Pulmonary arterial hypertension (PAH) is a fatal and rapidly progressive disease, and right ventricular failure is the main cause of death in patients with PAH. This study aims to determine the mechanical cues that can trigger the growth and remodelling of the heart. To this end, two bi-ventricular models of a control rat heart and a diseased rat heart with PAH are reconstructed, respectively, and then the growth amount is estimated by warping the PAH heart to the control heart. Finally, correlation analysis between mechanical cues (stress and strain) and growth tensors demonstrates principal strain may be a triggering cue for myocardial growth under PAH

Gao, Hao

Guan, Debao

Tian, Lian

Enlighten

\       Guan, D., Tian, L. and Gao, H. (2022) Growth and Remodelling of Right Ventricle Under Pulmonary Arterial Hypertension. In: 7th International Conference on Computational and Mathematical Biomedical Engineering (CMBE22), Milan, Italy, 27-29 Jun 2022     The material cannot be used for any other purpose without further permission of the publisher and is for private use only.  There may be differences between this version and the published version. You are advised to consult the publisher’s version if you wish to cite from it.    http://eprints.gla.ac.uk/277186/           Deposited on 19 August 2022      Enlighten – Research publications by members of the University of                  Glasgow http://eprints.gla.ac.uk   7th International Conference on Computational and Mathematical Biomedical Engineering - CMBE202127–29 June 2022, ItalyP. Nithiarasu and C. Vergara (Eds.)GROWTH AND REMODELLING OF RIGHT VENTRICLE UNDERPULMONARY ARTERIAL HYPERTENSIONDebao Guan1, Lian Tian2, and Hao Gao11School of Mathematics and Statistics, University of Glasgow, UK,{debao.guan,hao.gao}@glasgow.ac.uk2Strathclyde Institute of Pharmacy and Biomedical Sciences, University of Strathclyde, UK,lian.tian@strath.ac.ukSUMMARYPulmonary arterial hypertension (PAH) is a fatal and rapidly progressive disease, and right ventricularfailure is the main cause of death in patients with PAH. This study aims to determine the mechanicalcues that can trigger growth and remodelling of heart. To this end, two bi-ventricular models of acontrol rat heart and a diseased rat heart with PAH are reconstructed, respectively, then the growthamount is estimated by warping the PAH heart to the control heart. Finally, correlation analysisbetween mechanical cues (stress and strain) and growth tensors demonstrates principal strain may bea triggering cue for the myocardial growth under PAH.Key words: pulmonary arterial hypertension, growth and remodelling, rat heart1 INTRODUCTIONPulmonary arterial hypertension (PAH) is a fatal and rapidly progressive disease with a median sur-vival of 2.8 years if untreated. As PAH progresses, right ventricle (RV) undergoes significant growthand remodelling (G&R), such as hypertrophy, dilatation and fibrosis, and eventually fails to pumpsufficient blood into the pulmonary arteries, leading to death eventually. It is believed that the im-balanced mechanical environment under PAH plays a critical role in triggering RV G&R, while fewstudies have been focused on RV [1], which has historically received little attention from the medi-cal and scientific communities though we appreciate RV is equally essential as the left ventricle [2].Thus, there is an urgent need to develop mathematical models for RV biomechanics.This study aims to develop experiment-informed G&R models to provide new insights into the conse-quences of mechanobiology (strain/stress-driven) in RV failure under PAH for deciphering the onsetof adverse growth and remodelling (G&R) using the controlled rat experiments. Until now, simplifiedrat heart models with preserved main anatomical structures are reconstructed from ultrasound images,in which the left ventricle (LV) is included to provide the support of RV dynamics. The anatomicalchange of RV at different stages is further qualitatively computed through a large deformation diffeo-morphic mapping algorithm, which will be used for informing G&R laws. The preliminary resultsshow that the biomechanical RV-LV model at different PAH stages matches well in vivo pressure-volume loops and echocardiographic wall motions. Estimated growth amounts by comparing normaland PAH hearts show that growth mainly occurs at RV free wall (RVFW) while nearly no growth inthe septum. The correlation analysis shows that stress and strain both play an important role in G&R,with high correlations with principal strain and active tension.2 METHODOLOGY2.1 Animal model of PAH and acquisition of in vivo dataTo develop PAH of animal models, male Sprague Dawley rats received a single subcutaneous injectionof monocrotaline (MCT; 60 mg/kg). Control rats received phosphate-buffered saline (PBS; 2 mL/kg).In week 4 post-injection, MCT rats developed severe PAH. In vivo pressure-volume data were ob-tained via cardiac catherization in closed-chest rats using a micromanometer with high-fidelity 1.9-Frat pressure-volume catheter (Transonic, London, ON, Canada) as described [3]. Ultrasound imagesof long- and short-axis views of the hearts were obtained using a high-frequency ultrasound system(Vevo 2100; Visual Sonics, Toronto, ON, Canada) as shown in Figure 1, where a control rat heart andan MCT rat heart are compared in this work.(a) (b)Figure 1: The long- and short- axis views of the ultrasound images for control (a) and monocrotaline(MCT) rat hearts, respectively. The red curves outline the contours of ventricular walls.2.2 From image data to rat heart models3-D finite element bi-ventricular models of the control and MCT rat hearts in Figure 1 are constructed,and rule-based fibre structures are embedded into the geometries with fibre rotation angle form 60◦ atendocardium to −60◦ at epicardium. Then, lumped models for pulmonary and systemic circulationsystems are attached to the biventricular models in order to provide boundary conditions for diastolicfilling and systolic ejection, as shown in Figure 2.(a) (b)Figure 2: Schematic illustrations of rat heart model under control (a) and MCT (b) with simplecirculation systems and rule-based myofibre structures. f0 − s0 − n0 is the local material coordinatesystem, in which f0 is the local mean fibre direction, s0 is the sheet direction, i.e., transmural directionfrom endocardium to epicardium, and n0 is the sheet-normal direction.It is commonly accepted that the myocardium is a fibre reinforced anisotropic material. Three mainconstituents in myocardium, the ground matrix, myofibres and collagen fibres with the respectivevolume fractions ϕg, ϕm and ϕc, are considered in this study, and the total passive strain energyfunction isΨ = ϕg Ψg + ϕm Ψm + ϕc (Ψf +Ψs +Ψn) (1)where Ψg, Ψm, Ψf, Ψs and Ψn are the strain energy functions associated with the ground matrix,myofibres, collagen fibres parallel to myofibres and collagen fibres cross to myofibres along sheetand sheet-normal directions, and they areΨg =ag2(I1 − 3), Ψm =am2bm{exp[bm(I4m − 1)2]− 1},Ψi =ai2bi{exp[bi(max(I4i/λ2bc, 1)− 1)2]− 1}, i ∈ {f, s, n},(2)where I1 is the trace of right Cauchy–Green deformation tensor, I4i with i ∈ {m, f, s, n} is thesquare of fibre stretch along respective direction, and λbc is activating value, after which collagenfibres begin to contribute. Active contraction is achieved by including active stress σa = Tam̂⊗ m̂,where Ta is the active tension generated by myofibres and m̂ is the unit deformed myofibre direction.2.3 Estimation of growth between the control and MCT heartsHere, we estimate the amount of growth from the control heart to the MCT heart. Deformetrica1,an open-source package based on a large deformation diffeomorphic metric mapping framework, isemployed to warp the control heart to the MCT heart in Figure 2. A dense displacement field isestimated by minimizing a loss function that measures the distance between the external surfaces ofthe control (Cα) and MCT (Cβ) hearts. After warping Cα into Cβ , the displacement field for all nodeson the external surface of Cα is obtained, denoting uEx. The displacement vectors on the nodes lyingwithin the ventricular wall are then interpolated by solving a Laplace system with Dirichlet boundaryconditions, that is∇2u = 0, and u = uEx at external surface. (3)Following the finite deformation theory, the deformation gradient of warping the control heart to theMCT heart isG = ∇u+ I, (4)in which I is the identity matrix. Note that G and u are associated with the control heart, andJ = det(G) represents the volumetric growth amount from the control heart to the MCT heart.Growth amount along each material coordinate is Gij = G : i0 ⊗ j0 with i, j ∈ {f, s, n}.3 RESULTS AND CONCLUSIONSCurrent numerical simulations can reproduce the main characteristics of cardiac functions of rat heartsunder control and MCT states. Figure 3(a) shows the simulated pressure-volume loops of control andMCT rat hearts, in which RV end-systolic pressure increases by 170% from 25 mmHg in the controlheart to 67.5 mmHg in the MCT heart. Reduced RV pump function occurs in the MCT heart, halvedejection fraction of RV (26%) compared to that of the control heart (56%) though the stroke volumesare similar (0.15 ml vs 0.16 ml). The MCT heart also has a slightly decreased LV ejection fractioncompared to the control heart, 58% vs. 55%, which may be caused by the dilated RV that pushes theseptum towards the left side as shown in Figure 1 and thus restrains the diastolic filling of LV.Growth tensor is estimated by Eq. (4) by comparing the control and MCT hearts, and representa-tive element sets are collected from the LV free wall (LVFW), RVFW and the septum, respectively.Figure 3(b) compares the mean value of each entry of the growth tensor, in which growth mainlyoccurs along the fibre, sheet and sheet-normal axial directions. LV has balanced growth along threeorthogonal axes with a mean volumetric growth amount J̄ = 1.75 , whilst RV grows mainly along thesheet direction, i.e., thickening RVFW with J̄ = 2.7, followed by the septum with the least growth(J̄ = 1.3). The septum may have complex growth and remodelling process, as the shear growthcomponents are much bigger than those of LVFW and RVFW.Existing studies have suggested that mechanical cues (stress and stretch) can play a significant role inpathological myocardial growth [4]. Here, we further carried out the correlation analysis between themechanical states (the stress σii and square of stretch I4i along the material coordinates) and estimatedgrowth quantities (Gij). To determine the mechanical cues, we applied the boundary conditions ofthe MCT heart to the control heart. Our results demonstrate that growth tensor correlates with fibrestretch and stress well. For example, Figure 3(e) describes the correlation between the square ofstretch (I4f) at end of diastole and growth amount along the mean fibre direction at the septum, withthe correlation coefficient 0.77 (p < 0.005), whilst the correlations are not significant at LVFW andRVFW (Figure 3(c,d)). Figure 3(e) indicates larger fibre stretch at the septum suppresses the growthalong the mean fibre direction, different from the published growth rules that larger fibre stretch1http://www.deformetrica.org/(a) (b)(c) (d) (e)Figure 3: (a) Pressure-volume loops of the Control and MCT rat hearts. (b) Mean value of each entryin growth tensors at LVFW, RVFW and septum, respectively, from the Control shape to the MCTshape. Correlation relationship between square of fibre stretch (I4f) at end of diastole and growthamount along the mean fibre direction at LVFW (c), RVFW (d), and septum (e), respectively.contributes to bigger growth [4], this may be due to the complex growth tensor in the septum withlarge shear components.Our models based on ultrasound image data can achieve physiological cardiac functions under bothnormal and diseased conditions. The methodology to estimate growth tensor by warping the con-trol heart to the MCT heart provides an achievable approach to quantify growth amount along eachmaterial axis. Our results further show myocardial growth not only is spatially heterogeneous butalso is correlated with certain mechanical cues. The next work is to develop a high-fidelity G&Rrat RV model by combining detailed experiments with advanced mathematical modelling, which cancharacterize the adaptation of RV structure and function during the progression of PAH.Acknowledgement We are grateful for the funding provided by the UK EPSRC (EP/T017899/1,EP/S030875/1). D.Guan also acknowledges the funding from the school of mathematics and statistics,University of Glasgow through the EPSRC additional funding for mathematical science.REFERENCES[1] Avazmohammadi, R., Mendiola, E. A., Li, D. S., Vanderslice, P., Dixon, R. A. F., and Sacks, M.S.. Interactions between structural remodeling and hypertrophy in the right ventricle in responseto pulmonary arterial hypertension. Journal of biomechanical engineering, 141(9): 091016,2019.[2] Guan, D., Yao, J., Luo, X., and Gao, H.. Effect of myofibre architecture on ventricular pumpfunction by using a neonatal porcine heart model: from DT-MRI to rule-based methods. RoyalSociety open science, 7(4), 191655, 2020.[3] Tian, L., Xiong, P. Y., Alizadeh, E., Lima, P. D., Potus, F., Mewburn, J., ... and Archer, S. L.Supra-coronary aortic banding improves right ventricular function in experimental pulmonaryarterial hypertension in rats by increasing systolic right coronary artery perfusion. Acta Physio-logica, 229(4), e13483, 2020.[4] Göktepe, S., Abilez, O. J., Parker, K. K., and Kuhl, E.. A multiscale model for eccentric andconcentric cardiac growth through sarcomerogenesis. Journal of theoretical biology, 265(3),433-442, 2010.

Growth and Remodelling of Right Ventricle Under Pulmonary Arterial Hypertension

https://eprints.gla.ac.uk/277186/2/277186.pdf

Growth and Remodelling of Right Ventricle Under Pulmonary Arterial Hypertension

Abstract

Similar works

Full text

Available Versions

Enlighten