing biventricular PV-loop measurements in rats.     

Diastolic suction in heart failure: Impact of left ventricular geometry,untwist, and flow mechanics

Aims

Vector flow mapping (VFM) can be used to assess intraventricular hemodynamics quantitatively. This study assessed the magnitude of the suction flow kinetic energy with VFM and investigated the relation between left ventricular (LV) function and geometry in patients with an estimated elevated LV filling pressure.

Materials and methods

We studied 24 subjects with an elevated LV filling pressure (EFP group) and 36 normal subjects (normal group). Suction was defined as flow directed toward the apex during the period from soon after systolic ejection to before mitral inflow. The flow kinetic energy index was quantified as the sum of the product of the blood mass and velocity vector and its magnitude to the peak value was measured.

Key findings

Suction flow was observed in 12 (50%) EFP-group patients and 36 (100%) normal-group subjects. The magnitude of the suction kinetic energy index was significantly smaller in EFP versus normal group (2.7 ± 3.8 vs. 5.7 ± 4.4 g/s/cm², P < 0.01). The EFP-group patients with suction had a smaller LV end-systolic volume (ESV) (P < 0.01), greater ellipsoidal geometry (P < 0.05) and untwisting rate (P < 0.01) than the EFP-group patients without suction. A regression analysis indicated a significant linear relation between the suction kinetic energy index and LVEF (r = 0.43, P = 0.04), ESV (r = − 0.40, P = 0.05), eccentricity index (r = 0.44, P = 0.04), and untwisting rate (r = 0.51, P = 0.04).

Significance

The magnitude of the suction flow kinetic energy index derived from VFM may allow the quantitative assessment of the suction flow, which correlates with LV systolic function, geometry, and untwisting mechanics.     

Fiber stress profiles in the left ventricle of the heart during diastole: Effects of distension and hypertrophy

Pressure-volume and volume-dimensions relationships, obtained from excised dog left ventricles were used for calculating the stresses acting along the longitudinal axis of the individual myocardial fibers. The calculations were based on a set of empirical and theoretical equations. The pressure-volume relationship as well as the volume-dimensions relationships for the excised left ventricle were expressed in the form of empirical equations; the fiber orientation was written as a function of the fiber location within the left ventricular wall; finally, the fiber stress was determined by means of theoretically derived formulas. Simultaneous solutions for the fibers of a meridian cut through the left ventricular myocardial shell were obtained by means of a digital computer and presented in the form of diagrams. The results showed that at low degrees of distension of the left ventricle there are two zones of higher stresses at the equatorial area, one near the epicardium and one near the endocardium. As the distension proceeds under the effect of progressively increasing intraventricular pressure, these two zones become less well defined, whereas a new zone of higher stresses appears near the apex. At high degrees of distension, the ventricle assumes a more spherical shape and the equatorial zones of higher stresses are replaced by zones of lower stresses. Increase in the myocardial mass results in appearance of the equatorial lower stress zones at lower degrees of distension.