Thermoradiotherapy optimization strategies accounting for hyperthermia delivery uncertainties.

INTRODUCTION: The combined effect of hyperthermia and radiotherapy can be quantified by an enhanced equivalent radiation dose (EQDRT). Uncertainties in hyperthermia treatment planning and adjustments during treatment can impact achieved EQDRT. We developed and compared strategies for EQDRT optimization of radiotherapy plans, focusing on robustness against common adjustments. METHODS: Using Plan2Heat, we computed pre-planning hyperthermia plans and treatment adjustment scenarios for three cervical cancer patients. We imported these scenarios into RayStation 12A for optimization with four different strategies: (1) Conventional radiotherapy optimization prescribing 46 Gy to the planning target volume (PTV), (2) Nominal EQDRT optimization using the pre-planning scenario, targeting uniform 58 Gy in the gross tumor volume (GTV), keeping organs at risk (OAR) doses as in plan (1), (3) Robust EQDRT optimization, as (2) but adding adjusted scenarios for optimization, (4) Library of Plans (four plans), with strategy (2) criteria but optimizing on one adjusted scenario per plan. We calculated for each radiotherapy plan EQDRT distributions for pre-planning and adjusted scenarios, evaluating for each combination GTV coverage and homogeneity objectives. RESULTS: EQDRT95% increased from 49.9-50.9 Gy in strategy (1) to 56.1-57.4 Gy in strategy (2) with the pre-planning scenario, improving homogeneity in ∼10%. Strategy (2) demonstrated the best overall robustness, with 62% of all GTV objectives within tolerance. Strategy (3) had higher percentage of coverage objectives within tolerance than strategy (2) (68% vs 54%), but lower percentage for uniformity (44% vs 71%). Strategy (4) showed similar EQDRT95% and homogeneity for adjusted scenarios than strategy (2) for pre-planning scenario. D0.1% for OARs was increased by strategies (2-4) by up to ∼6 Gy. CONCLUSIONS: EQDRT optimization enhances EQDRT levels and uniformity compared to conventional optimization. Better overall robustness is achieved optimizing on the pre-planning hyperthermia plan. Robust optimization improves coverage but reduces homogeneity. A library of plans ensures coverage and uniformity when dealing with adjusted hyperthermia scenarios.

A phase-field model for non-small cell lung cancer under the effects of immunotherapy.

Formulating mathematical models that estimate tumor growth under therapy is vital for improving patient-specific treatment plans. In this context, we present our recent work on simulating non-small-scale cell lung cancer (NSCLC) in a simple, deterministic setting for two different patients receiving an immunotherapeutic treatment. At its core, our model consists of a Cahn-Hilliard-based phase-field model describing the evolution of proliferative and necrotic tumor cells. These are coupled to a simplified nutrient model that drives the growth of the proliferative cells and their decay into necrotic cells. The applied immunotherapy decreases the proliferative cell concentration. Here, we model the immunotherapeutic agent concentration in the entire lung over time by an ordinary differential equation (ODE). Finally, reaction terms provide a coupling between all these equations. By assuming spherical, symmetric tumor growth and constant nutrient inflow, we simplify this full 3D cancer simulation model to a reduced 1D model. We can then resort to patient data gathered from computed tomography (CT) scans over several years to calibrate our model. Our model covers the case in which the immunotherapy is successful and limits the tumor size, as well as the case predicting a sudden relapse, leading to exponential tumor growth. Finally, we move from the reduced model back to the full 3D cancer simulation in the lung tissue. Thereby, we demonstrate the predictive benefits that a more detailed patient-specific simulation including spatial information as a possible generalization within our framework could yield in the future.

Mutual-information based optimal experimental design for hyperpolarized [Formula: see text]C-pyruvate MRI.

A key parameter of interest recovered from hyperpolarized (HP) MRI measurements is the apparent pyruvate-to-lactate exchange rate, [Formula: see text], for measuring tumor metabolism. This manuscript presents an information-theory-based optimal experimental design approach that minimizes the uncertainty in the rate parameter, [Formula: see text], recovered from HP-MRI measurements. Mutual information is employed to measure the information content of the HP measurements with respect to the first-order exchange kinetics of the pyruvate conversion to lactate. Flip angles of the pulse sequence acquisition are optimized with respect to the mutual information. A time-varying flip angle scheme leads to a higher parameter optimization that can further improve the quantitative value of mutual information over a constant flip angle scheme. However, the constant flip angle scheme, 35 and 28 degrees for pyruvate and lactate measurements, leads to an accuracy and precision comparable to the variable flip angle schemes obtained from our method. Combining the comparable performance and practical implementation, optimized pyruvate and lactate flip angles of 35 and 28 degrees, respectively, are recommended.

Bridging Scales: a Hybrid Model to Simulate Vascular Tumor Growth and Treatment Response.

Cancer is a disease driven by random DNA mutations and the interaction of many complex phenomena. To improve the understanding and ultimately find more effective treatments, researchers leverage computer simulations mimicking the tumor growth in silico. The challenge here is to account for the many phenomena influencing the disease progression and treatment protocols. This work introduces a computational model to simulate vascular tumor growth and the response to drug treatments in 3D. It consists of two agent-based models for the tumor cells and the vasculature. Moreover, partial differential equations govern the diffusive dynamics of the nutrients, the vascular endothelial growth factor, and two cancer drugs. The model focuses explicitly on breast cancer cells over-expressing HER2 receptors and a treatment combining standard chemotherapy (Doxorubicin) and monoclonal antibodies with anti-angiogenic properties (Trastuzumab). However, large parts of the model generalize to other scenarios. We show that the model qualitatively captures the effects of the combination therapy by comparing our simulation results with previously published pre-clinical data. Furthermore, we demonstrate the scalability of the model and the associated C++ code by simulating a vascular tumor occupying a volume of 400mm3 using a total of 92.5 million agents.

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data.

Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2-3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.

Bayesian-based predictions of COVID-19 evolution in Texas using multispecies mixture-theoretic continuum models.

We consider a mixture-theoretic continuum model of the spread of COVID-19 in Texas. The model consists of multiple coupled partial differential reaction-diffusion equations governing the evolution of susceptible, exposed, infectious, recovered, and deceased fractions of the total population in a given region. We consider the problem of model calibration, validation, and prediction following a Bayesian learning approach implemented in OPAL (the Occam Plausibility Algorithm). Our goal is to incorporate COVID-19 data to calibrate the model in real-time and make meaningful predictions and specify the confidence level in the prediction by quantifying the uncertainty in key quantities of interests. Our results show smaller mortality rates in Texas than what is reported in the literature. We predict 7003 deceased cases by September 1, 2020 in Texas with 95 % CI 6802-7204. The model is validated for the total deceased cases, however, is found to be invalid for the total infected cases. We discuss possible improvements of the model.

A Coupled Mass Transport and Deformation Theory of Multi-constituent Tumor Growth.

We develop a general class of thermodynamically consistent, continuum models based on mixture theory with phase effects that describe the behavior of a mass of multiple interacting constituents. The constituents consist of solid species undergoing large elastic deformations and compressible viscous fluids. The fundamental building blocks framing the mixture theories consist of the mass balance law of diffusing species and microscopic (cellular scale) and macroscopic (tissue scale) force balances, as well as energy balance and the entropy production inequality derived from the first and second laws of thermodynamics. A general phase-field framework is developed by closing the system through postulating constitutive equations (i.e., specific forms of free energy and rate of dissipation potentials) to depict the growth of tumors in a microenvironment. A notable feature of this theory is that it contains a unified continuum mechanics framework for addressing the interactions of multiple species evolving in both space and time and involved in biological growth of soft tissues (e.g., tumor cells and nutrients). The formulation also accounts for the regulating roles of the mechanical deformation on the growth of tumors, through a physically and mathematically consistent coupled diffusion and deformation framework. A new algorithm for numerical approximation of the proposed model using mixed finite elements is presented. The results of numerical experiments indicate that the proposed theory captures critical features of avascular tumor growth in the various microenvironment of living tissue, in agreement with the experimental studies in the literature.

The 2019 mathematical oncology roadmap.

Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.

Calibration of Multi-Parameter Models of Avascular Tumor Growth Using Time Resolved Microscopy Data.

Two of the central challenges of using mathematical models for predicting the spatiotemporal development of tumors is the lack of appropriate data to calibrate the parameters of the model, and quantitative characterization of the uncertainties in both the experimental data and the modeling process itself. We present a sequence of experiments, with increasing complexity, designed to systematically calibrate the rates of apoptosis, proliferation, and necrosis, as well as mobility, within a phase-field tumor growth model. The in vitro experiments characterize the proliferation and death of human liver carcinoma cells under different initial cell concentrations, nutrient availabilities, and treatment conditions. A Bayesian framework is employed to quantify the uncertainties in model parameters. The average difference between the calibration and the data, across all time points is between 11.54% and 14.04% for the apoptosis experiments, 7.33% and 23.30% for the proliferation experiments, and 8.12% and 31.55% for the necrosis experiments. The results indicate the proposed experiment-computational approach is generalizable and appropriate for step-by-step calibration of multi-parameter models, yielding accurate estimations of model parameters related to rates of proliferation, apoptosis, and necrosis.

A HYBRID THREE-SCALE MODEL OF TUMOR GROWTH.

Cancer results from a complex interplay of different biological, chemical, and physical phenomena that span a wide range of time and length scales. Computational modeling may help to unfold the role of multiple evolving factors that exist and interact in the tumor microenvironment. Understanding these complex multiscale interactions is a crucial step towards predicting cancer growth and in developing effective therapies. We integrate different modeling approaches in a multiscale, avascular, hybrid tumor growth model encompassing tissue, cell, and sub-cell scales. At the tissue level, we consider the dispersion of nutrients and growth factors in the tumor microenvironment, which are modeled through reaction-diffusion equations. At the cell level, we use an agent based model (ABM) to describe normal and tumor cell dynamics, with normal cells kept in homeostasis and cancer cells differentiated apoptotic, hypoxic, and necrotic states. Cell movement is driven by the balance of a variety of forces according to Newton's second law, including those related to growth-induced stresses. Phenotypic transitions are defined by specific rule of behaviors that depend on microenvironment stimuli. We integrate in each cell/agent a branch of the epidermal growth factor receptor (EGFR) pathway. This pathway is modeled by a system of coupled nonlinear differential equations involving the mass laws of 20 molecules. The rates of change in the concentration of some key molecules trigger proliferation or migration advantage response. The bridge between cell and tissue scales is built through the reaction and source terms of the partial differential equations. Our hybrid model is built in a modular way, enabling the investigation of the role of different mechanisms at multiple scales on tumor progression. This strategy allows representating both the collective behavior due to cell assembly as well as microscopic intracellular phenomena described by signal transduction pathways. Here, we investigate the impact of some mechanisms associated with sustained proliferation on cancer progression. Specifically, we focus on the intracellular proliferation/migration-advantage-response driven by the EGFR pathway and on proliferation inhibition due to accumulation of growth-induced stresses. Simulations demonstrate that the model can adequately describe some complex mechanisms of tumor dynamics, including growth arrest in avascular tumors. Both the sub-cell model and growth-induced stresses give rise to heterogeneity in the tumor expansion and a rich variety of tumor behaviors.

Selection and Validation of Predictive Models of Radiation Effects on Tumor Growth Based on Noninvasive Imaging Data.

The use of mathematical and computational models for reliable predictions of tumor growth and decline in living organisms is one of the foremost challenges in modern predictive science, as it must cope with uncertainties in observational data, model selection, model parameters, and model inadequacy, all for very complex physical and biological systems. In this paper, large classes of parametric models of tumor growth in vascular tissue are discussed including models for radiation therapy. Observational data is obtained from MRI of a murine model of glioma and observed over a period of about three weeks, with X-ray radiation administered 14.5 days into the experimental program. Parametric models of tumor proliferation and decline are presented based on the balance laws of continuum mixture theory, particularly mass balance, and from accepted biological hypotheses on tumor growth. Among these are new model classes that include characterizations of effects of radiation and simple models of mechanical deformation of tumors. The Occam Plausibility Algorithm (OPAL) is implemented to provide a Bayesian statistical calibration of the model classes, 39 models in all, as well as the determination of the most plausible models in these classes relative to the observational data, and to assess model inadequacy through statistical validation processes. Discussions of the numerical analysis of finite element approximations of the system of stochastic, nonlinear partial differential equations characterizing the model classes, as well as the sampling algorithms for Monte Carlo and Markov chain Monte Carlo (MCMC) methods employed in solving the forward stochastic problem, and in computing posterior distributions of parameters and model plausibilities are provided. The results of the analyses described suggest that the general framework developed can provide a useful approach for predicting tumor growth and the effects of radiation.

A fully coupled space-time multiscale modeling framework for predicting tumor growth.

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.

Selection, calibration, and validation of models of tumor growth.

This paper presents general approaches for addressing some of the most important issues in predictive computational oncology concerned with developing classes of predictive models of tumor growth. First, the process of developing mathematical models of vascular tumors evolving in the complex, heterogeneous, macroenvironment of living tissue; second, the selection of the most plausible models among these classes, given relevant observational data; third, the statistical calibration and validation of models in these classes, and finally, the prediction of key Quantities of Interest (QOIs) relevant to patient survival and the effect of various therapies. The most challenging aspects of this endeavor is that all of these issues often involve confounding uncertainties: in observational data, in model parameters, in model selection, and in the features targeted in the prediction. Our approach can be referred to as "model agnostic" in that no single model is advocated; rather, a general approach that explores powerful mixture-theory representations of tissue behavior while accounting for a range of relevant biological factors is presented, which leads to many potentially predictive models. Then representative classes are identified which provide a starting point for the implementation of OPAL, the Occam Plausibility Algorithm (OPAL) which enables the modeler to select the most plausible models (for given data) and to determine if the model is a valid tool for predicting tumor growth and morphology (in vivo). All of these approaches account for uncertainties in the model, the observational data, the model parameters, and the target QOI. We demonstrate these processes by comparing a list of models for tumor growth, including reaction-diffusion models, phase-fields models, and models with and without mechanical deformation effects, for glioma growth measured in murine experiments. Examples are provided that exhibit quite acceptable predictions of tumor growth in laboratory animals while demonstrating successful implementations of OPAL.

Bayesian calibration, validation, and uncertainty quantification of diffuse interface models of tumor growth.

The idea that one can possibly develop computational models that predict the emergence, growth, or decline of tumors in living tissue is enormously intriguing as such predictions could revolutionize medicine and bring a new paradigm into the treatment and prevention of a class of the deadliest maladies affecting humankind. But at the heart of this subject is the notion of predictability itself, the ambiguity involved in selecting and implementing effective models, and the acquisition of relevant data, all factors that contribute to the difficulty of predicting such complex events as tumor growth with quantifiable uncertainty. In this work, we attempt to lay out a framework, based on Bayesian probability, for systematically addressing the questions of Validation, the process of investigating the accuracy with which a mathematical model is able to reproduce particular physical events, and Uncertainty quantification, developing measures of the degree of confidence with which a computer model predicts particular quantities of interest. For illustrative purposes, we exercise the process using virtual data for models of tumor growth based on diffuse-interface theories of mixtures utilizing virtual data.

Numerical simulation of a thermodynamically consistent four-species tumor growth model.

In this paper, we develop a thermodynamically consistent four-species model of tumor growth on the basis of the continuum theory of mixtures. Unique to this model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models. A mixed finite element spatial discretization is developed and implemented to provide numerical results demonstrating the range of solutions this model can produce. A time-stepping algorithm is then presented for this system, which is shown to be first order accurate and energy gradient stable. The results of an array of numerical experiments are presented, which demonstrate a wide range of solutions produced by various choices of model parameters.

Adaptive real-time bioheat transfer models for computer-driven MR-guided laser induced thermal therapy.

The treatment times of laser induced thermal therapies (LITT) guided by computational prediction are determined by the convergence behavior of partial differential equation (PDE)-constrained optimization problems. In this paper, we investigate the convergence behavior of a bioheat transfer constrained calibration problem to assess the feasibility of applying to real-time patient specific data. The calibration techniques utilize multiplanar thermal images obtained from the nondestructive in vivo heating of canine prostate. The calibration techniques attempt to adaptively recover the biothermal heterogeneities within the tissue on a patient-specific level and results in a formidable PDE constrained optimization problem to be solved in real time. A comprehensive calibration study is performed with both homogeneous and spatially heterogeneous biothermal model parameters with and without constitutive nonlinearities. Initial results presented here indicate that the calibration problems involving the inverse solution of thousands of model parameters can converge to a solution within three minutes and decrease the [see text for symbol](L) (2) (2) ((0, T; L) (2) ((Omega))) norm of the difference between computational prediction and the measured temperature values to a patient-specific regime.

Computational modeling and real-time control of patient-specific laser treatment of cancer.

An adaptive feedback control system is presented which employs a computational model of bioheat transfer in living tissue to guide, in real-time, laser treatments of prostate cancer monitored by magnetic resonance thermal imaging. The system is built on what can be referred to as cyberinfrastructure-a complex structure of high-speed network, large-scale parallel computing devices, laser optics, imaging, visualizations, inverse-analysis algorithms, mesh generation, and control systems that guide laser therapy to optimally control the ablation of cancerous tissue. The computational system has been successfully tested on in vivo, canine prostate. Over the course of an 18 min laser-induced thermal therapy performed at M.D. Anderson Cancer Center (MDACC) in Houston, Texas, the computational models were calibrated to intra-operative real-time thermal imaging treatment data and the calibrated models controlled the bioheat transfer to within 5 degrees C of the predetermined treatment plan. The computational arena is in Austin, Texas and managed at the Institute for Computational Engineering and Sciences (ICES). The system is designed to control the bioheat transfer remotely while simultaneously providing real-time remote visualization of the on-going treatment. Post-operative histology of the canine prostate reveal that the damage region was within the targeted 1.2 cm diameter treatment objective.

Nanoshell-mediated laser surgery simulation for prostate cancer treatment.

Laser surgery, or laser-induced thermal therapy, is a minimally invasive alternative or adjuvant to surgical resection in treating tumors embedded in vital organs with poorly defined boundaries. Its use, however, is limited due to the lack of precise control of heating and slow rate of thermal diffusion in the tissue. Nanoparticles, such as nanoshells, can act as intense heat absorbers when they are injected into tumors. These nanoshells can enhance thermal energy deposition into target regions to improve the ability for destroying larger cancerous tissue volumes with lower thermal doses. The goal of this paper is to present an integrated computer model using a so-called nested-block optimization algorithm to simulate laser surgery and provide transient temperature field predictions. In particular, this algorithm aims to capture changes in optical and thermal properties due to nanoshell inclusion and tissue property variation during laser surgery. Numerical results show that this model is able to characterize variation of tissue properties for laser surgical procedures and predict transient temperature fields comparable to those measured by in vivo magnetic resonance temperature imaging techniques. Note that the computational approach presented in the study is quite general and can be applied to other types of nanoparticle inclusions.

A two-state cell damage model under hyperthermic conditions: theory and in vitro experiments.

The ultimate goal of cancer treatment utilizing thermotherapy is to eradicate tumors and minimize damage to surrounding host tissues. To achieve this goal, it is important to develop an accurate cell damage model to characterize the population of cell death under various thermal conditions. The traditional Arrhenius model is often used to characterize the damaged cell population under the assumption that the rate of cell damage is proportional to exp(-EaRT), where Ea is the activation energy, R is the universal gas constant, and T is the absolute temperature. However, this model is unable to capture transition phenomena over the entire hyperthermia and ablation temperature range, particularly during the initial stage of heating. Inspired by classical statistical thermodynamic principles, we propose a general two-state model to characterize the entire cell population with two distinct and measurable subpopulations of cells, in which each cell is in one of the two microstates, viable (live) and damaged (dead), respectively. The resulting cell viability can be expressed as C(tau,T)=exp(-Phi(tau,T)kT)(1+exp(-Phi(tau,T)kT)), where k is a constant. The in vitro cell viability experiments revealed that the function Phi(tau,T) can be defined as a function that is linear in exposure time tau when the temperature T is fixed, and linear as well in terms of the reciprocal of temperature T when the variable tau is held as constant. To determine parameters in the function Phi(tau,T), we use in vitro cell viability data from the experiments conducted with human prostate cancerous (PC3) and normal (RWPE-1) cells exposed to thermotherapeutic protocols to correlate with the proposed cell damage model. Very good agreement between experimental data and the derived damage model is obtained. In addition, the new two-state model has the advantage that is less sensitive and more robust due to its well behaved model parameters.

Dynamic Data-Driven Finite Element Models for Laser Treatment of Cancer.

Elevating the temperature of cancerous cells is known to increase their susceptibility to subsequent radiation or chemotherapy treatments, and in the case in which a tumor exists as a well-defined region, higher intensity heat sources may be used to ablate the tissue. These facts are the basis for hyperthermia based cancer treatments. Of the many available modalities for delivering the heat source, the application of a laser heat source under the guidance of real-time treatment data has the potential to provide unprecedented control over the outcome of the treatment process [7, 18]. The goals of this work are to provide a precise mathematical framework for the real-time finite element solution of the problems of calibration, optimal heat source control, and goal-oriented error estimation applied to the equations of bioheat transfer and demonstrate that current finite element technology, parallel computer architecture, data transfer infrastructure, and thermal imaging modalities are capable of inducing a precise computer controlled temperature field within the biological domain.