Manuel K. Rausch

Computational modeling of growth: systemic and pulmonary hypertension in the heart

We introduce a novel constitutive model for growing soft biological tissue and study its performance in two characteristic cases of mechanically induced wall thickening of the heart. We adopt the concept of an incompatible growth configuration introducing the multiplicative decomposition of the deformation gradient into an elastic and a growth part. The key feature of the model is the definition of the evolution equation for the growth tensor which we motivate by pressure-overload-induced sarcomerogenesis. In response to the deposition of sarcomere units on the molecular level, the individual heart muscle cells increase in diameter, and the wall of the heart becomes progressively thicker. We present the underlying constitutive equations and their algorithmic implementation within an implicit nonlinear finite element framework. To demonstrate the features of the proposed approach, we study two classical growth phenomena in the heart: left and right ventricular wall thickening in response to systemic and pulmonary hypertension.

Mitral Valve Annuloplasty A Quantitative Clinical and Mechanical Comparison of Different Annuloplasty Devices

Mitral valve annuloplasty is a common surgical technique used in the repair of a leaking valve by implanting an annuloplasty device. To enhance repair durability, these devices are designed to increase leaflet coaptation, while preserving the native annular shape and motion; however, the precise impact of device implantation on annular deformation, strain, and curvature is unknown. In this article, we quantify how three frequently used devices significantly impair native annular dynamics. In controlled in vivo experiments, we surgically implanted 11 flexible-incomplete, 11 semi-rigid-complete, and 12 rigid-complete devices around the mitral annuli of 34 sheep, each tagged with 16 equally spaced tantalum markers. We recorded four-dimensional marker coordinates using biplane videofluoroscopy, first with device and then without, which were used to create mathematical models using piecewise cubic splines. Clinical metrics (characteristic anatomical distances) revealed significant global reduction in annular dynamics upon device implantation. Mechanical metrics (strain and curvature fields) explained this reduction via a local loss of anterior dilation and posterior contraction. Overall, all three devices unfavorably caused reduction in annular dynamics. The flexible-incomplete device, however, preserved native annular dynamics to a larger extent than the complete devices. Heterogeneous strain and curvature profiles suggest the need for heterogeneous support, which may spawn more rational design of annuloplasty devices using design concepts of functionally graded materials.

In-vivo dynamic strains of the ovine anterior mitral valve leaflet

Understanding the mechanics of the mitral valve is crucial in terms of designing and evaluating medical devices and techniques for mitral valve repair. In the current study we characterize the in vivo strains of the anterior mitral valve leaflet. On cardiopulmonary bypass, we sew miniature markers onto the leaflets of 57 sheep. During the cardiac cycle, the coordinates of these markers are recorded via biplane fluoroscopy. From the resulting four-dimensional data sets, we calculate areal, maximum principal, circumferential, and radial leaflet strains and display their profiles on the averaged leaflet geometry. Average peak areal strains are 13.8±6.3%, maximum principal strains are 13.0±4.7%, circumferential strains are 5.0±2.7%, and radial strains are 7.8±4.3%. Maximum principal strains are largest in the belly region, where they are aligned with the circumferential direction during diastole switching into the radial direction during systole. Circumferential strains are concentrated at the distal portion of the belly region close to the free edge of the leaflet, while radial strains are highest in the center of the leaflet, stretching from the posterior to the anterior commissure. In summary, leaflet strains display significant temporal, regional, and directional variations with largest values inside the belly region and toward the free edge. Characterizing strain distribution profiles might be of particular clinical significance when optimizing mitral valve repair techniques in terms of forces on suture lines and on medical devices.

Characterization of mitral valve annular dynamics in the beating heart

The objective of this study is to establish a mathematical characterization of the mitral valve annulus that allows a precise qualitative and quantitative assessment of annular dynamics in the beating heart. We define annular geometry through 16 miniature markers sewn onto the annuli of 55 sheep. Using biplane videofluoroscopy, we record marker coordinates in vivo. By approximating these 16 marker coordinates through piecewise cubic splines, we generate a smooth mathematical representation of the 55 mitral annuli. We time-align these 55 annulus representations with respect to characteristic hemodynamic time points to generate an averaged baseline annulus representation. To characterize annular physiology, we extract classical clinical metrics of annular form and function throughout the cardiac cycle. To characterize annular dynamics, we calculate displacements, strains, and curvature from the discrete mathematical representations. To illustrate potential future applications of this approach, we create rapid prototypes of the averaged mitral annulus at characteristic hemodynamic time points. In summary, this study introduces a novel mathematical model that allows us to identify temporal, regional, and inter-subject variations of clinical and mechanical metrics that characterize mitral annular form and function. Ultimately, this model can serve as a valuable tool to optimize both surgical and interventional approaches that aim at restoring mitral valve competence.

Rigid, Complete Annuloplasty Rings Increase Anterior Mitral Leaflet Strains in the Normal Beating Ovine Heart

Background— Annuloplasty ring or band implantation during surgical mitral valve repair perturbs mitral annular dimensions, dynamics, and shape, which have been associated with changes in anterior mitral leaflet (AML) strain patterns and suboptimal long-term repair durability. We hypothesized that rigid rings with nonphysiological three-dimensional shapes, but not saddle-shaped rigid rings or flexible bands, increase AML strains. Methods and Results— Sheep had 23 radiopaque markers inserted: 7 along the anterior mitral annulus and 16 equally spaced on the AML. True-sized Cosgrove-Edwards flexible, partial band (n=12), rigid, complete St Jude Medical rigid saddle-shaped (n=12), Carpentier-Edwards Physio (n=12), Edwards IMR ETlogix (n=11), and Edwards GeoForm (n=12) annuloplasty rings were implanted in a releasable fashion. Under acute open-chest conditions, 4-dimensional marker coordinates were obtained using biplane videofluoroscopy along with hemodynamic parameters with the ring inserted and after release. Marker coordinates were triangulated, and the largest maximum principal AML strains were determined during isovolumetric relaxation. No relevant changes in hemodynamics occurred. Compared with the respective control state, strains increased significantly with rigid saddle-shaped annuloplasty ring, Carpentier-Edwards Physio, Edwards IMR ETlogix, and Edwards GeoForm (0.14±0.05 versus 0.16±0.05, P=0.024, 0.15±0.03 versus 0.18±0.04, P=0.020, 0.11±0.05 versus 0.14±0.05, P=0.042, and 0.13±0.05 versus 0.16±0.05, P=0.009), but not with Cosgrove-Edwards band (0.15±0.05 versus 0.15±0.04, P=0.973). Conclusions— Regardless of three-dimensional shape, rigid, complete annuloplasty rings, but not a flexible, partial band, increased AML strains in the normal beating ovine heart. Clinical studies are needed to determine whether annuloplasty rings affect AML strains in patients, and, if so, whether ring-induced perturbations in leaflet strain states are linked to repair failure.

Evidence of adaptive mitral leaflet growth

Ischemic mitral regurgitation is mitral insufficiency caused by myocardial infarction. Recent studies suggest that mitral leaflets have the potential to grow and reduce the degree of regurgitation. Leaflet growth has been associated with papillary muscle displacement, but role of annular dilation in leaflet growth is unclear. We tested the hypothesis that chronic leaflet stretch, induced by papillary muscle tethering and annular dilation, triggers chronic leaflet growth. To decipher the mechanisms that drive the growth process, we further quantified regional and directional variations of growth. Five adult sheep underwent coronary snare and marker placement on the left ventricle, papillary muscles, mitral annulus, and mitral leaflet. After eight days, we tightened the snares to create inferior myocardial infarction. We recorded marker coordinates at baseline, acutely (immediately post-infarction), and chronically (five weeks post-infarction). From these coordinates, we calculated acute and chronic changes in ventricular, papillary muscle, and annular geometry along with acute and chronic leaflet strains. Chronic left ventricular dilation of 17.15% (p<0.001) induced chronic posterior papillary muscle displacement of 13.49 mm (p=0.07). Chronic mitral annular area, commissural and septal-lateral distances increased by 32.50% (p=0.010), 14.11% (p=0.007), and 10.84% (p=0.010). Chronic area, circumferential, and radial growth were 15.57%, 5.91%, and 3.58%, with non-significant regional variations (p=0.868). Our study demonstrates that mechanical stretch, induced by annular dilation and papillary muscle tethering, triggers mitral leaflet growth. Understanding the mechanisms of leaflet adaptation may open new avenues to pharmacologically or surgically manipulate mechanotransduction pathways to augment mitral leaflet area and reduce the degree of regurgitation.

Heterogeneous growth-induced prestrain in the heart

Even when entirely unloaded, biological structures are not stress-free, as shown by Y.C. Fung׳s seminal opening angle experiment on arteries and the left ventricle. As a result of this prestrain, subject-specific geometries extracted from medical imaging do not represent an unloaded reference configuration necessary for mechanical analysis, even if the structure is externally unloaded. Here we propose a new computational method to create physiological residual stress fields in subject-specific left ventricular geometries using the continuum theory of fictitious configurations combined with a fixed-point iteration. We also reproduced the opening angle experiment on four swine models, to characterize the range of normal opening angle values. The proposed method generates residual stress fields which can reliably reproduce the range of opening angles between 8.7±1.8 and 16.6±13.7 as measured experimentally. We demonstrate that including the effects of prestrain reduces the left ventricular stiffness by up to 40%, thus facilitating the ventricular filling, which has a significant impact on cardiac function. This method can improve the fidelity of subject-specific models to improve our understanding of cardiac diseases and to optimize treatment options.

Anterior Mitral Leaflet Curvature During the Cardiac Cycle in the Normal Ovine Heart

Background— The dynamic changes of anterior mitral leaflet (AML) curvature are of primary importance for optimal left ventricular filling and emptying but are incompletely characterized. Methods and Results— Sixteen radiopaque markers were sutured to the AML in 11 sheep, and 4-dimensional marker coordinates were acquired with biplane videofluoroscopy. A surface subdivision algorithm was applied to compute the curvature across the AML at midsystole and at maximal valve opening. Septal-lateral (SL) and commissure-commissure (CC) curvature profiles were calculated along the SL AML meridian (MSL)and CC AML meridian (MCC), respectively, with positive curvature being concave toward the left atrium. At midsystole, the MSL was concave near the mitral annulus, turned from concave to convex across the belly, and was convex along the free edge. At maximal valve opening, the MSL was flat near the annulus, turned from slightly concave to convex across the belly, and flattened toward the free edge. In contrast, the MCC was concave near both commissures and convex at the belly at midsystole but convex near both commissures and concave at the belly at maximal valve opening. Conclusions— While the SL curvature of the AML along the MSL is similar across the belly region at midsystole and early diastole, the CC curvature of the AML along the MCC flips, with the belly being convex to the left atrium at midsystole and concave at maximal valve opening. These curvature orientations suggest optimal left ventricular inflow and outflow shapes of the AML and should be preserved during catheter or surgical interventions.

How Do Annuloplasty Rings Affect Mitral Annular Strains in the Normal Beating Ovine Heart

Background— We hypothesized that annuloplasty ring implantation alters mitral annular strains in a normal beating ovine heart preparation. Methods and Results— Sheep had 16 radiopaque markers sewn equally spaced around the mitral annulus. Edwards Cosgrove partial flexible band (COS; n=12), St Jude complete rigid saddle-shaped annuloplasty ring (RSA; n=10), Carpentier-Edwards Physio (PHY; n=11), Edwards IMR ETlogix (ETL; n=11), and GeoForm (GEO; n=12) annuloplasty rings were implanted in a releasable fashion. Four-dimensional marker coordinates were obtained using biplane videofluoroscopy with the ring inserted (ring) and after ring release (control). From marker coordinates, a functional spatio-temporal representation of each annulus was generated through a best fit using 16 piecewise cubic Hermitian splines. Absolute total mitral annular ring strains were calculated from the relative change in length of the tangent vector to the annular curve as strains occurring from control to ring state at end-systole. In addition, average Green-Lagrange strains occurring from control to ring state at end-systole along the annulus were calculated. Absolute total mitral annular ring strains were smallest for COS and greatest for ETL. Strains for RSA, PHY, and GEO were similar. Except for COS in the septal mitral annular segment, all rings induced compressive strains along the entire annulus, with greatest values occurring at the lateral mitral annular segment. Conclusions— In healthy, beating ovine hearts, annuloplasty rings (COS, RSA, PHY, ETL, and GEO) induce compressive strains that are predominate in the lateral annular region, smallest for flexible partial bands (COS) and greatest for an asymmetrical rigid ring type with intrinsic septal-lateral downsizing (ETL). However, the ring type with the most drastic intrinsic septal-lateral downsizing (GEO) introduced strains similar to physiologically shaped rings (RSA and PHY), indicating that ring effects on annular strain profiles cannot be estimated from the degree of septal-lateral downsizing.

Human Cardiac Function Simulator for the Optimal Design of a Novel Annuloplasty Ring with a Sub-valvular Element for Correction of Ischemic Mitral Regurgitation

AbstractIschemic mitral regurgitation is associated with substantial risk of death. We sought to: (1) detail significant recent improvements to the Dassault Systèmes human cardiac function simulator (HCFS); (2) use the HCFS to simulate normal cardiac function as well as pathologic function in the setting of posterior left ventricular (LV) papillary muscle infarction; and (3) debut our novel device for correction of ischemic mitral regurgitation. We synthesized two recent studies of human myocardial mechanics. The first study presented the robust and integrative finite element HCFS. Its primary limitation was its poor diastolic performance with an LV ejection fraction below 20% caused by overly stiff ex vivo porcine tissue parameters. The second study derived improved diastolic myocardial material parameters using in vivo MRI data from five normal human subjects. We combined these models to simulate ischemic mitral regurgitation by computationally infarcting an LV region including the posterior papillary muscle. Contact between our novel device and the mitral valve apparatus was simulated using Dassault Systèmes SIMULIA software. Incorporating improved cardiac geometry and diastolic myocardial material properties in the HCFS resulted in a realistic LV ejection fraction of 55%. Simulating infarction of posterior papillary muscle caused regurgitant mitral valve mechanics. Implementation of our novel device corrected valve dysfunction. Improvements in the current study to the HCFS permit increasingly accurate study of myocardial mechanics. The first application of this simulator to abnormal human cardiac function suggests that our novel annuloplasty ring with a sub-valvular element will correct ischemic mitral regurgitation.