A Coupled Finite Element Model of Tumor Growth and Vascularization

Lloyd, Bryn; Szczerba, Dominik; Székely, Gábor

doi:10.1007/978-3-540-75759-7_106

Cited by 15 publications

(20 citation statements)

References 22 publications

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“…The growth model was presented in our previous paper (Lloyd et al 2007) and will only briefly be described here in order to keep this paper self-contained. Tumour development is assumed to be relatively slow; therefore, it is reasonable to surmise that over time the neighbouring tissue will accommodate for the stretching by increased growth or cell migration.…”

Section: (A ) Tissue Growthmentioning

confidence: 99%

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A computational framework for modelling solid tumour growth

Lloyd

Szczerba

Rudin

et al. 2008

Phil. Trans. R. Soc. A.

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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.

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Section: (A ) Tissue Growthmentioning

confidence: 99%

“…A first attempt for computational implementation is presented in Lloyd et al (2007). Here, we continue by including a detailed cellular-level simulation of oxygen transport to the tissue.…”

Section: Introductionmentioning

confidence: 99%

A computational framework for modelling solid tumour growth

Lloyd

Szczerba

Rudin

et al. 2008

Phil. Trans. R. Soc. A.

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“…West et al [20] shows that, regardless of the different masses and development times, mammals, birds, fishes, and mollusks, all share a common exponential tumor growth pattern. In this letter, we also assume the tumor growth follows this exponential law, which is defined as follows: (6) where, a, b, c, and d are the growth coefficients. The curve fitting based on the nonlinear least-squares method is used for computing the predicted ρ.…”

Section: F Tumor Growth Predictionmentioning

confidence: 99%

“…Representative methods include mathematical models [2], [3], [19], cellular automata [4], finite element [3], [5], [19], and angiogenesis-based methods [6].…”

Section: Introductionmentioning

confidence: 99%

FEM Based 3D Tumor Growth Prediction for Kidney Tumor

Chen

Summers

Yao

2010

Lecture Notes in Computer Science

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It is important to predict the tumor growth so that appropriate treatment can be planned in the early stage. In this letter, we propose a finite-element method (FEM)-based 3-D tumor growth prediction system using longitudinal kidney tumor images. To the best of our knowledge, this is the first kidney tumor growth prediction system. The kidney tissues are classified into three types: renal cortex, renal medulla, and renal pelvis. The reaction-diffusion model is applied as the tumor growth model. Different diffusion properties are considered in the model: the diffusion for renal medulla is considered as anisotropic, while those of renal cortex and renal pelvis are considered as isotropic. The FEM is employed to solve the diffusion model. Themodel parameters are estimated by the optimization of an objective function of overlap accuracy using a hybrid optimization parallel search package. The proposed method was tested on two longitudinal studies with seven time points on five tumors. The average true positive volume fraction and false positive volume fraction on all tumors is 91.4% and 4.0%, respectively. The experimental results showed the feasibility and efficacy of the proposed method.

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“…The quantitative analysis of the barium sulfate stained vessels of the tumor, however, remains questionable, since significant parts are not stained and parameters such as the bifurcation probability versus vessel diameter cannot be meaningfully extracted. Therefore, the value of our study for the validation of computer simulations on the tumor formation [8] is limited. Here, it is highly desirable to improve the spatial resolution of phase contrast techniques that usually offer enough contrast to visualize the vessel tree without any stain even in formalin solution [2].…”

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confidence: 99%

Visualization of tumor vessels using synchrotron radiation-based micro computed tomography

Lang

Dominietto

Müller

2009

J. Phys.: Conf. Ser.

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Abstract. The visualization of the vascular network is a prerequisite to understand the formation of cancerous tissue. Synchrotron radiation-based micro computed tomography (SR CT) provides the necessary micrometer resolution, to image the vessels down to the 3 to 5 m wide capillaries, the contrast differences between vessels and surrounding tissue, however, are too weak. Thus, in the present study highly X-ray absorbing barium sulfate micro-particles, which cannot penetrate through healthy vessel walls, were injected into the vessels. The acquired tomography data show that the stained vessels of the tumor tissue have different morphology and density with respect to the surrounding healthy tissue. The vessels of the cancerous tissue often exhibit spiral shapes.

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A Coupled Finite Element Model of Tumor Growth and Vascularization

Cited by 15 publications

References 22 publications

A computational framework for modelling solid tumour growth

A computational framework for modelling solid tumour growth

FEM Based 3D Tumor Growth Prediction for Kidney Tumor

Visualization of tumor vessels using synchrotron radiation-based micro computed tomography

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