publications

2024

1. Impact of tricuspid annuloplasty device shape and size on valve mechanics—a computational study

   Collin E. Haese, Mrudang Mathur, Chien-Yu Lin, and 3 more authors

   JTCVS Open, 2024
2. Geometric data of commercially available tricuspid valve annuloplasty devices

   Collin E. Haese, Mrudang Mathur, Marcin Malinowski, and 2 more authors

   Data in Brief, 2024
3. Leaflet remodeling reduces tricuspid valve function in a computational model

   Mrudang Mathur, Marcin Malinowski, Tomasz Jazwiec, and 2 more authors

   Journal of the Mechanical Behavior of Biomedical Materials, 2024

2023

1. Untangling the mechanisms of pulmonary arterial hypertension-induced right ventricular stiffening in a large animal model

   Sotirios Kakaletsis, Marcin Malinowski, J. Caleb Snider, and 8 more authors

   Acta Biomaterialia, 2023
2. Valvular Complex and Tissue Remodeling in Ovine Functional Tricuspid Regurgitation

   Artur Iwasieczko, Manikantam Gaddam, Boguslaw Gaweda, and 8 more authors

   European Journal of Cardio-Thoracic Surgery, Mar 2023

   Abs

   Pathophysiology of function tricuspid regurgitation (FTR) is incompletely understood. We set out to comprehensively evaluate geometric and tissue remodeling of the tricuspid valve complex in ovine FTR.Twenty adult sheep underwent left thoracotomy and pulmonary artery banding (PAB) to induce right heart pressure overload and FTR. After 8 weeks, 17 surviving animals and 10 healthy controls (CTL) underwent sternotomy, echocardiography, and implantation of sonomicrometry crystals on right ventricle and tricuspid valvular apparatus. Hemodynamic and sonomicrometry data were acquired in all animals after weaning from cardiopulmonary bypass. Leaflet tissue was harvested for pentachrome histologic analysis and biomechanical testing.Animal weight was 62±5 and 63±3 kg for CTL and PAB, respectively (p = 0.6). At terminal procedure, systolic pulmonary artery pressure was 22±3 and 40±7 mmHg for CTL and PAB, respectively (p = 0.0001). Mean TR grade (+0-4) was 0.8±0.4 and 3.2±1.2 (p = 0.0001) for control and banded animals, respectively. RV volume (126±13 vs 172±34 ml, p = 0.0019), tricuspid annular area (651±109 vs 865±247 mm2, p = 0.037), and area between papillary muscle tips (162±51 vs 302±75 mm2, p = 0.001) increased substantially while systolic excursion of anterior leaflet decreased significantly (23.8±6.1 vs 7.4±4.5 deg, p = 0.001) with banding. Total leaflet surface area increased from 806±94 to 953±148 mm2 (p = 0.009), and leaflets became thicker and stiffer.Detailed analysis of the tricuspid valve complex revealed significant ventricular, annular, subvalvular, and leaflet remodeling to be associated with ovine functional tricuspid regurgitation. Durable surgical repair of severe FTR may require a multi-level approach to the valvular apparatus.

3. A brief note on building augmented reality models for scientific visualization

   Mrudang Mathur, Josef M. Brozovich, and Manuel K. Rausch

   Finite Elements in Analysis and Design, Mar 2023

   Abs

   Augmented reality (AR) has revolutionized the video game industry by providing interactive, three-dimensional visualization. Interestingly, AR technology has only been sparsely used in scientific visualization. This is, at least in part, due to the significant technical challenges previously associated with creating and accessing such models. To ease access to AR for the scientific community, we introduce a novel visualization pipeline with which they can create and render AR models. We demonstrate our pipeline by means of finite element results, but note that our pipeline is generally applicable to data that may be represented through meshed surfaces. Specifically, we use two open-source software packages, ParaView and Blender. The models are then rendered through the ¡model-viewer¿ platform, which we access through Android and iOS smartphones. To demonstrate our pipeline, we build AR models from static and time-series results of finite element simulations discretized with continuum, shell, and beam elements. Moreover, we openly provide python scripts to automate this process. Thus, others may use our framework to create and render AR models for their own research and teaching activities.

2022

1. The impact of thickness heterogeneity on soft tissue biomechanics: a novel measurement technique and a demonstration on heart valve tissue

   Chien-Yu Lin, Mrudang Mathur, Marcin Malinowski, and 2 more authors

   Biomechanics and Modeling in Mechanobiology, Oct 2022
2. Biomechanical phenotyping of minuscule soft tissues: An example in the rodent tricuspid valve

   William D. Meador, Mrudang Mathur, Sotirios Kakaletsis, and 3 more authors

   Extreme Mechanics Letters, Aug 2022

   Abs

   The biomechanical phenotype of soft tissues – i.e., the sum of spatially- and directionally-varying mechanical properties – is a critical marker of tissue health and disease. While biomechanical phenotyping is always challenging, it is particularly difficult with minuscule tissues. For example, tissues from small animal models are often only millimeters in size, which prevents the use of traditional test methods, such as uniaxial tensile testing. To overcome this challenge, our current work describes and tests a novel experimental and numerical pipeline. First, we introduce a micro-bulge test device with which we pressurize and inflate minuscule soft tissues. We combine this micro-bulge device with an optical coherence tomography device to also image the samples during inflation. Based on pressure data and images we then perform inverse finite element simulations to identify our tissues’ unknown material parameters. For validation, we identify the material parameters of a thin sheet of latex rubber via both uniaxial tensile testing and via our novel pipeline. Next, we demonstrate our pipeline against anterior tricuspid valve leaflets from rats. The resulting material parameters for these tissues compare excellently with data collected in sheep via standard planar biaxial testing. Additionally, we show that our device is compatible with other imaging modalities such as 2-Photon microscopy. To this end, we image the in-situ microstructural changes of the leaflets during inflation using second-harmonic generation imaging. In summary, we introduce a novel pipeline to biomechanically phenotype minuscule soft tissues and demonstrate its value by phenotyping the biomechanics of the anterior tricuspid valve leaflets from rats.

3. Texas TriValve 1.0 : a reverse-engineered, open model of the human tricuspid valve

   Mrudang Mathur, William D. Meador, Marcin Malinowski, and 3 more authors

   Engineering with Computers, May 2022

   Abs

   Nearly 1.6 million Americans suffer from a leaking tricuspid heart valve. To make matters worse, current valve repair options are far from optimal leading to recurrence of leakage in up to 30% of patients. We submit that a critical step toward improving outcomes is to better understand the “forgotten” valve. High-fidelity computer models may help in this endeavour. However, the existing models are limited by averaged or idealized geometries, material properties, and boundary conditions. In our current work, we overcome the limitations of existing models by (reverse) engineering the tricuspid valve from a beating human heart in an organ preservation system. The resulting finite-element model faithfully captures the kinematics and kinetics of the native tricuspid valve as validated against echocardiographic data and others’ previous work. To showcase the value of our model, we also use it to simulate disease-induced and repair-induced changes to valve geometry and mechanics. Specifically, we simulate and compare the effectiveness of tricuspid valve repair via surgical annuloplasty and via transcatheter edge-to-edge repair. Importantly, our model is openly available for others to use. Thus, our model will allow us and others to perform virtual experiments on the healthy, diseased, and repaired tricuspid valve to better understand the valve itself and to optimize tricuspid valve repair for better patient outcomes.

2021

1. Right ventricular myocardial mechanics: Multi-modal deformation, microstructure, modeling, and comparison to the left ventricle

   Sotirios Kakaletsis, William D Meador, Mrudang Mathur, and 6 more authors

   Acta Biomaterialia, Mar 2021
2. Tricuspid Valve Anterior Leaflet Strains in Ovine Functional Tricuspid Regurgitation

   Tomasz Jazwiec, Marcin J. Malinowski, Haley Ferguson, and 4 more authors

   Seminars in Thoracic and Cardiovascular Surgery, Mar 2021
3. Tricuspid Chordae Tendineae Mechanics: Insertion Site, Leaflet, and Size-Specific Analysis and Constitutive Modelling

   K J Smith, M Mathur, W D Meador, and 7 more authors

   Experimental Mechanics, Jan 2021

   Abs

   Background: Tricuspid valve chordae tendineae play a vital role in our cardiovascular system. They function as “parachute cords” to the tricuspid leaflets to prevent prolapse during systole. However, in contrast to the tricuspid annulus and leaflets, the tricuspid chordae tendineae have received little attention. Few previous studies have described their mechanics and their structure-function relationship. Objective: In this study, we aimed to quantify the mechanics of tricuspid chordae tendineae based on their leaflet of origin, insertion site, and size. Methods: Specifically, we uniaxially stretched 53 tricuspid chordae tendineae from sheep and recorded their stress-strain behavior. We also analyzed the microstructure of the tricuspid chordae tendineae based on two-photon microscopy and histology. Finally, we compared eight different hyperelastic constitutive models and their ability to fit our data. Results: We found that tricuspid chordae tendineae are highly organized collageneous tissues, which are populated with cells throughout their thickness. In uniaxial stretching, this microstructure causes the classic J-shaped nonlinear stress-strain response known from other collageneous tissues. We found differences in stiffness between tricuspid chordae tendineae from the anterior, posterior, or septal leaflets only at small strains. Similarly, we found significant differences based on their insertion site or size also only at small strains. Of the models we fit to our data, we recommend the Ogden two-parameter model. This model fit the data excellently and required a minimal number of parameters. For future use, we identified and reported the Ogden material parameters for an average data set. Conclusion: The data presented in this study help to explain the mechanics and structure-function relationship of tricuspid chordae tendineae and provide a model recommendation (with parameters) for use in computational simulations of the tricuspid valve.

2020

1. The tricuspid valve also maladapts as shown in sheep with biventricular heart failure

   William D. Meador, Mrudang Mathur, Gabriella P. Sugerman, and 6 more authors

   eLife, Dec 2020

   Abs

   Over 1.6 million Americans suffer from significant tricuspid valve leakage. In most cases this leakage is designated as secondary. Thus, valve dysfunction is assumed to be due to valve-extrinsic factors. We challenge this paradigm and hypothesize that the tricuspid valve maladapts in those patients rendering the valve at least partially culpable for its dysfunction. As a first step in testing this hypothesis, we set out to demonstrate that the tricuspid valve maladapts in disease. To this end, we induced biventricular heart failure in sheep that developed tricuspid valve leakage. In the anterior leaflets of those animals, we investigated maladaptation on multiple scales. We demonstrated alterations on the protein and cell-level, leading to tissue growth, thickening, and stiffening. These data provide a new perspective on a poorly understood, yet highly prevalent disease. Our findings may motivate novel therapy options for many currently untreated patients with leaky tricuspid valves.

2. Tricuspid Valve Annuloplasty Alters Leaflet Mechanics

   Mrudang Mathur, William D. Meador, Tomasz Jazwiec, and 3 more authors

   Annals of Biomedical Engineering, Dec 2020

   Abs

   Tricuspid valve regurgitation is associated with significant morbidity and mortality. Its most common treatment option, tricuspid valve annuloplasty, is not optimally effective in the long-term. Toward identifying the causes for annuloplasty’s ineffectiveness, we have previously investigated the technique’s impact on the tricuspid annulus and the right ventricular epicardium. In our current work, we are extending our analysis to the anterior tricuspid valve leaflet. To this end, we adopted our previous strategy of performing DeVega suture annuloplasty as an experimental methodology that allows us to externally control the degree of cinching during annuloplasty. Thus, in ten sheep we successively cinched the annulus and quantified changes to leaflet motion, dynamics, and strain in the beating heart by combining sonomicrometry with our well-established mechanical framework. We found that successive cinching of the valve enforced earlier coaptation and thus reduced leaflet range of motion. Additionally, leaflet angular velocity during opening and closing decreased. Finally, we found that leaflet strains were also reduced. Specifically, radial and areal strains decreased as a function of annular cinching. Our findings are critical as they suggest that suture annuloplasty alters the mechanics of the tricuspid valve leaflets which may disrupt their resident cells’ mechanobiological equilibrium. Long-term, such disruption may stimulate tissue maladaptation which could contribute to annuloplasty’s sub-optimal effectiveness. Additionally, our data suggest that the extent to which annuloplasty alters leaflet mechanics can be controlled via degree of cinching. Hence, our data may provide direct surgical guidelines.

3. Tricuspid Annuloplasty Rings: A Quantitative Comparison of Size, Nonplanar Shape, and Stiffness

   Mrudang Mathur, Marcin Malinowski, Tomasz A Timek, and 1 more author

   The Annals of Thoracic Surgery, Nov 2020

   Abs

   Background: Functional tricuspid regurgitation due to annular and ventricular dilatation is increasingly recognized as a significant source of morbidity and mortality. To repair the annulus, surgeons implant one of many annuloplasty devices that differ in size, 3-dimensional (3D) shape, and stiffness. However, there have been no quantitative comparisons between various available devices. Methods: Three-dimensional scanning, micro-computed tomography imaging, analytical methods, and mechanical tests were used to compare 3 Edwards Lifesciences (Irvine, CA) and 3 Medtronic (Minneapolis, MN) annuloplasty devices of all available sizes. We measured in-plane metrics of maximum diameter, perimeter, area, height, as well as elevation and curvature profiles. Furthermore, we computed bending stiffness as well as the maximum and minimum axes of the bending stiffness. Results: Most annular prostheses differed little in their in-plane geometries but varied significantly in height. In-plane properties deviated significantly from measurements of healthy human tricuspid annuli. Height of the Edwards’ MC3 and Medtronic’s Contour 3D resembled healthy human tricuspid valve annuli, whereas the Edwards’ Physio and Classic, and Medtronic’s TriAd, did not. Additionally, the elevation profiles of the MC3 and Contour 3D and curvature profiles between all devices were consistent and matched those of healthy human annuli. The tested devices also differed in their bending stiffness, both in terms of absolute values and their maximum and minimum axes. Conclusions: Contoured devices, such as Edwards’ MC3 and Medtronic’s Contour 3D, most accurately resembled the healthy human tricuspid annulus but differed significantly in bending stiffness. To what extent prosthesis properties and shape affect tricuspid valve function remains to be determined.

4. The Effect of Downsizing on the Normal Tricuspid Annulus

   Mrudang Mathur, William D. Meador, Tomasz Jazwiec, and 3 more authors

   Annals of Biomedical Engineering, Feb 2020

   Abs

   Tricuspid annuloplasty is a surgical procedure that cinches the valve’s annulus in order to reduce regurgitant blood flow. One of its critical parameters is the degree of downsizing. To provide insight into the effect of downsizing, we studied the annulus of healthy sheep during suture annuloplasty. To this end, we implanted fiduciary markers along the annulus of sheep and subsequently performed a DeVega suture annuloplasty. We performed five downsizing steps in each animal while recording hemodynamic and sonomicrometry data in beating hearts. Subsequently, we used splines to approximate the annulus at baseline and at each downsizing step. Based on these approximations we computed clinical metrics of annular shape and dynamics, and the continuous field metrics height, strain, and curvature. With these data, we demonstrated that annular area reduction during downsizing was primarily driven by compression of the anterior annulus. Similarly, reduction in annular dynamics was driven by reduced contractility in the anterior annulus. Finally, changes in global height and eccentricity of the annulus could be explained by focal changes in the continuous height profile and changes in annular curvature. Our findings are important as they provide insight into a regularly performed surgical procedure and may inform the design of transcatheter devices that mimic suture annuloplasty.

5. A detailed mechanical and microstructural analysis of ovine tricuspid valve leaflets

   William D. Meador, Mrudang Mathur, Gabriella P. Sugerman, and 5 more authors

   Acta Biomaterialia, Jan 2020

   Abs

   The tricuspid valve ensures unidirectional blood flow from the right atrium to the right ventricle. The three tricuspid leaflets operate within a dynamic stress environment of shear, bending, tensile, and compressive forces, which is cyclically repeated nearly three billion times in a lifetime. Ostensibly, the microstructural and mechanical properties of the tricuspid leaflets have mechanobiologically evolved to optimally support their function under those forces. Yet, how the tricuspid leaflet microstructure determines its mechanical properties and whether this relationship differs between the three leaflets is unknown. Here we perform a microstructural and mechanical analysis in matched ovine tricuspid leaflet samples. We found that the microstructure and mechanical properties vary among the three tricuspid leaflets in sheep. Specifically, we found that tricuspid leaflet composition, collagen orientation, and valve cell nuclear morphology are spatially heterogeneous and vary across leaflet type. Furthermore, under biaxial tension, the leaflets’ mechanical behaviors exhibited unequal degrees of mechanical anisotropy. Most importantly, we found that the septal leaflet was stiffer in the radial direction and not the circumferential direction as with the other two leaflets. The differences we observed in leaflet microstructure coincide with the varying biaxial mechanics among leaflets. Our results demonstrate the structure-function relationship for each leaflet in the tricuspid valve. We anticipate our results to be vital toward developing more accurate, leaflet-specific tricuspid valve computational models. Furthermore, our results may be clinically important, informing differential surgical treatments of the tricuspid valve leaflets. Finally, the identified structure-function relationships may provide insight into the homeostatic and remodeling potential of valvular cells in altered mechanical environments, such as in diseased or repaired tricuspid valves. Statement of significance: Our work is significant as we investigated the structure-function relationship of ovine tricuspid valve leaflets. This is important as tricuspid valves fail frequently and our current approach to repairing them is suboptimal. Specifically, we related the distribution of structural and cellular elements, such as collagen, glycosaminoglycans, and cell nuclei, to each leaflet’s mechanical properties. We found that leaflets have different structures and that their mechanics differ. This may, in the future, inform leaflet-specific treatment strategies and help optimize surgical outcomes.

2019

1. Effect of carotid artery stenosis on neck skin tissue heat transfer

   Ashish Saxena, E. Y.K. Ng, Mrudang Mathur, and 2 more authors

   International Journal of Thermal Sciences, Nov 2019

   Abs

   The buildup of plaque in the carotid artery leads to the narrowing of the arterial lumen, known as stenosis. Arterial stenosis affects the supply of blood to the brain and may result in stroke if the plaque is dislodged. This study aims to evaluate stenosis influenced hemodynamics of the carotid artery and its effect on the bio-heat transfer to the external neck skin surface. Systolic and Diastolic carotid artery flow inlet conditions, using a finite volume numerical scheme, are simulated with the inclusion of varied stenosis degree in the carotid model (25%–90%). A 3-dimensional (3D) conjugate heat transfer study is performed on an idealized carotid artery geometry, encapsulated in a tissue model resembling the human neck. With no significant difference in the average external neck skin temperature, variation in the temperature contours is observed between stenosed and non-stenosed cases. With the increase in the carotid artery stenosis, a quantitative change, the presence of a colder region called ‘cold feature’, in external neck skin temperature features is reported. This numerical study will prove to be a strong basis for future patient-specific evaluations.

2. Tricuspid valve leaflet strains in the beating ovine heart

   M. Mathur, T. Jazwiec, W. D. Meador, and 5 more authors

   Biomechanics and Modeling in Mechanobiology, Oct 2019

   Abs

   The tricuspid leaflets coapt during systole to facilitate proper valve function and, thus, ensure efficient transport of deoxygenated blood to the lungs. Between their open state and closed state, the leaflets undergo large deformations. Quantification of these deformations is important for our basic scientific understanding of tricuspid valve function and for diagnostic or prognostic purposes. To date, tricuspid valve leaflet strains have never been directly quantified in vivo. To fill this gap in our knowledge, we implanted four sonomicrometry crystals per tricuspid leaflet and six crystals along the tricuspid annulus in a total of five sheep. In the beating ovine hearts, we recorded crystal coordinates alongside hemodynamic data. Once recorded, we used a finite strain kinematic framework to compute the temporal evolutions of area strain, radial strain, and circumferential strain for each leaflet. We found that leaflet strains were larger in the anterior leaflet than the posterior and septal leaflets. Additionally, we found that radial strains were larger than circumferential strains. Area strains were as large as 97% in the anterior leaflet, 31% in the posterior leaflet, and 31% in the septal leaflet. These data suggest that tricuspid valve leaflet strains are significantly larger than those in the mitral valve. Should our findings be confirmed they could suggest either that the mechanobiological equilibrium of tricuspid valve resident cells is different than that of mitral valve resident cells or that the mechanotransductive apparatus between the two varies. Either phenomenon may have important implications for the development of tricuspid valve-specific surgical techniques and medical devices.

3. Biomechanics of the tricuspid annulus: A review of the annulus’ in vivo dynamics with emphasis on ovine data

   Manuel K. Rausch, Mrudang Mathur, and William D. Meador

   GAMM-Mitteilungen, Sep 2019

   Abs

   The tricuspid annulus forms the boundary between the tricuspid valve leaflets and their surrounding perivalvular tissue of the right atrioventricular junction. Its shape changes throughout the cardiac cycle in response to the forces from the contracting right heart myocardium and the blood-valve interaction. Alterations to annular shape and dynamics in disease lead to valvular dysfunctions such as tricuspid regurgitation from which millions of patients suffer. Successful treatment of such dysfunction requires an in-depth understanding of the normal shape and dynamics of the tricuspid annulus and of the changes following disease and subsequent repair. In this manuscript we review what we know about the shape and dynamics of the normal tricuspid annulus and about the effects of both disease and repair based on noninvasive imaging studies and invasive fiduciary marker-based studies. We further show, by means of ovine data, that detailed engineering analyses of the tricuspid annulus provide regionally resolved insight into the kinematics of the annulus which would remain hidden if limiting analyses to simple geometric metrics.

4. Tricuspid valve biomechanics: A brief review

   William D. Meador, Mrudang Mathur, and Manuel K. Rausch

   In Advances in Heart Valve Biomechanics: Valvular Physiology, Mechanobiology, and Bioengineering, Sep 2019

   Abs

   The mechanics of the tricuspid valve are poorly understood. Today’s unsatisfying outcomes of tricuspid valve surgery, at least in part, may be due to this lack of knowledge. Therefore, the tricuspid valve in general, and its mechanics specifically, have recently received an increasing interest. This chapter briefly summarizes what we currently know about tricuspid valve mechanics. To this end, we separately review tricuspid leaflet mechanics, annular mechanics, and the chordae’s mechanics. Moreover, we categorize our discussion by the experimental environment in which these tissues were studied: in vivo, in vitro, and in silico. Finally, we make suggestions as to which areas of tricuspid valve mechanics should receive additional attention from the biomechanics community.