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In this present study, the heat transfer characteristics of a parallel miniature heat pipes system (mHPs) intended for desktop computer processor cooling was experimentally investigated. The experimental system consisted of six single copper tube mHPs slotted into two copper blocks at the evaporator section and fifteen parallel copper sheets at the condenser section. The copper blocks were placed above the heat source (on the top of the computer processor) and the condenser section was provided with external fins perpendicular to the mHPs. Four working fluids, namely acetone, ethanol, methanol, and propanol-2 were used independently to probe the working fluids' effect on the thermal performance of the system. Heat transfer characteristics of the mHPs were determined based on the principle of phase change of the working fluids at different temperatures to evaluate the thermal performance. The thermal conductance and thermal resistance of the system were determined as the parameters of thermal performance. The results indicated that the thermal characteristics of the heat pipe varied significantly for different temperatures of the heat source at the evaporator and different working fluids. It was obtained that the methanol is the best working fluid to be used in a mHPs in comparison with other working fluids (acetone, ethanol, and propanol 2). Furthermore, the lowest evaporator surface temperature was achieved with the methanol based system.

New directions in medical and biomedical sciences have gradually emerged over recent years that will change the way diseases are diagnosed and treated and are leading to the redirection of medicine toward patient-specific treatments. We refer to these new approaches for studying biomedical systems as predictive medicine, a new version of medical science that involves the use of advanced computer models of biomedical phenomena, high-performance computing, new experimental methods for model data calibration, modern imaging technologies, cutting-edge numerical algorithms for treating large stochastic systems, modern methods for model selection, calibration, validation, verification, and uncertainty quantification, and new approaches for drug design and delivery, all based on predictive models. The methodologies are designed to study events at multiple scales, from genetic data, to sub-cellular signaling mechanisms, to cell interactions, to tissue physics and chemistry, to organs in living human subjects. The present document surveys work on the development and implementation of predictive models of vascular tumor growth, covering aspects of what might be called modeling-and-experimentally based computational oncology. The work described is that of a multi-institutional team, centered at ICES with strong participation by members at M. D. Anderson Cancer Center and University of Texas at San Antonio. This exposition covers topics on signaling models, cell and cell-interaction models, tissue models based on multi-species mixture theories, models of angiogenesis, and beginning work of drug effects. A number of new parallel computer codes for implementing finite-element methods, multi-level Markov Chain Monte Carlo sampling methods, data classification methods, stochastic PDE solvers, statistical inverse algorithms for model calibration and validation, models of events at different spatial and temporal scales is presented. Importantly, new methods for model selection in the presence of uncertainties fundamental to predictive medical science, are described which are based on the notion of Bayesian model plausibilities. Also, as part of this general approach, new codes for determining the sensitivity of model outputs to variations in model parameters are described that provide a basis for assessing the importance of model parameters and controlling and reducing the number of relevant model parameters. Model specific data is to be accessible through careful and model-specific platforms in the Tumor Engineering Laboratory. We describe parallel computer platforms on which large-scale calculations are run as well as specific time-marching algorithms needed to treat stiff systems encountered in some phase-field mixture models. We also cover new non-invasive imaging and data classification methods that provide in vivo data for model validation. The study concludes with a brief discussion of future work and open challenges.

Most biological systems encountered in living organisms involve highly complex heterogeneous multi-component structures that exhibit different physical, chemical, and biological behavior at different spatial and temporal scales. The development of predictive mathematical and computational models of multiscale events in such systems is a major challenge in contemporary computational biomechanics, particularly the development of models of growing tumors in humans. The aim of this study is to develop a general framework for tumor growth prediction by considering major biological events at tissue, cellular, and subcellular scales. The key to developing such multiscale models is how to bridge spatial and temporal scales that range from 10-3 to 103 mm in space and from 10-6 to 107 s in time. In this paper, a fully coupled space-time multiscale framework for modeling tumor growth is developed. The framework consists of a tissue scale model, a model of cellular activities, and a subcellular transduction signaling pathway model. The tissue, cellular, and subcellular models in this framework are solved using partial differential equations for tissue growth, agent-based model for cellular events, and ordinary differential equations for signaling transduction pathway as a network at subcellular scale. The model is calibrated using experimental observations. Moreover, this model is biologically-driven from a signaling pathway, volumetrically-consistent between cellular and tissue scale in terms of tumor volume evolution in time, and a biophysically-sound tissue model that satisfies all conservation laws. The results show that the model is capable of predicting major characteristics of tumor growth such as the morphological instability, growth patterns of different cell phenotypes, compact regions of the higher cell density at the tumor region, and the reduction of growth rate due to drug delivery. The predicted treatment outcomes show a reduction in proliferation at different rates in response to different drug dosages. Moreover, the results of several 3D applications to tumor growth and the evolution of cellular and subcellular events are presented.

Introduction: We aim to develop a multiple spatio-temporal scale (MSTS) framework capable of bridging tissue, cellular, and subcellular scales. Our overarching hypothesis is that an accurate and precise MSTS model, initialized with patient-specific information, can dramatically outperform current standard-of-care for diagnosis and selecting therapy for the individual cancer patient. Methodology: We developed a MSTS framework for tumor growth and treatment outcome prediction. Our model incorporated chemotherapy so that we can predict changes in tumor volume due to various therapeutic regimens. The MSTS framework consists of a tissue scale model, a cellular activity and growth model, and a subcellular signaling pathway model. To predict tissue growth at the tissue scale, a continuum model is constructed where the biological tissue is represented as a mixture of multiple constituents with each of which represents either a volume fraction or concentration. The constituents interact with each other through mass and momentum exchange so that the governing equations are based on both mass and momentum conservation laws. The constitutive equations account for tissue heterogeneity, nonlinear behavior, and thermodynamic consistency. The system of partial differential equations is solved using finite element techniques. To bridge the tissue and cell scales, each finite element is discretized into virtual cell clusters to model cellular growth and proliferation by using an agent-based model to determine various cellular scale activities including cell division, cell death, and phenotypical alteration. The cellular scale is further discretized temporally to model the effects of selected signaling pathways (e.g., PI3K/AKT/mTOR pathway). In many cancers, mTOR pathway becomes hyperactive and promotes abnormal cell proliferation. The mechanism and effects of a mTOR inhibiting drug known as rapamycin are tested in silico. The subcellular scale is modeled using a set of ordinary differential equations. A statistical inverse algorithm is used to calibrate and validate the results using magnetic resonance imaging (MRI) data, and a Bayesian inference method is employed to account for the uncertainties in model parameters. Results: The 3D simulation results recapitulate, at various physical and biological conditions, different tumor characteristics including morphological instability, changes in the spatio-temporal distribution of different cell phenotypes and density, and the reduction of growth rate due to drug delivery. Thus, this model has the potential to be used for patient-specific prediction of tumor growth as well as personalized treatment planning. The novelties of this modeling framework are that (1) the events at each scale are modeled using different numerical techniques suitable for that specific scale in terms of both space and time, (2) a novel numerical technique is developed to bridge the scales and solved simultaneously, (3) the tissue scale model is thermodynamically consistent with consideration of tissue heterogeneity and nonlinear behaviors, (4) various cellular events such as the phenotypical alteration, apoptosis, necrosis, mitosis, etc. are modeled at the cellular scale, and (5) the mTOR signaling pathway, an important pathway for many different cancers, is modeled at the subcellular scale. Conclusions: Our MSTS model is capable of predicting tumor growth with considerations of various factors at different spatio-temporal scales. It can be potentially used as a patient-specific tumor growth model for in silico drug testing, treatment planning, and prognosis. A future version of this model can include cancer stem cells, angiogenesis, and metastasis. Citation Format: Mohammad Rahman, Yusheng Feng, Thomas E. Yankeelov, J. Tinsley Oden. Multiple spatio-temporal scale modeling with application to brain cancer. [abstract]. In: Proceedings of the AACR Special Conference on Engineering and Physical Sciences in Oncology; 2016 Jun 25-28; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2017;77(2 Suppl):Abstract nr A02.