Bryn A. Lloyd

Identification of Spring Parameters for Deformable Object Simulation

Mass spring models are frequently used to simulate deformable objects because of their conceptual simplicity and computational speed. Unfortunately, the model parameters are not related to elastic material constitutive laws in an obvious way. Several methods to set optimal parameters have been proposed but, so far, only with limited success. We analyze the parameter identification problem and show the difficulties, which have prevented previous work from reaching wide usage. Our main contribution is a new method to derive analytical expressions for the spring parameters from an isotropic linear elastic reference model. The method is described and expressions for several mesh topologies are derived. These include triangle, rectangle, and tetrahedron meshes. The formulas are validated by comparing the static deformation of the MSM with reference deformations simulated with the finite element method.

MIDA: A Multimodal Imaging-Based Detailed Anatomical Model of the Human Head and Neck

Computational modeling and simulations are increasingly being used to complement experimental testing for analysis of safety and efficacy of medical devices. Multiple voxel- and surface-based whole- and partial-body models have been proposed in the literature, typically with spatial resolution in the range of 1–2 mm and with 10–50 different tissue types resolved. We have developed a multimodal imaging-based detailed anatomical model of the human head and neck, named “MIDA”. The model was obtained by integrating three different magnetic resonance imaging (MRI) modalities, the parameters of which were tailored to enhance the signals of specific tissues: i) structural T1- and T2-weighted MRIs; a specific heavily T2-weighted MRI slab with high nerve contrast optimized to enhance the structures of the ear and eye; ii) magnetic resonance angiography (MRA) data to image the vasculature, and iii) diffusion tensor imaging (DTI) to obtain information on anisotropy and fiber orientation. The unique multimodal high-resolution approach allowed resolving 153 structures, including several distinct muscles, bones and skull layers, arteries and veins, nerves, as well as salivary glands. The model offers also a detailed characterization of eyes, ears, and deep brain structures. A special automatic atlas-based segmentation procedure was adopted to include a detailed map of the nuclei of the thalamus and midbrain into the head model. The suitability of the model to simulations involving different numerical methods, discretization approaches, as well as DTI-based tensorial electrical conductivity, was examined in a case-study, in which the electric field was generated by transcranial alternating current stimulation. The voxel- and the surface-based versions of the models are freely available to the scientific community.

A computational framework for modelling solid tumour growth

The biology of cancer is a complex interplay of many underlying processes, taking place at different scales both in space and time. A variety of theoretical models have been developed, which enable one to study certain components of the cancerous growth process. However, most previous approaches only focus on specific aspects of tumour development, largely ignoring the influence of the evolving tumour environment. In this paper, we present an integrative framework to simulate tumour growth, including those model components that are considered to be of major importance. We start by addressing issues at the tissue level, where the phenomena are modelled as continuum partial differential equations. We extend this model with relevant components at the cellular or even sub-cellular level in a vertical fashion. We present an implementation of this framework, covering the major processes and treat the mechanical deformation due to growth, the biochemical response to hypoxia, blood flow, oxygenation and the explicit development of a vascular system in a coupled way. The results demonstrate the feasibility of the approach and its applicability to in silico studies of the influence of different treatment strategies (like the usage of novel anti-cancer drugs) for more effective therapy design.

A coupled finite element model of tumor growth and vascularization

We present a model of solid tumor growth which can account for several stages of tumorigenesis, from the early avascular phase to the angiogenesis driven proliferation. The model combines several previously identified components in a consistent framework, including neoplastic tissue growth, blood and oxygen transport, and angiogenic sprouting. First experiments with the framework and comparisons with observations made on solid tumors in vivo illustrate the plausibility of the approach. Explanations of several experimental observations are naturally provided by the model. To the best of our knowledge this is the first report of a model coupling tumor growth and angiogenesis.

Modeling intravasation of liquid distension media in surgical simulators

During therapeutic hysteroscopy and transurethral resection of the prostate, intravasation of the liquid distension media into the vascular system of the patient occurs. We present a model which allows the integration of the intravasation process into surgical simulator systems. A linear network flow model is extended with a correction for non-Newtonian blood behavior in small vessels and an appropriate handling of vessel compliance. We employ a fast lookup scheme in order to allow for real-time simulation. Cutting of tissue is accounted for by adjusting pressure boundary conditions for all cut vessels. We investigate the influence of changing distention fluid pressure settings and of the position of tissue cuts. In addition, we quantify the intravasation occurring with different approaches of fluid control, and we compare the performance of direct and iterative solvers applied to the non-linear system of the compliant model. Our simulation predicts significant intravasation only on the venous side, and just in cases when larger veins are cut. The implemented methods allow the realistic control of bleeding for short-term and of the total resulting intravasation volume for long-term complication scenarios. While the simulation is fast enough to support real-time training, it is also adequate for explaining intravasation effects which were previously observed on a phenomenological level only.

Identification of Dynamic Mass Spring Parameters for Deformable Body Simulation

Mass spring systems (MSS) are frequently used to simulate deformable objects because of their conceptual simplicity and computational speed. Unfortunately, the model parameters (spring coefficients, masses) are not related to material constitutive laws in an obvious way. In our earlier work we proposed a method, which can be used to relate the parameters of the MSS to constitutive models, often used in continuum mechanics. In this report we have used this strategy to develop new formulae for the dynamic MSS parameters, i.e. the masses and the damping coefficients. This is the first report which identifies the damper coefficients analytically. In this work we restrict our attention to triangular meshes. Experimental evidence is given in support of our results.

A Multiphysics Model of Myoma Growth

We present a first attempt to create an in-silico model of a uterine leiomyoma, a typical exponent of a common benign tumor. We employ a finite element model to investigate the interaction between a chemically driven growth of the pathology and the mechanical response of the surrounding healthy tissue. The model includes neoplastic tissue growth, oxygen and growth factor transport as well as angiogenic sprouting. Neovascularisation is addressed implicitly by modeling proliferation of endothelial cells and their migration up the gradient of the angiogenic growth factor, produced in hypoxic regions of the tumor. The response of the surrounding healthy tissue in our model is that of a viscoelastic material, whereby a stress exerted by expanding neoplasm is slowly dissipated. By incorporating the interplay of four underlying processes we are able to explain experimental findings on the pathologys phenotype. The model has a potential to become a computer simulation tool to study various growing conditions and treatment strategies and to predict post-treatment conditions of a benign tumor.

Modelling intravasation of liquid distension media in surgical simulators

We simulate the intravasation of liquid distention media into the systemic circulation as it occurs during hysteroscopy and transurethral resection of the prostate. A linear network flow model is extended with a correction for non-newtonian blood behaviour in small vessels and an appropriate handling of vessel compliance. We then integrate a fast lookup scheme in order to allow for real-time simulation. Cutting of tissue is accounted for by adjusting pressure boundary conditions for all cut vessels. We investigate the influence of changing distention fluid pressure settings and of the position of tissue cuts. Our simulation predicts significant intravasation only on the venous side, and just in cases when larger veins are cut. The implemented methods allow the realistic control of bleeding for short-term and the total resulting intravasation volume for long-term complication scenarios. While the simulation is fast enough to support real-time training, it is also adequate for explaining intravasation effects which were previously observed on a phenomenological level only.

A Mechano-Chemical Model of a Solid Tumor for Therapy Outcome Predictions

Experimental investigations of tumors often result in data reflecting very complex underlying mechanisms. Computer models of such phenomena enable their analysis and may lead to novel and more efficient therapy strategies. We present a generalized finite element mechano-chemical model of a solid tumor and assess its suitability for predicting therapy outcome. The model includes hosting tissue, tumor cells (vital and necrotic), nutrient, blood vessels and a growth inhibitor. At a certain time instant of the tumor development virtual therapies are performed and their outcomes are presented. The model is initiated with parameters either obtained directly from the available literature or estimated using multi-scale modeling. First results indicate the usefulness of multi-physics tumor models for predicting therapy response.

Optimization of case-specific vascular tree models based on vessel size imaging

We analyze a problem, which is relevant for physiological modeling of vascular networks: the initialization and optimization of specific, individual models of a functioning vessel network. We do not try to describe the process of growing vessels. Rather, the model properties are optimized via similarity metrics between the artificial vessel network and suitable image data. A vascular network model has many degrees of freedom to optimize and it can be assumed that there are many different optimal solutions. In order to reduce the variability between different solutions we enforce certain physiological properties, for instance Murrays Law, which must be fulfilled by an optimal network. We propose and validate several similarity metrics, which can be used to optimize the radii of the vascular tree.