An Iterative Diffeomorphic Algorithm for Registration of Subdivision Surfaces: Application to Congenital Heart Disease.

In this paper, we present a new diffeomorphic registration algorithm for the registration of 3D models to 3D points. A biventricular template is iteratively fitted to the data by a series of implicitly constrained diffeomorphic linear least squares fits with decreasing regularization weights before performing an explicitly constrained diffeomorphic fit. The algorithm has been tested on a set of manual contours from 20 patients with a variety of congenital heart disease. Registration accuracy was assessed by calculating the mean point-to-point distance and the Dice overlap metric. Results showed that the method was able to accurately fit the biventricular model to 3D points and that the deformable model was able to fit all the pathologies while being diffeomorphic. The algorithm took approximately 5 minutes to fit each case, with an average of 52,580 points per case.

Caveolae in ventricular myocytes are required for stretch-dependent conduction slowing.

Mechanical stretch of cardiac muscle modulates action potential propagation velocity, causing potentially arrhythmogenic conduction slowing. The mechanisms by which stretch alters cardiac conduction remain unknown, but previous studies suggest that stretch can affect the conformation of caveolae in myocytes and other cell types. We tested the hypothesis that slowing of action potential conduction due to cardiac myocyte stretch is dependent on caveolae. Cardiac action potential propagation velocities, measured by optical mapping in isolated mouse hearts and in micropatterned mouse cardiomyocyte cultures, decreased reversibly with volume loading or stretch, respectively (by 19±5% and 26±4%). Stretch-dependent conduction slowing was not altered by stretch-activated channel blockade with gadolinium or by GsMTx-4 peptide, but was inhibited when caveolae were disrupted via genetic deletion of caveolin-3 (Cav3 KO) or membrane cholesterol depletion by methyl-ß-cyclodextrin. In wild-type mouse hearts, stretch coincided with recruitment of caveolae to the sarcolemma, as observed by electron microscopy. In myocytes from wild-type but not Cav3 KO mice, stretch significantly increased cell membrane capacitance (by 98±64%), electrical time constant (by 285±149%), and lipid recruitment to the bilayer (by 84±39%). Recruitment of caveolae to the sarcolemma during physiologic cardiomyocyte stretch slows ventricular action potential propagation by increasing cell membrane capacitance.

Cardiac resynchronization: insight from experimental and computational models.

Cardiac resynchronization therapy (CRT) is a promising therapy for heart failure patients with a conduction disturbance, such as left bundle branch block. The aim of CRT is to resynchronize contraction between and within ventricles. However, about 30% of patients do not respond to this therapy. Therefore, a better understanding is needed for the relation between electrical and mechanical activation. In this paper, we focus on to what extent animal experiments and mathematical models can help in order to understand the pathophysiology of asynchrony to further improve CRT.

Complex distributions of residual stress and strain in the mouse left ventricle: experimental and theoretical models.

Most soft biological tissues, including ventricular myocardium, are not stress free when all external loads are removed. Residual stress has implications for mechanical performance of the heart, and may be an indicator of patterns of regional growth and remodeling. Cross-sectional rings of arrested ventricles opened up when a radial cut was made (initial mean opening angles were 64 +/- 17 degrees), but further circumferential cuts revealed the presence of additional residual stresses in the tissue with further opening of the rings. In normal mouse hearts, the inner half of a short-axis ring opened more than the outer half, and this change was dependent on apex-base location. At the apex the inner section vs. outer section opening angles were 226 +/- 47 degrees vs. 89 +/- 28 degrees, while at the base the same two angles were 160 +/- 30 degrees vs. 123 +/- 35 degrees. A simple theoretical cylindrical shell model with incompressible hyperelastic material properties was used to model the experimental deformations based on the cutting experiments. The model predicts different residual stress fields depending on the nature of the opening after the circumferential cut (which is done after the conventional radial cut). The observed opening angles were consistent with steep stress gradients near the endocardium compared with those predicted if the first cut was assumed to relieve all residual stresses. These results imply a more complex distribution of residual stress and strain in ventricular myocardium than previously thought.

Regional septal dysfunction in a three-dimensional computational model of focal myofiber disarray.

MLC2v/ras transgenic mice display a phenotype characteristic of hypertrophic cardiomyopathy, with septal hypertrophy and focal myocyte disarray. Experimental measurements of septal wall mechanics in ras transgenic mice have previously shown that regions of myocyte disarray have reduced principal systolic shortening, torsional systolic shear, and sarcomere length. To investigate the mechanisms of this regional dysfunction, a three-dimensional prolate spheroidal finite-element model was used to simulate filling and ejection in the hypertrophied mouse left ventricle with septal disarray. Focally disarrayed septal myocardium was modeled by randomly distributed three-dimensional regions of altered material properties based on measured statistical distributions of muscle fiber angular dispersion. Material properties in disarrayed regions were modeled by decreased systolic anisotropy derived from increased fiber angle dispersion and decreased systolic tension development associated with reduced sarcomere lengths. Compared with measurements in ras transgenic mice, the model showed similar heterogeneity of septal systolic strain with the largest reductions in principal shortening and torsional shear in regions of greatest disarray. Average systolic principal shortening on the right ventricular septal surface of the model was -0.114 for normal regions and -0.065 for disarrayed regions; for torsional shear, these values were 0.047 and 0.019, respectively. These model results suggest that regional dysfunction in ras transgenic mice may be explained in part by the observed structural defects, including myofiber dispersion and reduced sarcomere length, which contributed about equally to predicted dysfunction in the disarrayed myocardium.

Transmural distribution of three-dimensional systolic strains in stunned myocardium.

BACKGROUND: Regional function in stunned myocardium is usually thought to be more depressed in the endocardium than the epicardium. This has been attributed to the greater loss of blood flow at the endocardium during ischemia. METHODS AND RESULTS: We measured transmural distributions of 3D systolic strains relative to local myofiber axes in open-chest anesthetized dogs before 15 minutes of left anterior descending coronary artery occlusion and during 2 hours of reperfusion. During ischemia, regional myocardial blood flow was reduced 84% at the endocardium and 32% at the epicardium (P<0.005, n=7), but changes in end-systolic fiber length from baseline were transmurally uniform. Relative to baseline, radial segments in stunned tissue were significantly thinner at the endocardium than the epicardium at end systole (24+/-5% versus 16+/-3%; P<0.05, n=8), consistent with previous reports. Unlike radial and cross-fiber segments, however, the increase of end-systolic fiber lengths in stunned myocardium had no significant transmural gradient (23+/-8% epicardium versus 21+/-4% endocardium). We also observed significant 3D diastolic dysfunction in the ischemic-reperfused region transmurally. CONCLUSIONS: Myocardial ischemia/reperfusion in the dog results in a significant transmural gradient of dysfunction between epicardial and endocardial layers in radial and cross-fiber segments, but not for fiber segments, despite a gradient in blood flow reduction during ischemia. Perhaps systolic fiber dysfunction rather than the degree of perfusion deficit during the preceding ischemic period may be the main determinant of myocardial dysfunction during reperfusion.

Age-associated cardiac dysfunction in Drosophila melanogaster.

The fruit fly, Drosophila melanogaster, has served as a valuable model/organism for the study of aging and was the first organism possessing a circulatory system to have its genome completely sequenced. However, little is known about the function of the heartlike organ of flies during the aging process. We have developed methods for studying cardiac function in vivo in adult flies. Using 2 different cardiovascular stress methods (elevated ambient temperature and external electrical pacing), we found that maximal heart rate is significantly and reproducibly reduced with aging in Drosophila, analogous to observations in elderly humans. We also describe for the first time several other aspects of the cardiac physiology of young adult and aging Drosophila, including an age-associated increase in rhythm disturbances. These observations suggest that the study of declining cardiac function in aging flies may serve as a genetically tractable model for genome-wide mutational screening for genes that participate in or protect against cardiac aging and disease.

Model-based analysis of optically mapped epicardial activation patterns and conduction velocity.

A novel parametric model-based method was developed to quantify epicardial conduction patterns and velocity in an isolated Langendorff-perfused rabbit heart. The method incorporated geometric and anatomical features of the left and right ventricles into the analysis. Optical images of propagation were obtained using the voltage-sensitive dye DI-4-ANEPPS, and a high-speed digital camera. Activation maps were extracted from these images and interpolated onto a three-dimensional finite-element model of epicardial geometry and fiber structure. Activation time was expressed as a function of local parametric coordinates, and a conduction velocity vector field was computed from the gradient of the scalar field. Activation times measured using bipolar electrodes did not differ significantly from times measured using the optical mapping technique. The method was able to detect a 34% decrease in average fiber velocity and a 28% decrease in average cross-fiber velocity following the addition of 0.5 mM heptanol into the perfusate. The combination of optical mapping with a three-dimensional geometric model of the ventricles provides a new tool to quantify wave-front propagation relative to anatomy at a relatively high spatial resolution.

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.

Structural basis of regional dysfunction in acutely ischemic myocardium.

OBJECTIVE: Impaired systolic function in the normally perfused myocardium adjacent to an ischemic region - the functional border zone - is thought to result from mechanical interactions across the perfusion boundary. We investigated how segment orientation and vessel involved affect regional strains in the functional border zone and whether altered stresses associated with a step transition in contractility can explain the functional border zone. METHODS AND RESULTS: Regional epicardial strain distributions were obtained from measured displacements of radiopaque markers in open-chest anesthetized canines, and related to local myofiber angles and blood flows. The functional border zone for fiber strain was significantly narrower than that for cross-fiber strain and significantly wider for left anterior descending (LAD) than left circumflex (LCx) coronary occlusion (1.23 vs. 0.45 cm). A detailed three-dimensional computational model with a one-to-one relation between perfusion and myofilament activation and no transitional zone of intermediate contractility showed close agreement with these observations and significantly elevated stresses in the border zone. Differences between LAD and LCx occlusions in the model were due to differences in left ventricular systolic pressure and not to differences in perfusion boundary or muscle fiber orientation. The border zone was narrower for fiber strain than cross-fiber strain because systolic stiffness is greatest along the muscle fiber direction. CONCLUSION: Abnormal regional mechanics in the acute ischemic border arise from increased wall stresses without a transitional zone of intermediate contractility. Perfusion is more tightly coupled to fiber than cross-fiber strain, and a wider functional border zone of fiber strain during LAD than LCx occlusion is primarily due to higher regional wall stresses rather than anatomic variations.

Regional dysfunction correlates with myofiber disarray in transgenic mice with ventricular expression of ras.

A hallmark of certain cardiac diseases such as familial hypertrophic cardiomyopathy is focal myofiber disarray. Regional ventricular dysfunction occurs in human subjects with hypertrophic cardiomyopathy; however, no direct evidence exists to correlate regional dysfunction with myofiber disarray. We used a transgenic mouse, which exhibits regional myofiber disarray via ventricular expression of the human oncogene ras, to investigate the relationship between myofiber disarray and septal surface strain. An isolated ejecting mouse heart preparation was used to record deformation of markers on the septal surface and to determine nonhomogeneous septal surface strain maps. Myofiber disarray made in histological tissue sections was correlated with gradients in surface systolic shortening. Significantly smaller maximum principal shortening was associated with disarray located near the right ventricle (RV) septal surface. There was also significantly smaller surface shear strain associated with disarray located either near the RV surface or at the midwall. Because surface shear is a local indicator of torsion, we conclude that myofiber disarray is associated with reduced septal torsion and reduced surface shortening.

Structural and mechanical factors influencing infarct scar collagen organization.

Although large collagen fibers in myocardial infarct scar are highly organized, little is known about mechanisms controlling this organization. The preexisting extracellular matrix may act as a scaffold along which fibroblasts migrate. Conversely, deformation within the ischemic area could guide fibroblasts so new collagen is oriented to counteract the stretch. To investigate these potential mechanisms, we infarcted three groups of pigs. Group 1 served as infarct controls. Group 2 had the endocardium slit longitudinally to alter local systolic deformation. Group 3 had a plug sectioned from ischemic tissue and rotated 90 degrees. The slit altered systolic deformation in the infarcted tissue, changing circumferential strain from expansion to compression and increasing radial strain and shears and the variability of collagen fiber angles but not the mean angle. In the plug pigs, when deformation, matrix orientation, and continuity are altered in the infarct area, the result is complete disarray in the organization of collagen within the infarct scar.

Nicotine-modified postinfarction left ventricular remodeling.

Cigarette smoking has been noted to impair wound healing in tissues such as skin, bone, and gut. This study was designed to examine whether nicotine adversely affects postinfarction cardiac wound healing and remodeling in an experimental model of myocardial infarction. For this purpose, two groups of rats were studied. The control group received a simple bandage, and the nicotine group had a section (1.75 mg/day) of a nicotine patch attached on their backs. After a 7-day treatment period, an anterior wall infarction was induced. A bandage-free 7-day healing period followed, after which hearts were isolated for mechanical tests. Nicotine-treated rats developed significantly enlarged left ventricles with thin, infarcted walls and a rightward shift in the passive pressure-volume relationship. Pressure-strain analysis also indicated possible changes in the material properties of the wound for nicotine-treated rats. In conclusion, nicotine has significant adverse effects on postinfarction healing and left ventricular remodeling. These observations have important clinical implications because of the enhanced risk for development of heart failure.

Measurement of orientation and distribution of cellular alignment and cytoskeletal organization.

Endothelial cells elongate and align with the direction of applied fluid shear stress. Previously, automated methods for analysis of cell orientation distribution have used Fourier- or fractal-based methods. We used intensity gradients in images of control and sheared endothelial cells to measure orientation distributions. Automated measurements of mean orientation and angular deviation compared favorably with manual measurements. There was a significantly greater angular deviation in images of control cells compared with sheared cells. Automated methods were also used to quantify organization of cytoskeletal fibers using the local angular deviation and a measure of the local coalignment of fibers called the coalignment ratio. The local angular deviation of microtubules and microfilaments was significantly smaller in sheared cells compared with control. The coalignment of cytoskeletal fibers was significantly greater in sheared cells. We conclude that image intensity gradients can be used rapidly, accurately, and objectively to measure cell orientation distributions and cytoskeletal filament organization.

Automated measurement of myofiber disarray in transgenic mice with ventricular expression of ras.

Quantitative assessment of myofiber disarray associated with diseases such as familial hypertrophic cardiomyopathy (FHC) can be performed by estimating local angular deviation of fiber orientation in histologic sections. The large number of measurements required to estimate angular deviation prohibits manual measurement. We describe methods for automated measurement of local orientation and angular deviation in tissue sections from transgenic mice with ventricular expression of ras, proposed as a model of FHC. Images of histologic tissue sections from normal and transgenic mice were analyzed using image processing techniques to estimate local orientation of myofibers. Results from the automated methods were compared with manual measurements. Automated methods estimated differing mean orientation in 7-20% of normal sections and 17-29% of transgenic tissue sections with differing dispersions in 23-30% of normal sections and 25% of transgenic tissue sections. Automated methods estimate 24.47+/-13.03% of total ventricular mass affected by disarray that is comparable to a previous estimate of 21.7% in the same mouse model. Automated methods are a rapid and accurate alternative to manual measurement for estimation of mean orientation and angular deviation in myocardial tissue sections. Differences between manual and automated methods may be attributed to the substantially larger number of measurements made by automated methods. Automated methods are particularly appropriate for use in determining local variation in orientation such as focal myofiber disarray associated with FHC. The generality of these methods suggests they may have use in other biological fields such as quantifying cellular alignment.

Stress and strain as regulators of myocardial growth.

The response of the heart to altered hemodynamic loading is growth or remodeling of myocytes and the extracellular matrix. In order to describe and mathematically model this dynamic and complex system of growing and resorbing tissue, the stimulating factor for tissue growth must be found, and up to now is not known. Most evidence, both in tissue and at the cellular level, points to a mechanical factor as the stimulus, and most likely a deformation signal is transduced to initiate protein synthesis. At the cellular level mechanotransduction likely takes place at the cellular membrane, although multiple biochemical and mechanical pathways have been proposed which induce transcription in the nucleus and eventual protein upregulation. The results of a recent mathematical analysis based on experimental data suggest that end-diastolic fiber strain at the tissue level may be the stimulus to one mode of tissue growth: volume-overload hypertrophy. This is the only mechanical factor that we found to be normalized after volume overload hypertrophy. But other studies do not agree with this result, and other modes of hypertrophy may be regulated by different factors or combinations of factors.

Regional myocardial perfusion and mechanics: a model-based method of analysis.

A new parametric model-based method has been developed that allows epicardial strain distributions to be computed on the left ventricular free wall in normal and ischemic myocardium and integrated with the regional distributions of anatomic and physiological measurements so that underlying relationships can be explored. An array of radiopaque markers was sewn on the anterior wall of the left ventricle (LV) in three anesthetized open-chest canines, and their positions were recorded using biplane video fluoroscopy before and 2 min after occlusion of the left anterior descending coronary artery. The three-dimensional (3D) anatomy of the LV and epicardial fiber angles were measured post-mortem using a 3D probe. A prolate spheroidal finite element model was fitted to the epicardial surface points (with <0.2 mm accuracy) and fiber angles (<5 degrees error). Regional myocardial blood flows (MBFs) were measured using fluorescent microspheres and fitted into the model (<0.3 ml min(-1) g(-1) error). Epicardial fiber and cross-fiber strain distributions were computed by allowing the model to deform from end-diastole to end-systole according to the recorded motion of the surface markers. Systolic fiber strain varied from -0.05 to 0.01 within the region of the markers during baseline, and regional MBF varied from 1.5 to 2.0 ml min(-1) g(-1). During 2 min ischemia, regional MBF was less than 0.3 ml min(-1) g(-1) in the ischemic region and 1.0 ml min(-1) g(-1) in the nonischemic region, and fiber strain ranged from 0.05 in the central ischemic zone to -0.025 in the remote nonischemic tissue. This analysis revealed a zone of impaired fiber shortening extending into the normally perfused myocardium that was significantly wider at the base than the apex. A validation analysis showed that a regularizing function can be optimized to minimize both fitting errors and numerical oscillations in the computed strain fields.

Flow-function relations during graded coronary occlusions in the dog: effects of transmural location and segment orientation.

OBJECTIVE: The sensitive relationship between regional myocardial perfusion and local systolic deformation during acute myocardial ischemia is not independent of the transmural location or segment orientation. The aim of this study was to determine the effects of fiber orientation and transmural location on the relationships between regional myocardial flow and three-dimensional systolic wall strain during graded coronary artery occlusions. METHODS: Transmural distributions of three-dimensional strain (by biplane radiography of implanted radiopaque markers) and myocardial blood flows (using fluorescent microspheres) were measured in the ischemic region during graded left anterior descending (LAD) coronary artery occlusions in 12 anesthetized dogs. RESULTS: Occlusion of the coronary artery did not significantly alter mean heart rate or end-systolic pressure. As flow decreased during graded occlusions, ischemia significantly changed systolic circumferential, longitudinal, radial, fiber and cross-fiber strains (p < 0.004). There was a significant effect of transmural position on circumferential, cross-fiber and radial strains, but not on fiber or longitudinal strains. Ischemia significantly altered all normal strains: circumferential, longitudinal, fiber, cross-fiber and radial. There was a strong interaction effect between transmural location and blood flow for circumferential, cross-fiber and radial strains, but not fiber or longitudinal strains. CONCLUSION: During non-transmural ischemia, there is evidence of strong transmural tethering in the cross-fiber direction, whereas the fiber-strain flow relation is independent of transmural position. Thus, whether the relationship between local myocardial bloodflow and systolic strain during acute ischemia is dependent on transmural location, depends on segment orientation.

Protection against myocardial dysfunction after a brief ischemic period in transgenic mice expressing inducible heat shock protein 70.

Brief ischemic periods lead to myocardial dysfunction without myocardial infarction. It has been shown that expression of inducible HSP70 in hearts of transgenic mice leads to decreased infarct size, but it remains unclear if HSP70 can also protect against myocardial dysfunction after brief ischemia. To investigate this question, we developed a mouse model in which regional myocardial function can be measured before and after a temporary ischemic event in vivo. In addition, myocardial function was determined after brief episodes of global ischemia in an isolated Langendorff heart. HSP70-positive mice and transgene negative littermates underwent 8 min of regional myocardial ischemia created by occlusion of the left descending coronary artery, followed by 60 min of reperfusion. This procedure did not result in a myocardial infarction. Regional epicardial strain was used as a sensitive indicator for changes in myocardial function after cardiac ischemia. Maximum principal strain was significantly greater in HSP70-positive mice with 88+/-6% of preischemic values vs. 58+/-6% in transgene-negative mice (P < 0.05). Similarly, in isolated Langendorff perfused hearts of HSP70-positive and transgene-negative littermates exposed to 10 min of global ischemia and 90 min of reperfusion, HSP70 transgenic hearts showed a better-preserved ventricular peak systolic pressure. Thus, we conclude that expression of HSP70 protects against postischemic myocardial dysfunction as shown by better preserved myocardial function.