Yusheng Feng

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.

Parallel Domain Decomposition Solver for Adaptive hp Finite Element Methods

In this paper, the development and implementation of highly parallelizable domain decomposition solvers for adaptive hp finite element methods is discussed. Two-level orthogonalization is used to obtain a reduced system which is preconditioned by a coarse grid operator. The condition number of the preconditioned system, for Poisson problems in two space dimensions, is proved to be bounded by C(1 + Hp/h)2(1 + log p)2 and Cp(1 + Hp/h)2(1 + log p)2 for different choices of coarse grid operators, where H is the subdomain size, p is the maximum spectral order, h is the size of the smallest element in the subdomain, and C is a constant independent of the mesh parameters. The work here extends the work of Bramble et al. [Math Comp., 47 (1986), pp. 103--134] on the h-version and Babuska et al. [SIAM J. Numer. Anal., 29 (1991), pp. 624--661] on the p-version of the finite element method. A preliminary version of this solver was first announced by Oden, Patra, and Feng in [Domain Decomposition Solver for Adaptive hp Finite Elements, VII Conference on Domain Decomposition, State College, PA, October 1993]. Numerical experiments show fast convergence of the solver and good control of the condition number on a variety of discretizations.

Local and pollution error estimation for finite element approximations of elliptic boundary value problems

This paper addresses the issue of local elementwise error estimation of finite element approximations of elliptic boundary value problems. The characterization of element error as local and pollution error component is presented and the relationship between energy norms of local errors and that predicted by means of a posteriori error estimators is investigated. In addition, techniques for calculating element indicators of local error, pollution error, and other error indicators are presented.

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.

Measurement and mathematical modeling of thermally induced injury and heat shock protein expression kinetics in normal and cancerous prostate cells

Purpose: Hyperthermia can induce heat shock protein (HSP) expression in tumours, which will cause enhanced tumour viability and increased resistance to additional thermal, chemotherapy, and radiation treatments. The study objective was to determine the relationship of hyperthermia protocols with HSP expression kinetics and cell death and develop corresponding computational predictive models of normal and cancerous prostate cell response. Methods: HSP expression kinetics and cell viability were measured in PC3 prostate cancer and RWPE-1 normal prostate cells subjected to hyperthermia protocols of 44° to 60°C for 1 to 30 min. Hsp27, Hsp60, and Hsp70 expression kinetics were determined by western blotting and visualised with immunofluorescence and confocal microscopy. Based on measured HSP expression data, a mathematical model was developed for predicting thermally induced HSP expression. Cell viability was measured with propidium iodide staining and flow cytometry to quantify the injury parameters necessary for predicting cell death following hyperthermia. Results: Significant Hsp27 and Hsp70 levels were induced in both cell types with maximum HSP expression occurring at 16 h post-heating, and diminishing substantially after 72 h. PC3 cells were slightly more sensitive to thermal stress than RWPE-1 cells. Arrhenius analysis of injury data suggested a transition between injury mechanisms at 54°C. HSP expression and injury models were effective at predicting cellular response to hyperthermia. Conclusion: Measurement of thermally induced HSP expression kinetics and cell viability associated with hyperthermia enabled development of thermal dosimetry guidelines and predictive models for HSP expression and cell injury as a function of thermal stress to investigate and design more effective hyperthermia therapies.

Model-based planning and real-time predictive control for laser-induced thermal therapy

In this article, the major idea and mathematical aspects of model-based planning and real-time predictive control for laser-induced thermal therapy (LITT) are presented. In particular, a computational framework and its major components developed by authors in recent years are reviewed. The framework provides the backbone for not only treatment planning but also real-time surgical monitoring and control with a focus on MR thermometry enabled predictive control and applications to image-guided LITT, or MRgLITT. Although this computational framework is designed for LITT in treating prostate cancer, it is further applicable to other thermal therapies in focal lesions induced by radio-frequency (RF), microwave and high-intensity-focused ultrasound (HIFU). Moreover, the model-based dynamic closed-loop predictive control algorithms in the framework, facilitated by the coupling of mathematical modelling and computer simulation with real-time imaging feedback, has great potential to enable a novel methodology in thermal medicine. Such technology could dramatically increase treatment efficacy and reduce morbidity.

High-fidelity Computer Models for Prospective Treatment Planning of Radiofrequency Ablation with In Vitro Experimental Correlation

PURPOSE To evaluate the accuracy of computer simulation in predicting the thermal damage region produced by a radiofrequency (RF) ablation procedure in an in vitro perfused bovine liver model. The thermal dose end point in the liver model is used to assess quantitatively computer prediction for use in prospective treatment planning of RF ablation procedures. MATERIALS AND METHODS Geometric details of the tri-cooled tip electrode were modeled. The resistive heating of a pulsed voltage delivery was simulated in four dimensions using finite element models (FEM) implemented on high-performance parallel computing architectures. A range of physically realistic blood perfusion parameters, 3.6-53.6 kg/sec/m(3), was considered in the computer model. An Arrhenius damage model was used to predict the thermal dose. Dice similarity coefficients (DSC) were the metric of comparison between computational predictions and T1-weighted contrast-enhanced images of the damage obtained from a RF procedure performed on an in vitro perfused bovine liver model. RESULTS For a perfusion parameter greater than 16.3 kg/sec/m(3), simulations predict the temporal evolution of the damaged volume is perfusion limited and will reach a maximum value. Over a range of physically meaningful perfusion values, 16.3-33.1 kg/sec/m(3), the predicted thermal dose reaches the maximum damage volume within 2 minutes of the delivery and is in good agreement (DSC > 0.7) with experimental measurements obtained from the perfused liver model. CONCLUSIONS As measured by the computed volumetric DSC, computer prediction accuracy of the thermal dose shows good correlation with ablation lesions measured in vitro in perfused bovine liver models over a range of physically realistic perfusion values.

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 ||·||L 2 2 (0,T;L 2 (¿)) norm of the difference between computational prediction and the measured temperature values to a patient-specific regime.

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.

LOCAL AND POLLUTION ERROR ESTIMATION FOR STOKESIAN FLOWS

SUMMARY We describe in this paper an algebraic technique for estimating local and pollution errors in finite element approximations of Stokesian flows. # 1998 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Fluids, 27: 33‐39 (1998)