A generative model of hyperelastic strain energy density functions for multiple tissue brain deformation

PURPOSE: Estimation of brain deformation is crucial during neurosurgery. Whilst mechanical characterisation captures stress-strain relationships of tissue, biomechanical models are limited by experimental conditions. This results in variability reported in the literature. The aim of this work was to demonstrate a generative model of strain energy density functions can estimate the elastic properties of tissue using observed brain deformation. METHODS: For the generative model a Gaussian Process regression learns elastic potentials from 73 manuscripts. We evaluate the use of neo-Hookean, Mooney-Rivlin and 1-term Ogden meta-models to guarantee stability. Single and multiple tissue experiments validate the ability of our generative model to estimate tissue properties on a synthetic brain model and in eight temporal lobe resection cases where deformation is observed between pre- and post-operative images. RESULTS: Estimated parameters on a synthetic model are close to the known reference with a root-mean-square error (RMSE) of 0.1 mm and 0.2 mm between surface nodes for single and multiple tissue experiments. In clinical cases, we were able to recover brain deformation from pre- to post-operative images reducing RMSE of differences from 1.37 to 1.08 mm on the ventricle surface and from 5.89 to 4.84 mm on the resection cavity surface. CONCLUSION: Our generative model can capture uncertainties related to mechanical characterisation of tissue. When fitting samples from elastography and linear studies, all meta-models performed similarly. The Ogden meta-model performed the best on hyperelastic studies. We were able to predict elastic parameters in a reference model on a synthetic phantom. However, deformation observed in clinical cases is only partly explained using our generative model

Development of a Spinal Cord Injury Model using the Material Point Method

Spinal cord injury (SCI) is characterised by permanent loss of motor and sensory function. The primary damage from the initial mechanical insult is exacerbated by the secondary patho-physiological cascade. Research into neuroprotective interventions to preserve tissue and reduce the damage caused by the secondary injury is hampered, in part, due to a lack of understanding of the link between the biomechanics of the primary traumatic injury and the subsequent evolution of the secondary injury. Hence, there is a need to better understand the biomechanics of SCI, the distinct injury patterns produced, and how these affect the evolution of the secondary cascade. Computational models using finite element methods (FEM) have been established as a useful tool for investigating SCI biomechanics. These may be used to obtain data that is difficult or impossible to capture through in vivo and in vitro experiments, in particular; stress and strain fields within the neural tissue. However, the complexity of these models is limited by difficulties. These include: problems coping with large deformations over short periods of time due to mesh tangling, difficulties in incorporating the fluid structure interactions, and scalability issues when attempting to make use of high performance computing facilities, utilising large numbers of processors. This work has involved the creation of a computational spinal cord injury using the Material Point Method (MPM) and MPMICE (MPM for Implicit, Continuous Fluid, Eulerian), alternative computational methods that overcome these limitations. The model incorporates the neural spinal cord tissue, the dura mater, and the cerebrospinal fluid. This model has been validated against equivalent experimental and FEM results. MPM/MPMICE was found to be a viable alternative to FEM for modelling SCI computationally, with the potential to enable more complex and anatomically detailed models through the utilisation of increased parallel computation

Unraveling the complexity of vascular tone regulation: a multiscale computational approach to integrating chemo-mechano-biological pathways with cardiovascular biomechanics

Vascular tone regulation is a crucial aspect of cardiovascular physiology, with significant implications for overall cardiovascular health. However, the precise physiological mechanisms governing smooth muscle cell contraction and relaxation remain uncertain. The complexity of vascular tone regulation stems from its multiscale and multifactorial nature, involving global hemodynamics, local flow conditions, tissue mechanics, and biochemical pathways. Bridging this knowledge gap and translating it into clinical practice presents a challenge. In this paper, a computational model is presented to integrate chemo-mechano-biological pathways with cardiovascular biomechanics, aiming to unravel the intricacies of vascular tone regulation. The computational framework combines an algebraic description of global hemodynamics with detailed finite element analyses at the scale of vascular segments for describing their passive and active mechanical response, as well as the molecular transport problem linked with chemo-biological pathways triggered by wall shear stresses. Their coupling is accounted for by considering a two-way interaction. Specifically, the focus is on the role of nitric oxide-related molecular pathways, which play a critical role in modulating smooth muscle contraction and relaxation to maintain vascular tone. The computational framework is employed to examine the interplay between localized alterations in the biomechanical response of a specific vessel segment—such as those induced by calcifications or endothelial dysfunction–and the broader global hemodynamic conditions—both under basal and altered states. The proposed approach aims to advance our understanding of vascular tone regulation and its impact on cardiovascular health. By incorporating chemo-mechano-biological mechanisms into in silico models, this study allows us to investigate cardiovascular responses to multifactorial stimuli and incorporate the role of adaptive homeostasis in computational biomechanics frameworks

Patient-specific simulation for autonomous surgery

An Autonomous Robotic Surgical System (ARSS) has to interact with the complex anatomical environment, which is deforming and whose properties are often uncertain. Within this context, an ARSS can benefit from the availability of patient-specific simulation of the anatomy. For example, simulation can provide a safe and controlled environment for the design, test and validation of the autonomous capabilities. Moreover, it can be used to generate large amounts of patient-specific data that can be exploited to learn models and/or tasks. The aim of this Thesis is to investigate the different ways in which simulation can support an ARSS and to propose solutions to favor its employability in robotic surgery. We first address all the phases needed to create such a simulation, from model choice in the pre-operative phase based on the available knowledge to its intra-operative update to compensate for inaccurate parametrization. We propose to rely on deep neural networks trained with synthetic data both to generate a patient-specific model and to design a strategy to update model parametrization starting directly from intra-operative sensor data. Afterwards, we test how simulation can assist the ARSS, both for task learning and during task execution. We show that simulation can be used to efficiently train approaches that require multiple interactions with the environment, compensating for the riskiness to acquire data from real surgical robotic systems. Finally, we propose a modular framework for autonomous surgery that includes deliberative functions to handle real anatomical environments with uncertain parameters. The integration of a personalized simulation proves fundamental both for optimal task planning and to enhance and monitor real execution. The contributions presented in this Thesis have the potential to introduce significant step changes in the development and actual performance of autonomous robotic surgical systems, making them closer to applicability to real clinical conditions

Stochastic modelling and analysis of homogeneous hyperelastic solids

Combining finite elasticity and information theory, a stochastic method is devel oped in order to accurately predict and assess the behaviour of materials, and also to model experimental data. An explicit strategy to calibrate homogeneous isotropic hyperelastic models to mean values and the standard deviation of ei ther the stress-strain function or the nonlinear shear modulus is devised, and the technique of using Bayes Theorem to select the optimal model to represent the ma terial or data in question is presented, specifically here in relation to manufactured silicone specimens. An analysis of the behaviour of solid materials under various deformations, including necking instability, the inflation of cylindrical tubes and spheres, and the cavitation of spherical shells, when the material is stochastic, is demonstrated, before an extension to the dynamic finite deformations of stochastic hyperelastic solids, including the shear motion of a cuboid, the quasi-equilibrated radial-axial motion of a cylindrical tube, and the quasi-equilibrated radial motion of a spherical shell, is explored. Ultimately, it is determined that the amplitude and period of oscillation of stochastic bodies are characterised by probability dis tributions. Overall, the aim is to highlight the need for mathematical modelling to consider the variability obtained in experimental data, in the mechanical re sponses of materials, or in testing protocols, with a view to enhancing the accuracy of the mathematical modelling techniques employed, and, as a result, to provide an improved assessment or prediction of the behaviour of the materials in question

Debonding and stretching of biogenic cellular structures

Plant material can regulate the mechanical properties of its cellular structure by changing: (i) the structure of the cell wall, (ii) the cell core pressure, and (iii) the cell-cell cohesion. The relevant scale at which such phenomena occur, though beyond the capacity of the human eye, can be followed by mechanical analysis and mathematical models based on micro-structural evidence. This thesis focuses on two fundamental mechanical aspects. First, it concerns the mechanism of cell debonding, as this is key in explaining the softening of fruit and legumes during storage or cooking, and is decisive for the perceived quality of food products. Particular attention is given to the mathematical modelling of damage through shear deformation as this has been largely neglected in the literature due to many theoretical and computational difficulties. Second, it provides a multiscale hyperelastic framework which relates the stresses and strains of a whole structure to those at the cell level, and vice versa. Specifically, the non-linear elastic moduli at the macroscopic level are derived systematically from those at the cell level