An updated Lagrangian constrained mixture model of pathological cardiac growth and remodelling

Progressive left ventricular (LV) growth and remodelling (G & R) is often induced by volume and pressure overload, characterized by structural and functional adaptation through myocyte hypertrophy and ex-tracellular matrix remodelling, which are dynamically regulated by biomechanical factors, inflammation, neurohormonal pathways, etc. When prolonged, it can eventually lead to irreversible heart failure. In this study, we have developed a new framework for modelling pathological cardiac G & R based on constrained mixture theory using an updated reference configuration, which is triggered by altered biomechanical factors to restore biomechanical homeostasis. Eccentric and concentric growth, and their combination have been explored in a patient-specific human LV model under volume and pressure overload. Eccentric growth is triggered by overstretching of myofibres due to volume overload, i.e. mitral regurgitation, whilst concentric growth is driven by excessive contractile stress due to pressure overload, i.e. aortic stenosis. Different biological constituent's adaptations under pathological conditions are integrated together, which are the ground matrix, myofibres and collagen network. We have shown that this constrained mixture -motivated G & R model can capture different phenotypes of maladaptive LV G & R, such as chamber dilation and wall thinning under volume overload, wall thickening under pressure overload, and more complex patterns under both pressure and volume overload. We have further demonstrated how collagen G & R would affect LV structural and functional adaption by providing mechanistic insight on anti-fibrotic inter-ventions. This updated Lagrangian constrained mixture based myocardial G & R model has the potential to understand the turnover processes of myocytes and collagen due to altered local mechanical stimuli in heart diseases, and in providing mechanistic links between biomechanical factors and biological adaption at both the organ and cellular levels. Once calibrated with patient data, it can be used for assessing heart failure risk and designing optimal treatment therapies.Computational modelling of cardiac G & R has shown high promise to provide insight into heart disease management when mechanistic understandings are quantified between biomechanical factors and un-derlying cellular adaptation processes. The kinematic growth theory has been dominantly used to phe-nomenologically describe the biological G & R process but neglecting underlying cellular mechanisms. We have developed a constrained mixture based G & R model with updated reference by taking into ac-count different mechanobiological processes in the ground matrix, myocytes and collagen fibres. This G & R model can serve as a basis for developing more advanced myocardial G & R models further informed by patient data to assess heart failure risk, predict disease progression, select the optimal treatment by hypothesis testing, and eventually towards a truly precision cardiology using in-silico models.& COPY; 2023 The Author(s). Published by Elsevier Ltd on behalf of Acta Materialia Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )