Search

Physical forces are recognized to play a critical role in shaping the micro-environment of tumors. Compression of cancer and stromal cells, as well as blood and lymphatic vessels, are direct consequences of mechanical solid stress, the compressive and tensile mechanical forces exerted by the solid components of the tissue. By altering the mechanical micro-environment of tumors, elevated solid stress can affect their pathophysiology, driving tumors to more aggressive phenotypes and compromise therapeutic outcome [1]. Mechanical stress also affects healthy tissue: It causes neuronal loss in brain tissue [2], and is linked to neurological deficits and reduced survival in patients with glioblastoma (GBM) [3], the most common malignant primary brain tumor in adults. Given their far-reaching micro- and macroscopic consequences, tumor-induced mechanical forces may provide mechanistic insights into inter and intra-tumor heterogeneities, differential response to treatment and other phenotypical characteristics. In this contribution, we survey the literature of spatial tumor growth modeling from a perspective of macroscopic tissue mechanics to assess the current status of mechanically-coupled growth models and to identify opportunities for further research: We summarize the types of modeling approaches previously used for capturing tumor-induced mechanical effects and their biological or physiological consequences. Based on this review, we identify the scenarios in which accounting for tissue mechanics proved to improve calibration to and prediction of clinical data. Drawing from examples of our [4] and others’ research on mechanically-coupled growth modeling for GBM, we discuss challenges involved in the implementation and calibration of such models. In this context, we identify areas of mechanically-coupled growth modeling where further research is needed and explore application opportunities that such models may open.

Data in support of modeling assumptions

Data in support of results

Mathematical analysis of CARRGO model structural identifyability

Elevated tumor mass-effect is associated to poor prognosis in GBM [1,2]. However, tumor mass-effect is poorly quantified in clinical practice. Recently, Steed et al. [2] proposed ‘Lateral ventricle displacement’ (LVd), defined as the change in center-of-mass position of the lateral ventricles between an undeformed reference and the tumor-bearing anatomy, as quantitative imaging measure of mass-effect. They found that the magnitude of LVd in GBM patients can be associated with overall survival. These results show the clinical importance of tumor mass-effect in GBM, warranting robust clinical measures. This study characterizes image-derived estimates of tumor mass-effect by their ability to measure mass-effect accurately and reliably. We use a mathematical model to simulate tumor growth, which allows us to control and objectively quantify ‘mass-effect’ [3]. For given simulation parameters and growth location, we compute estimates of mass-effect from anatomical deformation during the growth process. We use multiple regression analysis to evaluate the ability of different estimates to explain the tumor’s objective mass-effect, measured by the tumor-induced pressure on the skull. References: [1] Gamburg et al. IJROBP, 2000, 48, 5: 1359–62 [2] Steed et al. Scientific Reports, 2018, 8: 2827 [3] Abler et al. Neuro-Oncology, 2017, 19, suppl 6: vi245.

Glioblastoma (GBM) is the most frequent malignant brain tumor in adults. Its growth is characterized by infiltration of surrounding healthy tissue, and the formation of a necrotic core. GBM presents with varying degree of mass-effect which results in healthy-tissue deformation, midline shift or herniation. Biomechanical forces, such as those resulting from displacive tumor growth, shape the tumor environment, contribute to tumor progression [1] and may affect treatment response and outcome. We hypothesize that different growth “phenotypes” can be distinguished by mathematical models that estimate the forces responsible for tissue displacement. However, most approaches for estimating brain tumor growth parameters from patient imaging do not account for the tumor’s mass-effect. We have previously developed a mechanically–coupled reaction-diffusion model [2] that captures three dominant aspects of macroscopic GBM growth: (a) tumor cell proliferation, (b) the diffuse invasion of the growing tumor into surrounding healthy tissue, and (c) the resulting mass effect. Here, we propose an optimization approach to estimate three patient-specific parameters of this model: tumor cell proliferation rate, cell motility, as well as a coupling coefficient that links local tumor cell concentration to tumor-induced mechanical strains. The forward problem is solved using the Finite Element Method. The inverse problem is formulated as a PDE constrained optimization problem that aims at minimizing the difference between observed and predicted tumor cell distribution and induced displacements. Target fields are inferred from magnetic resonance (MR) images at different observation time points. The efficient solution of the inverse problem relies on the adjoint method and FENICS dolphin-adjoint [3] for its implementation. Performance of the parameter estimation approach was evaluated on synthetic data generated by solving the forward problem on a brain atlas. MR images from the public TCGA-GBM data set were used for tests on clinical data. References [1] R. K. Jain et al. Annu. Rev. Biomed. Eng. 16.1 (2014), pp. 321–346. [2] D. Abler and P. Büchler. CMBBE. Ed. by A. Gefen and D. Weihs (2018), pp. 57–64. [3] P. Farrell, et al. SIAM J. Sci. Comput 35.4 (2013), pp. C369-C393.

Glioblastoma (GBM), the most frequent malignant brain tumor in adults, is char- acterized by rapid growth and healthy tissue invasion. Long-term prognosis for GBM remains poor with median overall survival between 1 y to 2 y [15]. GBM presents with different growth phenotypes, ranging from invasive tumors without notable mass-effect to strongly displacing lesions. Biomechanical forces, such as those resulting from displacive tumor growth, shape the tumor environment and contribute to tumor progression [9]. We present an extended version of a mechanically–coupled reaction-diffusion model of brain tu- mor growth [1] that simulates tumor evolution over time and across different brain regions using literature-based parameter estimates for tumor cell proliferation, as well as isotropic motility, and mechanical tissue properties. This model yielded realistic estimates of the mechanical impact of a growing tumor on intra-cranial pressure. However, comparison to imaging data showed that asymmetric shapes could not be reproduced by isotropic growth assumptions. We modified this model to account for structural tissue anisotropy which is known to affect the directionality of tumor cell migration and may influence the mechanical behavior of brain tissue. Tumors were seeded at multiple locations in a human MR-DTI brain atlas and their spatio-temporal evolution was simulated using the Finite-Element Method. We evaluated the impact of tissue anisotropy on the model’s ability to reproduce the aspherical shapes of real pathologies by comparing predicted lesions to publicly available GBM imaging data. We found the impact on tumor shape to be strongly location dependent and highest for tumors located in brain regions that are characterized by a single dominant white matter direction, such as the corpus callosum. However, despite strongly anisotropic growth assumptions, all simulated tumors remained more spherical than real lesions at the corresponding location and similar volume. This finding is in agreement with previous studies [17, 6] suggesting that anisotropic cell migration along white matter fiber tracks is not a major determinant of tumor shape in the setting of reaction-diffusion based tumor growth models and for most locations across the brain.

BACKGROUND A large proportion of age-related fecal incontinence is attributed to weakness or degeneration of the muscles composing the anal continence organ. However, the individual role of these muscles and their functional interplay remain poorly understood. METHODS This study employs a novel technique based on the combination of MR imaging and FLIP measurements (MR-FLIP) to obtain anatomical and mechanical information simultaneously. Unlike previous methods used to assess the mechanics of the continence organ, MR-FLIP allows inter-individual comparisons and statistical analysis of the sphincter morpho-mechanical parameters. The anatomy as well as voluntary and involuntary mechanical properties of the anal continence organ were characterized in 20 healthy senior volunteers. RESULTS Results showed that the external anal sphincter (EAS) forms a funnel-like shape with wall thickness increasing by a factor of 2.5 from distal (6 ± 0 mm) to proximal (15 ± 3 mm). Both voluntary and involuntary mechanical properties in this region correlate strongly with the thickness of the muscle. The positions of least compliance and maximal orifice closing were both located toward the proximal EAS end. In addition, maximal contraction during squeeze maneuvers was reached after 2 s, but high muscle fatigue was measured during a 7 s holding phase, corresponding to about 60% loss of the energy produced by the muscles during the contraction phase. CONCLUSIONS This work reports baseline parameters describing the morpho-mechanical condition of the sphincter muscle of healthy elderly volunteers. New parameters were also proposed to quantify the active properties of the muscles based on the mechanical energy associated with muscle contraction and fatigue. This information could be used to assess patients suffering from AI or for the design of novel implants.

GBMs present with different growth phenotypes, ranging from invasive lesions without notable mass-effect to strongly displacing lesions that induce mechanical stresses and result in healthy-tissue deformation, midline shift or herniation. Biomechanical forces, such as those resulting from displacive tumor growth, are recognized to shape the tumor environment and to contribute to tumor progression. We therefore expect that biomechanical forces exerted by lesions on the brain parenchyma have implications on the biophysical level, and that they may affect treatment response and outcome. To better understand the role of biomechanics in the formation of different GBM phenotypes we started developing a framework for the predictive mathematical modeling of mechanical tumor-healthy tissue interaction on the macroscopic level. The tumor’s mass-effect is represented by a solid-mechanics model of brain tissue that computes tumor-induced strain based on local tumor cell concentration. The framework allows to seed tumors at multiple locations in a human brain atlas. It simulates tumor evolution over time and across different brain regions using literature-based parameter estimates for tumor cell proliferation, as well as isotropic motility, and mechanical tissue properties. Despite its simplicity, the mathematical model yielded realistic estimates of the mechanical impact of a growing tumor on intra-cranial pressure. However, comparison to publicly available GBM imaging data showed that asymmetric shapes could not be reproduced by isotropic growth assumptions. Here we present and evaluate an extended version of this mechanically-coupled reaction-diffusion model that takes into account tissue anisotropies based on MRI diffusion tensor imaging (MR-DTI). Structural anisotropies in brain tissue have been found to affect the directionality of tumor cell migration and are critical to mechanical behavior. This makes them likely to play a role also in the development of GBM phenotypes.

Purpose:Glioblastoma multiforme (GBM) grows rapidly, infiltrating, compressing and displacing surrounding healthy tissue. Most previous studies focused on modeling GBM invasion dynamics, thereby neglecting its mass-effect. This study investigates the influence of biomechanical forces caused by the growing tumor on its shape. Methods:A mathematical model was developed to simulate GBM invasion and the mechanical interaction between tumor and healthy tissue. Cell proliferation and invasion was modeled as reaction-diffusion process; a solid-mechanics model of brain tissue was used to represent the mass-effect. Both models are coupled by relating local increase in tumor cell concentration to the generation of isotropic strain in the tissue, and solved using the Finite-Element Method (FEM). The model accounts for multiple brain regions with values for proliferation, isotropic diffusion and mechanical properties derived from literature. Tumors were seeded at multiple locations in FEM models based on the SRI24 human brain atlas. Simulation results for three sets of growth parameters were compared to actual tumors obtained from publicly available GBM datasets. Results:The temporal evolution of tumor cell concentration was simulated, together with the mechanical impact of tumor growth in terms of displacement and tissue stresses. Parameter choices for different levels of growth and invasiveness were correctly reflected in simulation results. However, statistical evaluation of tumor shape showed simulated tumors to be more symmetric than their real counterparts. Conclusion:In contrast to most previous study, the present model accounts not only for the tumor's growth and invasive characteristics, but also for its mass-effect. The study confirms observations from pure growth-invasion models that tumor shape depends on seed position. It extends their findings by showing that inclusion of tumor mechanics, using isotropic material and diffusion properties, is not sufficient to reproduce asymmetric shapes found in real tumors, thus indicating the importance of tissue anisotropy for GBM simulation. Funding Support, Disclosures, and Conflict of Interest: This project has received funding from the European Union Seventh Framework Programme for research, technological development and demonstration under grant agreement 600841.