Computational Biomechanics for Medicine

In this chapter the concept of computational vademecum is presented and analyzed in detail when applied for the real-time simulation in the field of computational surgery. In essence, a computational vademecum is an off-line computer simulation of a physical process in which different variables have been considered as parameters, thus giving rise to a high-dimensional problem. To avoid the numerical difficulties associated with meshing high-dimensional domains, and also their respective post-processing, proper generalized decomposition (PGD) methods have been employed. These allow to express the high-dimensional solution as a finite sum of separable functions, that can be post-processed on-line at tremendously high feedback rates, even on the order of kHz.

Most of the abdominal aortic aneurysms (AAA) include an intraluminal thrombus (ILT) deposited on their internal wall. Active proteolytic enzymes in the ILT may cause bio-chemically weakening the aneurysmal wall, which leads to elevation of the aneurysm rupture risk. On the other hand, lack of oxygen on the aneurysmal wall beneath a thick ILT (hypoxia) causes proteolytic activity on the wall as a secondary effect. In this paper we develop an axisymmetric growth and remodeling model of the AAA considering the bio-chemical effects of the ILT mentioned above. We then estimate the model parameters using nine patients’ longitudinal CT data. The parametric study shows that AAA’s radius and volume increases significantly in existence of ILT because of both hypoxia and proteolytic activity. However, the relation between the AAA volume and its maximum diameter slightly changes due to hypoxia while this relation highly changes because of the proteolytic activity in the luminal layer of the ILT. We also show that our numerical results for the AAA expansion as a function of its maximum diameter can be very close to the clinical data with a proper estimation of the model parameters.

In this paper we present a three-dimensional (3D) tumourous cell growth model using a hybrid cellular automata (CA) and continuum-based method. The CA model is employed to simulate the competition between normal and cancer cells, whilst the continuum model is used for quantifying the oxygen diffusion in a 3D domain. A set of rules are implemented to govern cancerous/normal cell colony evolution. The vasculature, which is the constant source of oxygen and nutrients, is simulated using a constrained constructive optimization (CCO) algorithm. The diffusion equation of oxygen across the domain with an additional term to describe the oxygen uptake by cells was solved using a finite difference scheme. With this method we are able to simulate cancer cell growth under various hypoxia and oxygenated scenarios. It is clear from the simulations that different parameters in the diffusion equation and CA rules lead to drastically different growth patterns which may be physiologically relevant. In conclusion the proposed computational method provides a flexible framework that can be further extended to incorporate drug effects and intracellular signalling models.

We present an algorithm for modelling swelling and shrinking of soft tissues based on the total Lagrangian formulation of the finite element (FE) method. Explicit time integration with adaptive dynamic relaxation is used to compute the steady state solution. The algorithm can easily handle geometric and material nonlinearities, and is very efficient because it allows pre-computation of important solution parameters and does not require solution of large systems of equations. Swelling and shrinking behaviour is modelled by applying a multiplicative decomposition of the deformation gradient to separate the total deformation into swelling/shrinking and elastic components. A hyperelastic constitutive law is used to model the elastic behaviour of the material. Accuracy of the algorithm is confirmed by successful verification against an established FE code. The algorithm involves only vector operations and is well suited for parallel implementation for increased computational speed.

We briefly review the iterative solution of the inverse problem in elasticity, which is posed as a constrained optimization method. The objective function minimizes the discrepancy between a measured and a computed displacement field in the L-2 norm and is subject to the static equations of equilibrium in elasticity. We realize that this inverse formulation is sensitive to Dirichlet and Neumann boundary conditions, i.e., sensitive to varying spatial deformations in the region of interest. This problem arises in particular, when solving the inverse problem for more than one inclusion in a homogeneous background, where the inclusions represent diseased tissues such as cysts, benign tumors, malignant tumors, etc. In order to address this issue, we propose to introduce a new formulation of the objective function, where the displacement correlation term is spatially weighted. We refer to this new formulation as the spatially weighted objective function and show that it improves the uniqueness of the inverse problem solution.

In applications where the organic soft tissue undergoes large deformations, traditional finite element methods can fail due to element distortion. In this context, meshless methods, which require no mesh for defining the interpolation field, can offer stable solutions. In meshless method, the moving least square (MLS) shape functions have been widely used for approximating the unknown field functions using the scattered field nodes. However, the classical MLS places strict requirements on the nodal distributions inside the support domain in order to maintain the non-singularity of the moment matrix. These limitations are preventing the practical use of higher order polynomial basis in classical MLS for randomly distributed nodes despite their capability for more accurate approximation of complex deformation fields. A modified moving least squares (MMLS) approximation has been recently developed by ISML. This paper assesses the interpolation capabilities of the MMLS. The proposed meshless method based on MMLS is used for computing the extension of a soft tissue sample and for a brain deformation simulation in 2D. The results are compared with the commercial finite element software ABAQUS. The simulation results demonstrate the superior performance of the MMLS over classical MLS with linear basis functions in terms of accuracy of the solution.

We propose a new methodology for automated landmark detection for breast MR images that combines statistical shape modelling and template matching into a single framework. The method trains a statistical shape model (SSM) of breast skin surface using 30 manually labelled landmarks, followed by generation of template patches for each landmark. Template patches are matched across the unseen image to produce correlation maps. Correlation maps of the landmarks and the shape model are used to generate a first estimate of the landmarks referred to as “shape predicted landmarks”. These landmarks are refined using local maximum search in individual landmarks correlation maps. The algorithm was validated on 30 MR images using a leave-one-out approach. The results reveal that the method is robust and capable of localising landmarks with an error of 3.41 ± 2.10 mm.

This study investigated mechanical properties of brain–skull interface, important for surgery simulation and injury biomechanics. Direct examination of brain–skull interface is difficult due to its delicate nature and complex geometry that follows the skull and brain surface. Hence, we conducted uniaxial compression tests on samples containing skull, meninges and brain. We combined sophisticated measurement data with non-linear finite element analysis to obtain the properties of brain–skull interface. Skull was considered a rigid object as forces obtained were very small to induce any measurable deformation on it. Surface contact model between brain and skull was used to simulate the brain–skull interface. Good correlation between sample deformation in experiment and simulation was used to confirm the brain–skull interface property.

The Corvis ST is a new clinical device that records in vivo cross-sectional images showing corneal deformation during application of a focussed air pulse. The aim of this work was to use a fluid–structure interaction (FSI) analysis to simulate this scenario. The one-way coupling of FSI was based on the multi-field analysis (MFX) framework within the ANSYS software. The pressure forces generated from the air pulse were used as the boundary condition to drive the corneal deformation. In this preliminary work a nonlinear isotropic Neo-Hookean material was used to model the cornea. The data generated from the Corvis device, such as the applanation length, the cornea deflection amplitude, and the original image sequence, were used to calibrate and validate the corneal model. In conclusion this work established the FSI pipeline for analysis of the biomechanical properties of the cornea using the Corvis device.

Patient-specific respiratory motion modeling may help to understand pathophysiology and predict therapy planning. The respiratory motion modifies the shape and position of internal organs. This may degrade the quality of such medical acts as radiotherapy or laparoscopy. Predicting the breathing movement is complex, and it is considered as one of the most challenging areas of medical research. This paper presents a biomechanical model of the respiratory system, based on the finite element method (FEM), including the biomechanical behavior of the diaphragm as well as rib kinematics computations, on the assumption that breathing is controlled by two independent actors: the thorax and diaphragm muscles. In order to predict the type of the (geometrical or material) nonlinearities, a quantitative comparison of the clinical data was applied on 12 patients. We propose two nonlinear hyperelastic models: the Saint-Venant Kirchhoff and Mooney–Rivlin models. Our results demonstrate that the nonlinear hyperelastic Mooney–Rivlin model of the diaphragm behaves similarly to the linear elastic model with large displacement (Saint-Venant Kirchhoff). The results suggest that the approach of small strains (within the large displacement) may be globally maintained in the modeling of the diaphragm, and demonstrate that the accuracy of the proposed FEM is capable to predict the respiratory motion with an average surface error in a diaphragm/lungs region of interest contact of 2. 0 ± 2. 3 mm for the contact surface between lungs and diaphragm. The comparison study between the FEM simulations and the CT scan images demonstrates the effectiveness of our physics-based model.

Clinical evaluation of the mechanical condition in musculoskeletal soft tissues is challenging due to the wide range in morphology, size, and function of the anatomical structures. Virtual biomechanical simulations in 3D anatomical models reconstructed from medical imaging provide an instrument to receive feedback on realistic mechanics and deformation, but require an adequate computational representation of the anisotropic fibrous architecture. In this study, we investigate the application of a Laplacian based approach as a collective basis to generate fiber bundle orientations in 3D anatomical models of the various musculoskeletal soft tissue structures. Methodological adaptations for specific cases are evaluated, while feasibility is demonstrated in anatomical examples of muscles and joint connective tissue structures.

Periacetabular osteotomy (PAO) is an effective approach for surgical treatment of hip dysplasia in young patients. The aim of PAO is to increase acetabular coverage of the femoral head and to reduce contact pressures by reorienting the acetabulum fragment after PAO. The success of PAO significantly depends on the surgeon’s experience. Previously, we have developed a computer-assisted planning and navigation system for PAO, which allows for not only quantifying the 3D hip morphology with geometric parameters such as acetabular orientation (expressed as inclination and anteversion angles), lateral center edge (LCE) angle, and femoral head coverage for a computer-assisted diagnosis of hip dysplasia but also virtual PAO surgical planning and simulation. In this paper, based on this previously developed PAO planning and navigation system, we developed a patient-specific 3D finite element (FE) model to investigate the optimal acetabulum reorientation after PAO. Our experimental results showed that an optimal position of the acetabulum can be achieved that maximizes contact area and at the same time minimizes peak contact pressure in pelvic and femoral cartilages. In conclusion, our computer-assisted planning and navigation system with FE modeling can be a promising tool to determine the optimal PAO planning strategy.