Optimization of cardiac fiber orientation for homogeneous fiber strain at beginning of ejection

Multiscale fiber remodeling in the infarcted left ventricle using a stress-based reorientation law

The organization of myofibers and extra cellular matrix within the myocardium plays a significant role in defining cardiac function. When pathological events occur, such as myocardial infarction (MI), this organization can become disrupted, leading to degraded pumping performance. The current study proposes a multiscale finite element (FE) framework to determine realistic fiber distributions in the left ventricle (LV). This is achieved by implementing a stress-based fiber reorientation law, which seeks to align the fibers with local traction vectors, such that contractile force and load bearing capabilities are maximized. By utilizing the total stress (passive and active), both myofibers and collagen fibers are reoriented. Simulations are conducted to predict the baseline fiber configuration in a normal LV as well as the adverse fiber reorientation that occurs due to different size MIs. The baseline model successfully captures the transmural variation of helical fiber angles within the LV wall, as well as the transverse fiber angle variation from base to apex. In the models of MI, the patterns of fiber reorientation in the infarct, border zone, and remote regions closely align with previous experimental findings, with a significant increase in fibers oriented in a left-handed helical configuration and increased dispersion in the infarct region. Furthermore, the severity of fiber reorientation and impairment of pumping performance both showed a correlation with the size of the infarct. The proposed multiscale modeling framework allows for the effective prediction of adverse remodeling and offers the potential for assessing the effectiveness of therapeutic interventions in the future. STATEMENT OF SIGNIFICANCE: The organization of muscle and collagen fibers within the heart plays a significant role in defining cardiac function. This organization can become disrupted after a heart attack, leading to degraded pumping performance. In the current study, we implemented a stress-based fiber reorientation law into a computer model of the heart, which seeks to realign the fibers such that contractile force and load bearing capabilities are maximized. The primary goal was to evaluate the effects of different sized heart attacks. We observed substantial fiber remodeling in the heart, which matched experimental observations. The proposed computational framework allows for the effective prediction of adverse remodeling and offers the potential for assessing the effectiveness of therapeutic interventions in the future.

Multiscale simulations of left ventricular growth and remodeling

Cardiomyocytes can adapt their size, shape, and orientation in response to altered biomechanical or biochemical stimuli. The process by which the heart undergoes structural changes-affecting both geometry and material properties-in response to altered ventricular loading, altered hormonal levels, or mutant sarcomeric proteins is broadly known as cardiac growth and remodeling (G&R). Although it is likely that cardiac G&R initially occurs as an adaptive response of the heart to the underlying stimuli, prolonged pathological changes can lead to increased risk of atrial fibrillation, heart failure, and sudden death. During the past few decades, computational models have been extensively used to investigate the mechanisms of cardiac G&R, as a complement to experimental measurements. These models have provided an opportunity to quantitatively study the relationships between the underlying stimuli (primarily mechanical) and the adverse outcomes of cardiac G&R, i.e., alterations in ventricular size and function. State-of-the-art computational models have shown promise in predicting the progression of cardiac G&R. However, there are still limitations that need to be addressed in future works to advance the field. In this review, we first outline the current state of computational models of cardiac growth and myofiber remodeling. Then, we discuss the potential limitations of current models of cardiac G&R that need to be addressed before they can be utilized in clinical care. Finally, we briefly discuss the next feasible steps and future directions that could advance the field of cardiac G&R.

Anisotropic Cardiac Conduction

Anisotropy is the property of directional dependence. In cardiac tissue, conduction velocity is anisotropic and its orientation is determined by myocyte direction. Cell shape and size, excitability, myocardial fibrosis, gap junction distribution and function are all considered to contribute to anisotropic conduction. In disease states, anisotropic conduction may be enhanced, and is implicated, in the genesis of pathological arrhythmias. The principal mechanism responsible for enhanced anisotropy in disease remains uncertain. Possible contributors include changes in cellular excitability, changes in gap junction distribution or function and cellular uncoupling through interstitial fibrosis. It has recently been demonstrated that myocyte orientation may be identified using diffusion tensor magnetic resonance imaging in explanted hearts, and multisite pacing protocols have been proposed to estimate myocyte orientation and anisotropic conduction in vivo. These tools have the potential to contribute to the understanding of the role of myocyte disarray and anisotropic conduction in arrhythmic states.

Using Systolic Local Mechanical Load to Predict Fiber Orientation in Ventricles

A simple rule adopted for myofiber reorientation in the ventricles is pursued by taking the microscopic branching network of myocytes into account. The macroscopic active tension generated on the microscopic branching structure is modeled by a multidirectional active stress tensor, which is defined as a function of the strains in the branching directions. In our reorientation algorithm, the principal direction of the branching network is updated so that it turns in the direction of greater active tension in the isovolumetric systole. Updates are performed step-by-step after the mechanical equilibrium has been attained with the current fiber structure. Starting from a nearly flat distribution of the principal fiber orientation along the circumferential direction, the reoriented fiber helix angles range from 70 to 40° at epicardium and from 60 to 80° at endocardium, in agreement with experimental observations. The helical ventricular myocardial band of Torrent-Guasp’s model and the apical spiral structure of Rushmer’s model are also reconstructed by our algorithm. Applying our algorithm to the infarcted ventricle model, the fiber structure near the infarcted site is remodeled so that the helix angle becomes steeper with respect to the circumferential direction near the epicardial surface. Based on our numerical analysis, we draw the following conclusions. (i) The multidirectional active tension based on the microscopic branching network is potentially used to seek tighter connection with neighboring aggregates. (ii) The thickening and thinning transitions in response to active tension in each myocyte allow the macroscopic principal fiber orientation of the microscopic branching network to move toward the direction of greater active tension. (iii) The force–velocity relationship is the key factor in transferring the fiber shortening strain to the magnitude of active tensions used in the myofiber reorientation. (iv) The algorithm naturally leads to homogeneity in the macroscopic active tension and the fiber shortening strain, and results in near-optimal pumping performance. (v) However, the reorientation mechanism may degrade the pumping performance if there is severely inhomogeneous contractility resulting from infarction. Our goal is to provide a tool to predict the fiber architecture of various heart disease patients for numerical simulations of their treatment plans.

Transmural gradients of myocardial structure and mechanics: Implications for fiber stress and strain in pressure overload

Although a truly complete understanding of whole heart activation, contraction, and deformation is well beyond our current reach, a significant amount of effort has been devoted to discovering and understanding the mechanisms by which myocardial structure determines cardiac function to better treat patients with cardiac disease. Several experimental studies have shown that transmural fiber strain is relatively uniform in both diastole and systole, in contrast to predictions from traditional mechanical theory. Similarly, mathematical models have largely predicted uniform fiber stress across the wall. The development of this uniform pattern of fiber stress and strain during filling and ejection is due to heterogeneous transmural distributions of several myocardial structures. This review summarizes these transmural gradients, their contributions to fiber mechanics, and the potential functional effects of their remodeling during pressure overload hypertrophy.

Cardiac motion estimation by optimizing transmural homogeneity of the myofiber strain and its validation with multimodal sequences

Quantitative motion analysis from cardiac imaging is important to study the function of heart. Most of existing image-based motion estimation methods model the myocardium as an isotropically elastic continuum. We propose a novel anisotropic regularization method which enforces the transmural homogeneity of the strain along myofiber. The myofiber orientation in the end-diastolic frame is obtained by registering it with a diffusion tensor atlas. Our method is formulated in a diffeomorphic registration framework, and tested on multimodal cardiac image sequences of two subjects using 3D echocardiography and cine and tagged MRI. Results show that the estimated transformations in our method are more smooth and more accurate than those in isotropic regularization.

The upstream boundary condition influences the leaflet opening dynamics in the numerical FSI simulation of an aortic BMHV

In this paper, the influence of the upstream boundary condition in the numerical simulation of an aortic bileaflet mechanical heart valve (BMHV) is studied. Three three-dimensional cases with different upstream boundary conditions are compared. The first case consists of a rigid straight tube with a velocity profile at its inlet. In the second case, the upstream geometry is a contracting left ventricle (LV), positioned symmetrically with respect to the valve. In the last case, the LV is positioned asymmetrical with respect to the valve. The cases are used to simulate the same three-dimensional BMHV. The change in time of the LV volume is calculated such that the flow rate through the valve is identical in each case. The opening dynamics of the BMHV are modelled using fluid-structure interaction. The simulations show that differences occur in the leaflet movement of the three cases. In particular, with the asymmetric LV, one of the leaflets impacts the blocking mechanism at its open position with a 34% higher velocity than when using the velocity profile, and with an 88% higher velocity than in the symmetric LV case. Therefore, when simulating such an impact, the upstream boundary condition needs to be chosen carefully.

Mapping molecular agents distributions in whole mice hearts using born-normalized optical projection tomography

To date there is a lack of tools to map the spatio-temporal dynamics of diverse cells in experimental heart models. Conventional histology is labor intensive with limited coverage, whereas many imaging techniques do not have sufficiently high enough spatial resolution to map cell distributions. We have designed and built a high resolution, dual channel Born-normalized near-infrared fluorescence optical projection tomography system to quantitatively and spatially resolve molecular agents distribution within whole murine heart. We validated the use of the system in a mouse model of monocytes/macrophages recruitment during myocardial infarction. While acquired, data were processed and reconstructed in real time. Tomographic analysis and visualization of the key inflammatory components were obtained via a mathematical formalism based on left ventricular modeling. We observed extensive monocyte recruitment within and around the infarcted areas and discovered that monocytes were also extensively recruited into non-ischemic myocardium, beyond that of injured tissue, such as the septum.

Modeling of cardiac growth and remodeling of myofiber orientation

The heart has the ability to respond to long-term changes in its environment through changes in mass (growth), shape (morphogenesis) and tissue properties (remodeling). For improved quantitative understanding of cardiac growth and remodeling (G&R) experimental studies need to be complemented by mathematical models. This paper reviews models for cardiac growth and remodeling of myofiber orientation, as induced by mechanical stimuli. A distinction is made between optimization models, that focus on the end stage of G&R, and adaptation models, that aim to more closely describe the mechanistic relation between stimulus and effect. While many models demonstrate qualitatively promising results, a lot of questions remain, e.g. with respect to the choice of the stimulus for G&R or the long-term stability of the outcome of the model. A continued effort combining information on mechanotransduction at the cellular level, experimental observations on G&R at organ level, and testing of hypotheses on stimulus-effect relations in mathematical models is needed to answer these questions on cardiac G&R. Ultimately, models of cardiac G&R seem indispensable for patient-specific modeling, both to reconstruct the actual state of the heart and to assess the long-term effect of potential interventions.

Left-ventricular shape determines intramyocardial mechanical heterogeneity

Left-ventricular remodeling is considered to be an important mechanism of disease progression leading to mechanical dysfunction of the heart. However, the interaction between the physiological changes in the remodeling process and the associated mechanical dysfunction is still poorly understood. Clinically, it has been observed that the left ventricle often undergoes large shape changes, but the importance of left-ventricular shape as a contributing factor to alterations in mechanical function has not been clearly determined. Therefore, the interaction between left-ventricular shape and systolic mechanical function was examined in a computational finite-element study. Hereto, finite-element models were constructed with varying shapes, ranging from an elongated ellipsoid to a sphere. A realistic transmural gradient in fiber orientation was considered. The passive myocardium was described by an incompressible hyperelastic material law with transverse isotropic symmetry. Activation was governed by the eikonal-diffusion equation. Contraction was incorporated using a Hill model. For each shape, simulations were performed in which passive filling was followed by isovolumic contraction and ejection. It was found that the intramyocardial distributions of fiber stress, strain, and stroke work density were shape dependent. Ejection performance was reduced with increasing sphericity, which was regionally related to a reduction in the active fiber stress development, fiber shortening, and stroke work in the midwall and subepicardial region at the midheight level in the left-ventricular wall. Based on these results, we conclude that a significant interaction exists between left-ventricular shape and regional myofiber mechanics, but the importance for left-ventricular remodeling requires further investigation.

The influence of left-ventricular shape on end-diastolic fiber stress and strain

Passive filling is a major determinant for the pump performance of the left ventricle and is determined by the filling pressure and the ventricular compliance. We quantified the influence of left-ventricular shape on the overall compliance and the distribution of passive fiber stress and strain during the filling period in normal myocardium. Hereto, fiber stress and strain were calculated in a finite element analysis during the inflation of left ventricles of different shape, ranging from an elongated ellipsoid to a sphere, but keeping the initial cavity and wall volume constant. The passive myocardium was described by an incompressible hyperelastic material law with transverse isotropic symmetry along the muscle fiber directions. A realistic transmural gradient in fiber orientation was assumed. While compliance was not altered, the transmural distribution of both passive fiber stress and strain was highly dependent on ventricular shape, where more spherical ventricles exhibited a higher subendocardial gradient in both quantities.

Influence of left-ventricular shape on passive filling properties and end-diastolic fiber stress and strain

Passive filling is a major determinant for the pump performance of the left ventricle and is determined by the filling pressure and the ventricular compliance. In the quantification of the passive mechanical behaviour of the left ventricle and its compliance, focus has been mainly on fiber orientation and constitutive parameters. Although it has been shown that the left-ventricular shape plays an important role in cardiac (patho-)physiology, the dependency on left-ventricular shape has never been studied in detail. Therefore, we have quantified the influence of left-ventricular shape on the overall compliance and the intramyocardial distribution of passive fiber stress and strain during the passive filling period. Hereto, fiber stress and strain were calculated in a finite element analysis of passive inflation of left ventricles with different shapes, ranging from an elongated ellipsoid to a sphere, but keeping the initial cavity volume constant. For each shape, the wall volume was varied to obtain ventricles with different wall thickness. The passive myocardium was described by an incompressible hyperelastic material law with transverse isotropic symmetry along the muscle fiber directions. A realistic transmural distribution in fiber orientation was assumed. We found that compliance was not altered substantially, but the transmural distribution of both passive fiber stress and strain was highly dependent on regional wall curvature and thickness. A low curvature wall was characterized by a maximum in the transmural fiber stress and strain in the mid-wall region, while a steep subendocardial transmural gradient was present in a high curvature wall. The transmural fiber stress and strain gradients in a low and high curvature wall were, respectively, flattened and steepened by an increase in wall thickness.

Determinants of left ventricular shear strain

Mathematical models of cardiac mechanics can potentially be used to relate abnormal cardiac deformation, as measured noninvasively by ultrasound strain rate imaging or magnetic resonance tagging (MRT), to the underlying pathology. However, with current models, the correct prediction of wall shear strain has proven to be difficult, even for the normal healthy heart. Discrepancies between simulated and measured strains have been attributed to 1) inadequate modeling of passive tissue behavior, 2) neglecting active stress development perpendicular to the myofiber direction, or 3) neglecting crossover of myofibers in between subendocardial and subepicardial layers. In this study, we used a finite-element model of left ventricular (LV) mechanics to investigate the sensitivity of midwall circumferential-radial shear strain (E(cr)) to settings of parameters determining passive shear stiffness, cross-fiber active stress development, and transmural crossover of myofibers. Simulated time courses of midwall LV E(cr) were compared with time courses obtained in three healthy volunteers using MRT. E(cr) as measured in the volunteers during the cardiac cycle was characterized by an amplitude of approximately 0.1. In the simulations, a realistic amplitude of the E(cr) signal could be obtained by tuning either of the three model components mentioned above. However, a realistic time course of E(cr), with virtually no change of E(cr) during isovolumic contraction and a correct base-to-apex gradient of E(cr) during ejection, could only be obtained by including transmural crossover of myofibers. Thus, accounting for this crossover seems to be essential for a realistic model of LV wall mechanics.

Normal and pathological NCAT image and phantom data based on physiologically realistic left ventricle finite-element models

The four-dimensional (4-D) NURBS-based cardiac-torso (NCAT) phantom, which provides a realistic model of the normal human anatomy and cardiac and respiratory motions, is used in medical imaging research to evaluate and improve imaging devices and techniques, especially dynamic cardiac applications. One limitation of the phantom is that it lacks the ability to accurately simulate altered functions of the heart that result from cardiac pathologies such as coronary artery disease (CAD). The goal of this work was to enhance the 4-D NCAT phantom by incorporating a physiologically based, finite-element (FE) mechanical model of the left ventricle (LV) to simulate both normal and abnormal cardiac motions. The geometry of the FE mechanical model was based on gated high-resolution X-ray multislice computed tomography (MSCT) data of a healthy male subject. The myocardial wall was represented as a transversely isotropic hyperelastic material, with the fiber angle varying from -90 degrees at the epicardial surface, through 0 degrees at the midwall, to 90 degrees at the endocardial surface. A time-varying elastance model was used to simulate fiber contraction, and physiological intraventricular systolic pressure-time curves were applied to simulate the cardiac motion over the entire cardiac cycle. To demonstrate the ability of the FE mechanical model to accurately simulate the normal cardiac motion as well as the abnormal motions indicative of CAD, a normal case and two pathologic cases were simulated and analyzed. In the first pathologic model, a subendocardial anterior ischemic region was defined. A second model was created with a transmural ischemic region defined in the same location. The FE-based deformations were incorporated into the 4-D NCAT cardiac model through the control points that define the cardiac structures in the phantom which were set to move according to the predictions of the mechanical model. A simulation study was performed using the FE-NCAT combination to investigate how the differences in contractile function between the subendocardial and transmural infarcts manifest themselves in myocardial Single photon emission computed tomography (SPECT) images. The normal FE model produced strain distributions that were consistent with those reported in the literature and a motion consistent with that defined in the normal 4-D NCAT beating heart model based on tagged magnetic resonance imaging (MRI) data. The addition of a subendocardial ischemic region changed the average transmural circumferential strain from a contractile value of -0.09 to a tensile value of 0.02. The addition of a transmural ischemic region changed average circumferential strain to a value of 0.13, which is consistent with data reported in the literature. Model results demonstrated differences in contractile function between subendocardial and transmural infarcts and how these differences in function are documented in simulated myocardial SPECT images produced using the 4-D NCAT phantom. Compared with the original NCAT beating heart model, the FE mechanical model produced a more accurate simulation for the cardiac motion abnormalities. Such a model, when incorporated into the 4-D NCAT phantom, has great potential for use in cardiac imaging research. With its enhanced physiologically based cardiac model, the 4-D NCAT phantom can be used to simulate realistic, predictive imaging data of a patient population with varying whole-body anatomy and with varying healthy and diseased states of the heart that will provide a known truth from which to evaluate and improve existing and emerging 4-D imaging techniques used in the diagnosis of cardiac disease.

A finite element model of the human left ventricular systole

Local wall stress is the pivotal determinant of the heart muscle's systolic function. Under in vivo conditions, however, such stresses cannot be measured systematically and quantitatively. In contrast, imaging techniques based on magnetic resonance (MR) allow the determination of the deformation pattern of the left ventricle (LV) in vivo with high accuracy. The question arises to what extent deformation measurements are significant and might provide a possibility for future diagnostic purposes. The contractile forces cause deformation of LV myocardial tissue in terms of wall thickening, longitudinal shortening, twisting rotation and radial constriction. The myocardium is thereby understood to act as a densely interlaced mesh. Yet, whole cycle image sequences display a distribution of wall strains as function of space and time heralding a significant amount of inhomogeneity even under healthy conditions. We made similar observations previously by direct measurement of local contractile activity. The major reasons for these inhomogeneities derive from regional deviations of the ventricular walls from an ideal spheroidal shape along with marked disparities in focal fibre orientation. In response to a lack of diagnostic tools able to measure wall stress in clinical routine, this communication is aimed at an analysis and functional interpretation of the deformation pattern of an exemplary human heart at end-systole. To this end, the finite element (FE) method was used to simulate the three-dimensional deformations of the left ventricular myocardium due to contractile fibre forces at end-systole. The anisotropy associated with the fibre structure of the myocardial tissue was included in the form of a fibre orientation vector field which was reconstructed from the measured fibre trajectories in a post mortem human heart. Contraction was modelled by an additive second Piola-Kirchhoff active stress tensor. As a first conclusion, it became evident that longitudinal fibre forces, cross-fibre forces and shear along with systolic fibre rearrangement have to be taken into account for a useful modelling of systolic deformation. Second, a realistic geometry and fibre architecture lead to typical and substantially inhomogeneous deformation patterns as they are recorded in real hearts. We therefore, expect that the measurement of systolic deformation might provide useful diagnostic information.

Regional ventricular wall thickening reflects changes in cardiac fiber and sheet structure during contraction: quantification with diffusion tensor MRI

Dynamic changes of myocardial fiber and sheet structure are key determinants of regional ventricular function. However, quantitative characterization of the contraction-related changes in fiber and sheet structure has not been reported. The objective of this study was to quantify cardiac fiber and sheet structure at selected phases of the cardiac cycle. Diffusion tensor MRI was performed on isolated, perfused Sprague-Dawley rat hearts arrested or fixed in three states as follows: 1) potassium arrested (PA), which represents end diastole; 2) barium-induced contracture with volume (BV+), which represents isovolumic contraction or early systole; and 3) barium-induced contracture without volume (BV-), which represents end systole. Myocardial fiber orientations at the base, midventricle, and apex were determined from the primary eigenvectors of the diffusion tensor. Sheet structure was determined from the secondary and tertiary eigenvectors at the same locations. We observed that the transmural distribution of the myofiber helix angle remained unchanged as contraction proceeded from PA to BV+, but endocardial and epicardial fibers became more longitudinally orientated in the BV- group. Although sheet structure exhibited significant regional variations, changes in sheet structure during myocardial contraction were relatively uniform across regions. The magnitude of the sheet angle, which is an index of local sheet slope, decreased by 23 and 44% in BV+ and BV- groups, respectively, which suggests more radial orientation of the sheet. In summary, we have shown for the first time that geometric changes in both sheet and fiber orientation provide a substantial mechanism for radial wall thickening independent of active components due to myofiber shortening. Our results provide direct evidence that sheet reorientation is a primary determinant of myocardial wall thickening.

Finite element modelling and simulations in cardiovascular mechanics and cardiology: A bibliography 1993–2004

The paper gives a bibliographical review of the finite element modelling and simulations in cardiovascular mechanics and cardiology from the theoretical as well as practical points of views. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1993 and 2004. At the end of this paper, more than 890 references are given dealing with subjects as: Cardiovascular soft tissue modelling; material properties; mechanisms of cardiovascular components; blood flow; artificial components; cardiac diseases examination; surgery; and other topics.

Improved Prediction of the Collagen Fiber Architecture in the Aortic Heart Valve

Living tissues show an adaptive response to mechanical loading by changing their internal structure and morphology. Understanding this response is essential for successful tissue engineering of load-bearing structures, such as the aortic valve. In this study, mechanically induced remodeling of the collagen architecture in the aortic valve was investigated. It was hypothesized that, in uniaxially loaded regions, the fibers aligned with the tensile principal stretch direction. For biaxial loading conditions, on the other hand, it was assumed that the collagen fibers aligned with directions situated between the principal stretch directions. This hypothesis has already been applied successfully to study collagen remodeling in arteries. The predicted fiber architecture represented a branching network and resembled the macroscopically visible collagen bundles in the native leaflet. In addition, the complex biaxial mechanical behavior of the native valve could be simulated qualitatively with the predicted fiber directions. The results of the present model might be used to gain further insight into the response of tissue engineered constructs during mechanical conditioning.

Optimizing ventricular fibers: uniform strain or stress, but not ATP consumption, leads to high efficiency

The aim of this study was to investigate the influence of fiber orientation in the left ventricular (LV) wall on the ejection fraction, efficiency, and heterogeneity of the distributions of developed fiber stress, strain and ATP consumption. A finite element model of LV mechanics was used with active properties of the cardiac muscle described by the Huxley-type cross-bridge model. The computed variances of sarcomere length (SL(var)), developed stress (DS(var)), and ATP consumption (ATP(var)) have several minima at different transmural courses of helix fiber angle. We identified only one region in the used design space with high ejection fraction, high efficiency of the LV and relatively small SL(var), DS(var), and ATP(var). This region corresponds to the physiological distribution of the helix fiber angle in the LV wall. Transmural fiber angle can be predicted by minimizing SL(var) and DS(var), but not ATP(var). If ATP(var) was minimized, then the transverse fiber angle was considerably underestimated. The results suggest that ATP consumption distribution is not regulating the fiber orientation in the heart.

Characterization of the normal cardiac myofiber field in goat measured with MR-diffusion tensor imaging

Cardiac myofiber orientation is a crucial determinant of the distribution of myocardial wall stress. Myofiber orientation is commonly quantified by helix and transverse angles. Accuracy of reported helix angles is limited. Reported transverse angle data are incomplete. We measured cardiac myofiber orientation postmortem in five healthy goat hearts using magnetic resonance-diffusion tensor imaging. A novel local wall-bound coordinate system was derived from the characteristics of the fiber field. The transmural course of the helix angle corresponded to data reported in literature. The mean midwall transverse angle ranged from -12 +/- 4 degrees near the apex to +9.0 +/- 4 degrees near the base of the left ventricle, which is in agreement with the course predicted by Rijcken et al. (18) using a uniform load hypothesis. The divergence of the myofiber field was computed, which is a measure for the extent to which wall stress is transmitted through the myofiber alone. It appeared to be <0.07 mm(-1) throughout the myocardial walls except for the fusion sites between the left and right ventricles and the insertion sites of the papillary muscles.

Biomechanics of cardiovascular development

It long has been known that mechanical forces play a role in the development of the cardiovascular system, but only recently have biomechanical engineers begun to explore this field. This paper reviews some of this work. First, an overview of the relevant biology is discussed. Next, a mechanical theory is presented that can be used to model developmental processes. The theory includes the effects of finite volumetric growth and active contractile forces. Finally, applications of this and other theories to problems of cardiovascular development are discussed, and some future directions are suggested. The intent is to stimulate further interest among engineers in this important area of research.

Myocardial mechanics and collagen structure in the osteogenesis imperfecta murine (oim)

Because the amount and structure of type I collagen are thought to affect the mechanics of ventricular myocardium, we investigated myocardial collagen structure and passive mechanical function in the osteogenesis imperfecta murine (oim) model of pro-alpha2(I) collagen deficiency, previously shown to have less collagen and impaired biomechanics in tendon and bone. Compared with wild-type littermates, homozygous oim hearts exhibited 35% lower collagen area fraction (P:<0.05), 38% lower collagen fiber number density (P:<0.05), and 42% smaller collagen fiber diameter (P:<0.05). Compared with wild-type, oim left ventricular (LV) collagen concentration was 45% lower (P:<0.0001) and nonreducible pyridinoline cross-link concentration was 22% higher (P:<0.03). Mean LV volume during passive inflation from 0 to 30 mm Hg in isolated hearts was 1.4-fold larger for oim than wild-type (P:=NS). Uniaxial stress-strain relations in resting right ventricular papillary muscles exhibited 60% greater strains (P:<0.01), 90% higher compliance (P:=0.05), and 64% higher nonlinearity (P:<0.05) in oim. Mean opening angle, after relief of residual stresses in resting LV myocardium, was 121+/-9 degrees in oim compared with 45+/-4 degrees in wild-type (P:<0.0001). Mean myofiber angle in oim was 23+/-8 degrees greater than wild-type (P:<0.02). Decreased myocardial collagen diameter and amount in oim is associated with significantly decreased fiber and chamber stiffness despite modestly increased collagen cross-linking. Altered myofiber angles and residual stress may be beneficial adaptations to these mechanical alterations to maintain uniformity of transmural fiber strain. In addition to supporting and organizing myocytes, myocardial collagen contributes directly to ventricular stiffness at high and low loads and can influence stress-free state and myofiber architecture.