The nonlinear elastic and viscoelastic passive properties of left ventricular papillary muscle of a Guinea pig heart

Investigations of cardiac fibrosis rheology by in vitro cardiac tissue modeling with 3D cellular spheroids

Cardiac fibrosis refers to the abnormal accumulation of extracellular matrix within the cardiac muscle, leading to increased stiffness and impaired heart function. From a rheological standpoint, knowledge about myocardial behavior is still lacking, partially due to a lack of appropriate techniques to investigate the rheology of in vitro cardiac tissue models. 3D multicellular cardiac spheroids are powerful and versatile platforms for modeling healthy and fibrotic cardiac tissue in vitro and studying how their mechanical properties are modulated. In this study, cardiac spheroids were created by co-culturing neonatal rat ventricular cardiomyocytes and fibroblasts in definite ratios using the hanging-drop method. The rheological characterization of such models was performed by Atomic Force Microscopy-based stress-relaxation measurements on the whole spheroid. After strain application, a viscoelastic bi-exponential relaxation was observed, characterized by a fast relaxation time (τ1) followed by a slower one (τ2). In particular, spheroids with higher fibroblasts density showed reduction for both relaxation times comparing to control, with a more pronounced decrement of τ1 with respect to τ2. Such response was found compatible with the increased production of extracellular matrix within these spheroids, which recapitulates the main feature of the fibrosis pathophysiology. These results demonstrate how the rheological characteristics of cardiac tissue vary as a function of cellular composition and extracellular matrix, confirming the suitability of such system as an in vitro preclinical model of cardiac fibrosis.

Automated model discovery for muscle using constitutive recurrent neural networks

The stiffness of soft biological tissues not only depends on the applied deformation, but also on the deformation rate. To model this type of behavior, traditional approaches select a specific time-dependent constitutive model and fit its parameters to experimental data. Instead, a new trend now suggests a machine-learning based approach that simultaneously discovers both the best model and best parameters to explain given data. Recent studies have shown that feed-forward constitutive neural networks can robustly discover constitutive models and parameters for hyperelastic materials. However, feed-forward architectures fail to capture the history dependence of viscoelastic soft tissues. Here we combine a feed-forward constitutive neural network for the hyperelastic response and a recurrent neural network for the viscous response inspired by the theory of quasi-linear viscoelasticity. Our novel rheologically-informed network architecture discovers the time-independent initial stress using the feed-forward network and the time-dependent relaxation using the recurrent network. We train and test our combined network using unconfined compression relaxation experiments of passive skeletal muscle and compare our discovered model to a neo Hookean standard linear solid, to an advanced mechanics-based model, and to a vanilla recurrent neural network with no mechanics knowledge. We demonstrate that, for limited experimental data, our new constitutive recurrent neural network discovers models and parameters that satisfy basic physical principles and generalize well to unseen data. We discover a Mooney-Rivlin type two-term initial stored energy function that is linear in the first invariant I1 and quadratic in the second invariant I2 with stiffness parameters of 0.60 kPa and 0.55 kPa. We also discover a Prony-series type relaxation function with time constants of 0.362s, 2.54s, and 52.0s with coefficients of 0.89, 0.05, and 0.03. Our newly discovered model outperforms both the neo Hookean standard linear solid and the vanilla recurrent neural network in terms of prediction accuracy on unseen data. Our results suggest that constitutive recurrent neural networks can autonomously discover both model and parameters that best explain experimental data of soft viscoelastic tissues. Our source code, data, and examples are available at https://github.com/LivingMatterLab.

Estimation of anisotropic properties of CMR patient-specific left ventricle using the virtual field method

Left ventricle (LV) myocardial dysfunction has been recently investigated using the estimation of isotropic myocardial stiffness from magnetic resonance imaging (MRI). However, Myocardium is known to have a 3D complex geometry with anisotropic stiffness. The assessment of the anisotropy properties characterizes structural changes in myocardium as a consequence of heart failure (HF). From image data, the virtual field method (VFM) can determine material stiffness in a non-invasive manner. In the present work, the objective is to compare two inverse identification methods, given the isotropic and anisotropic models in the characterization of properties of myocardium in acute lymphoblastic leukemia (ALL) survivors using VFM and MRI. Two types of VFM approach are presented. Using the first, the virtual displacements (VFs) allow whole-field LV to be imposed into VFM formulation and caused to directly estimate two independent parameters from isotropic constitutive relation. With the second, anisotropic parameters are estimated using piece-wise (Finite element-based) VFM. The resulting values showed significant differences between the subjects in comparative study of leukemia survivors, and variance in estimated parameters by two different VFM approach. This approach would be an efficient tool to characterize early cardiac dysfunction. This work elucidates the benefits and shortcomings of using VFM to determine anisotropic parameters of LV myocardium in linear elastic and of using the FEM application to generate meshes of patient-specific LVs from MRI images.

Proposal and validation of polyconvex strain-energy function for biological soft tissues

BACKGROUND

Mechanical simulations for biological tissues are effective technology for development of medical equipment, because it can be used to evaluate mechanical influences on the tissues. For such simulations, mechanical properties of biological tissues are required. For most biological soft tissues, stress tends to increase monotonically as strain increases.

OBJECTIVE

Proposal of a strain-energy function that can guarantee monotonically increasing trend of biological soft tissue stress-strain relationships and applicability confirmation of the proposed function for biological soft tissues.

METHOD

Based on convexity of invariants, a polyconvex strain-energy function that can reproduce monotonically increasing trend was derived. In addition, to confirm its applicability, curve-fitting of the function to stress-strain relationships of several biological soft tissues was performed.

RESULTS

A function depending on the first invariant alone was derived. The derived function does not provide such inappropriate negative stress in the tensile region provided by several conventional strain-energy functions.

CONCLUSIONS

The derived function can reproduce the monotonically increasing trend and is proposed as an appropriate function for biological soft tissues. In addition, as is well-known for functions depending the first invariant alone, uniaxial-compression and equibiaxial-tension of several biological soft tissues can be approximated by curve-fitting to uniaxial-tension alone using the proposed function.

Personalized intervention cardiology with transcatheter aortic valve replacement made possible with a non-invasive monitoring and diagnostic framework

One of the most common acute and chronic cardiovascular disease conditions is aortic stenosis, a disease in which the aortic valve is damaged and can no longer function properly. Moreover, aortic stenosis commonly exists in combination with other conditions causing so many patients suffer from the most general and fundamentally challenging condition: complex valvular, ventricular and vascular disease (C3VD). Transcatheter aortic valve replacement (TAVR) is a new less invasive intervention and is a growing alternative for patients with aortic stenosis. Although blood flow quantification is critical for accurate and early diagnosis of C3VD in both pre and post-TAVR, proper diagnostic methods are still lacking because the fluid-dynamics methods that can be used as engines of new diagnostic tools are not well developed yet. Despite remarkable advances in medical imaging, imaging on its own is not enough to quantify the blood flow effectively. Moreover, understanding of C3VD in both pre and post-TAVR and its progression has been hindered by the absence of a proper non-invasive tool for the assessment of the cardiovascular function. To enable the development of new non-invasive diagnostic methods, we developed an innovative image-based patient-specific computational fluid dynamics framework for patients with C3VD who undergo TAVR to quantify metrics of: (1) global circulatory function; (2) global cardiac function as well as (3) local cardiac fluid dynamics. This framework is based on an innovative non-invasive Doppler-based patient-specific lumped-parameter algorithm and a 3-D strongly-coupled fluid-solid interaction. We validated the framework against clinical cardiac catheterization and Doppler echocardiographic measurements and demonstrated its diagnostic utility by providing novel analyses and interpretations of clinical data in eleven C3VD patients in pre and post-TAVR status. Our findings position this framework as a promising new non-invasive diagnostic tool that can provide blood flow metrics while posing no risk to the patient. The diagnostic information, that the framework can provide, is vitally needed to improve clinical outcomes, to assess patient risk and to plan treatment.

Artificial papillary muscle device for off-pump transapical mitral valve repair

OBJECTIVE

New transapical minimally invasive artificial chordae implantation devices are a promising alternative to traditional open-heart repair, with the potential for decreased postoperative morbidity and reduced recovery time. However, these devices can place increased stress on the artificial chordae. We designed an artificial papillary muscle to alleviate artificial chordae stresses and thus increase repair durability.

METHODS

The artificial papillary muscle device is a narrow elastic column with an inner core that can be implanted during the minimally invasive transapical procedure via the same ventricular incision site. The device was 3-dimensionally printed in biocompatible silicone for this study. To test efficacy, porcine mitral valves (n = 6) were mounted in a heart simulator, and isolated regurgitation was induced. Each valve was repaired with a polytetrafluoroethylene suture with apical anchoring followed by artificial papillary muscle anchoring. In each case, a high-resolution Fiber Bragg Grating sensor recorded forces on the suture.

RESULTS

Hemodynamic data confirmed that both repairs-with and without the artificial papillary muscle device-were successful in eliminating mitral regurgitation. Both the peak artificial chordae force and the rate of change of force at the onset of systole were significantly lower with the device compared with apical anchoring without the device (P < .001 and P < .001, respectively).

CONCLUSIONS

Our novel artificial papillary muscle could integrate with minimally invasive repairs to shorten the artificial chordae and behave as an elastic damper, thus reducing sharp increases in force. With our device, we have the potential to improve the durability of off-pump transapical mitral valve repair procedures.

Modulating nonlinear elastic behavior of biodegradable shape memory elastomer and small intestinal submucosa(SIS) composites for soft tissue repair

Structural repair of soft tissue for regenerative therapies can be advanced by developing biocompatible and bioresorbable materials with mechanical properties similar to the tissue targeted for therapy. Developing new materials modeling soft tissue mechanics can mitigate many limitations of material based therapies, specifically concerning the mechanical stress and deformation the material imposes on surrounding tissue structures. However, many elastomeric materials used in soft tissue repair lack the ability to be delivered through minimally invasive surgical (MIS) or transcatheter routes and require open surgical approaches for placement and application. We have developed a biocompatible and fully biodegradable shape memory elastomer, poly-(glycerol dodecanedioate) (PGD), which fulfills the requirements for hyperelasticity and exhibits shape memory behavior to serve as a novel substrate material for regenerative therapy in minimally invasive clinical procedures. Our previous work demonstrated control over the tangent modulus at 12.5% compressive strain between 1 and 3 MPa by increasing the crosslinking density in the polymer. In order to improve control over a broader range of mechanical properties, nonlinear behavior, and toughness, we 1) varied PGD physical crosslink density, 2) incorporated sheets of porcine small intestinal submucosa (SIS, Cook Biotech, Inc.) with varying thickness, and 3) mixed lyophilized SIS particulates into PGD at different weight percentages. Tensile testing (ASTM D412a) revealed PGD containing SIS sheets of were stiffer than controls (p < 0.01). Incorporating lyophilized SIS particulates into PGD increased the strain to failure (p < 0.001) compared to PGD controls. Test specimens with 1 ply sheets had greater tear strength (ASTM D624c) compared to PGD tear specimens prepared control specimens (p < 0.001). However, incorporating SIS particulates decreased tear strength of PGD-SIS 0.5 wt% particulate composites (p < 0.01) compared to PGD controls. Incorporating 2 ply and 4 ply sheets and 0.5 wt% particulates into PGD decreased the fixity and recovery of composite materials compared to controls (p < 0.01). Nonlinear modeling of stress strain curves under uniaxial tension demonstrated tunability of PGD-SIS composite materials to model various nonlinear soft tissues. These findings support the use of shape memory PGD-SIS composite materials towards the design of implantable devices for a variety of soft tissue regeneration applications by minimally invasive surgery.

A deformable model for navigated laparoscopic gastrectomy based on finite elemental method

Background: Accurate registration for surgical navigation of laparoscopic surgery is highly challenging due to vessel deformation. Here, we describe the design of a deformable model with improved matching accuracy by applying the finite element method (FEM).Material and methods: ANSYS software was used to simulate an FEM model of the vessel after pull-up based on laparoscopic gastrectomy requirements. The central line of the FEM model and the central line of the ground truth were drawn and compared. Based on the material and parameters determined from the animal experiment, a perigastric vessel FEM model of a gastric cancer patient was created, and its accuracy in a laparoscopic gastrectomy surgical scene was evaluated.Results: In the animal experiment, the FEM model created with Ogden foam material exhibited better results. The average distance between the two central lines was 6.5mm, and the average distance between their closest points was 3.8 mm. In the laparoscopic gastrectomy surgical scene, the FEM model and the true artery deformation demonstrated good coincidence.Conclusion: In this study, a deformable vessel model based on FEM was constructed using preoperative CT images to improve matching accuracy and to supply a reference for further research on deformation matching to facilitate laparoscopic gastrectomy navigation.

Contribution of computational model for assessment of heart tissue local stress caused by suture in LVAD implantation

STUDY

Implantation of a Left Ventricular Assist Device (LVAD) may produce both excessive local tissue stress and resulting strain-induced tissue rupture that are potential iatrogenic factors influencing the success of the surgical attachment of the LVAD into the myocardium. By using a computational simulation compared to mechanical tests, we sought to investigate the characteristics of stress-induced suture material on porcine myocardium.

METHODS

Tensile strength experiments (n = 8) were performed on bulk left myocardium to establish a hyperelastic reduced polynomial constitutive law. Simultaneously, suture strength tests on left myocardium (n = 6) were performed with a standard tensile test setup. Experiments were made on bulk ventricular wall with a single U-suture (polypropylene 3-0) and a PTFE pledget. Then, a Finite Element simulation of a LVAD suture case was performed. Strength versus displacement behavior was compared between mechanical and numerical experiments. Local stress fields in the model were thus analyzed.

RESULTS

A strong correlation between the experimental and the numerical responses was observed, validating the relevance of the numerical model. A secure damage limit of 100 kPa on heart tissue was defined from mechanical suture testing and used to describe numerical results. The impact of suture on heart tissue could be accurately determined through new parameters of numerical data (stress diffusion, triaxiality stress). Finally, an ideal spacing between sutures of 2 mm was proposed.

CONCLUSION

Our computational model showed a reliable ability to provide and predict various local tissue stresses created by suture penetration into the myocardium. In addition, this model contributed to providing valuable information useful to design less traumatic sutures for LVAD implantation. Therefore, our computational model is a promising tool to predict and optimize LVAD myocardial suture.

DYNAMIC ANALYSIS OF HEALTHY AND EDGE-TO-EDGE REPAIRED MITRAL VALVE BEHAVIOR SUBJECTED TO HIGH G ACCELERATIONS

As the mitral leaflets have the greatest area among heart valves and bear the highest pressure load during systole, high G accelerations may result in mitral valve dysfunctions and it might affect the cardiovascular system drastically. In this study, dynamic behavior of healthy and repaired human mitral valves have been numerically simulated during the Early Systolic Phase and the Rapid Filling Phase in a cardiac cycle in high G accelerated environments. The aim of this study is to investigate the effects of accelerations on the stress and strain patterns and the configuration of human mitral valve. The geometrical model of the mitral valve has been developed based on in vivo and ex vivo anatomical measurements and the anisotropic nonlinear behavior of mitral leaflets has been modeled by a discrete constitutive approach. Mitral valve behavior has been simulated using an explicit dynamic finite element method to take into account inertial effects and dynamic responses. Analysis results reveal beside different stress–strain patterns generated on mitral leaflets, abnormal deformed configurations result from accelerations which can affect the circulation and the cardiovascular system. It is observed that situations similar to mitral diseases could rise from high G accelerated environments even though the valve maintains its normal physiological structure.

Unrealistic statistics: how average constitutive coefficients can produce non-physical results

The coefficients of constitutive models are frequently averaged in order to concisely summarize the complex, nonlinear, material properties of biomedical materials. However, when dealing with nonlinear systems, average inputs (e.g. average constitutive coefficients) often fail to generate average behavior. This raises an important issue because average nonlinear constitutive coefficients of biomedical materials are commonly reported in the literature. This paper provides examples which demonstrate that average constitutive coefficients applied to nonlinear constitutive laws in the field of biomedical material characterization can fail to produce average stress-strain responses and in some cases produce non-physical responses. Results are presented from a literature survey which indicates that approximately 90% of tissue measurement studies that employ a nonlinear constitutive model report average nonlinear constitutive coefficients. We suggest that reviewers and editors of future measurement studies discourage the reporting of average nonlinear constitutive coefficients. Reporting of individual coefficient sets for each test sample should be considered and discussed as designation for a "best practice" in the field of biomedical material characterization.

An inverse finite element method for determining the tissue compressibility of human left ventricular wall during the cardiac cycle

The determination of the myocardium's tissue properties is important in constructing functional finite element (FE) models of the human heart. To obtain accurate properties especially for functional modeling of a heart, tissue properties have to be determined in vivo. At present, there are only few in vivo methods that can be applied to characterize the internal myocardium tissue mechanics. This work introduced and evaluated an FE inverse method to determine the myocardial tissue compressibility. Specifically, it combined an inverse FE method with the experimentally-measured left ventricular (LV) internal cavity pressure and volume versus time curves. Results indicated that the FE inverse method showed good correlation between LV repolarization and the variations in the myocardium tissue bulk modulus K (K = 1/compressibility), as well as provided an ability to describe in vivo human myocardium material behavior. The myocardium bulk modulus can be effectively used as a diagnostic tool of the heart ejection fraction. The model developed is proved to be robust and efficient. It offers a new perspective and means to the study of living-myocardium tissue properties, as it shows the variation of the bulk modulus throughout the cardiac cycle.

The mechanics of hyaluronic acid/adipic acid dihydrazide hydrogel: towards developing a vessel for delivery of preadipocytes to native tissues

Promising treatment approaches in repairing tissue defects include implementation of regenerative medicine strategies, particularly delivery of preadipocytes to sites where adipose tissue damage needs to be repaired or where fat needs to be generated. In this study, we suggest that the injectable hyaluronic acid/adipic acid dihydrazide (HA/ADH) hydrogel may be an adipose-tissue-like material in terms of biological compatibility as well as mechanical behavior. First, we show that the hydrogel enables and supports growth, proliferation and differentiation of 3T3-L1 preadipocytes. Second, given that adipose tissue is a weight-bearing biological structure, we investigate the large deformation mechanical behavior of the hydrogel with and without embedded preadipocytes, by performing confined and unconfined compression tests and then calibrating a strain energy density (SED) function to the results. Four test groups were examined: (1) Hydrogel specimens right after the preparation without cells, (2) and (3) 3-days-cultured hydrogel specimens with and without cells, respectively, and (4) 6-days-cultured hydrogel specimens with cells. A one-term Ogden SED was found to adequately describe the hyperelastic behavior of the hydrogel specimens in all experimental groups. Importantly, we found that the mechanical properties of the hydrogel, when subjected to compression, are in good agreement with those of native adipose tissue, with the better fit occurring 3-6 days after preparation of the hydrogel. Third, computational finite element studies of the mechanical (stress-strain) behavior of the HA/ADH hydrogel when containing mature adipocytes indicated that the stiffnesses of the constructs were mildly affected by the presence of the adipocytes. Hence, we conclude that injectable HA/ADH hydrogel may serve as a vessel for protecting preadipocytes during, and at a short-term after delivery to native tissues, e.g. in research towards regenerative medicine in tissue reconstructions.