Cardiovascular diseases (CVDs) are the leading cause of mortality and morbidity today, myocardial
infarction (MI) an effect of IschaemicHeartDisease (IHD) contributes to the majority of such cases,
accounting for upto 31 % of global mortality. Advancements in medical diagnostics, interventions,
therapies and prognosis are hindered by the complex dynamics within tissuemicro-structure due
to observed changes after the onset of a disease. Modelling and simulation of soft tissue growth
and remodelling proves to be a significant tool to simulate instances of disease progression and
provide results helpful towards the medical field.
A 1D novel constrained mixture model of the left ventricular myocardiumis presented using an
incompressible, isotropic, elastic, sphericalmembrane approximation, taking into consideration
the micro-structural constituents i.e. ground matrix, cardiomyocytes and collagen fibres. The
constituents are assigned strain energy functions, along with mass density terms to account
for their quantitative presence in the tissue. Collagen fibre stretches are represented with a
distribution function accounting for their existence in different stretches in the tissue. Scenarios
are presented where the homoeostatic state of the collagen fibres adapt via evolution of the
distribution function, which provide understanding on the configurations and mass changes that
could be simulated to understand their implications on the structure and function of the tissue. It
was observed that the model simulates plausible changes in the tissue function when collagen
fibres are configured in the load bearing configuration rather than in the crimped form.
A soft tissue growth and remodelling framework (STGRF) developed in Python, around the finite
element simulation package (ANSYS ® Mechanical APDL) provides us with tools to develop
biomechanical problems pertaining to the built-in fibre-reinforced, hyperelastic, incompressible
soft tissue material model; employing stress-based differential equations for simulating tissue
remodelling and growth. A key feature is the abstraction of the underlying coding using high
level Python scripts, to ease the end-user into focussing on their research problem rather than
be encumbered by programming ideologies. The STGRF, sees it’s applications in two distinct
problems in this thesis. (A) An idealised LV subjected to myocardial infarction, using stressbased
formulations to simulate tissue extra-cellular matrix adaptation to the progression of the
disease. A fibroblast field, mediated by the collagen fibre stretches is introduced to regulate
growth/ atrophy of the collagen mass density in the myocardium. Two cases are explored to
understand the impact of evolving homoeostatic Cauchy stresses for each volume element, versus,
a constant homoeostatic Cauchy stress state which the tissue attempts to maintain throughout
the time period of the disease. Lower dilatations in the wall structure and lower mass deposition
is observed when evolving the homoeostatic stress. (B) A finite element model of the medial
gastrocnemiusmuscle subjected to sustained overstretch is considered and remodelling of the
muscle and tendinous regions is observed. The novelty lies in the definition of themuscle, tendon and aponeurosis regions, reflected in the material parameter ascription to said regions. Using
stress-based differential equations, remodelling of the muscle and tendinous regions are observed
with varying rate constants. The model is purely exploratory in terms of remodelling of the distinct
regions in the gastrocnemius muscle and future sophistications could aid in better understanding
rehabilitation therapies, surgical techniques involved in muscle extension or purely adaptation to
a variety of external mechanical stimuli and environments.
Mathematical and computational modelling enables us replicate models based on specific elements
in disease which are difficult to capture experimentally or clinically. This sheds light on
the possiblemechanisms in play and delineate the processes in order to better understand the
changes in tissue structure and function.
