MIP Models and BB Strategies in Brachytherapy Treatment Optimization

Brachytherapy (brachy being derived from a Greek word meaning short) is the treatment by means of radioactive sources that are placed at short distances from the target cells. This form of therapy is becoming common in the treatment of early stage prostate cancer, the most common cancer and the second leading cause of cancer deaths among American males. We consider the use of mixed-integer programming (MIP) models and branch-and-bound (BB) methods to optimize the placement within the prostate of the radioactive seeds used in this procedure. Several different optimization models are considered along with a number of branchand- bound strategies. With appropriate combinations of modelling and solution strategies, nearoptimal seed placements can be generated for each two-dimensional ultrasound section of the prostate in less than five minutes on a 333-MHz workstation. The original three-dimensional problem can then be solved by considering an appropriately interrelated sequence of these two-dimensional problems.     

核事故应急决策中水体放射性核素扩散仿真分析

放射性核素浓度的确定是放射性事故应急救援和辐射防护等工作的基础和前提,是放射性事故应急救援的重要组成部分.在一维扩散模型的基础上,建立了放射性核素瞬时污染点源三维扩散模型、连续污染点源三维扩散模型、连续污染点源三维扩散稳态模型,并编写程序,实现了对放射性核素污染扩散的快速仿真分析,较好模拟了水体中放射性核素的扩散趋势.研究结果在核事故应急救援过程中,可为相关部门制定救援方案及应急决策提供科学依据.     

Mixed Integer Programming Approaches to Treatment Planning for Brachytherapy – Application to Permanent Prostate Implants

Mixed integer programming models and computational strategies developed for treatment planning optimization in brachytherapy are described. The problem involves the designation of optimal placement of radioactive sources (seeds) inside a tumor site. Two MIP models are described. The resulting MIP instances are difficult to solve, due in large part to dense constraint matrices with large disparities in the magnitudes of the nonzero entries. A matrix reduction and approximation scheme is presented as a computational strategy for dealing with the dense matrices. Penalty-based primal heuristic and branching strategies to assist in the solution process are also described. Numerical results are presented for 20 MIP instances associated with prostate cancer cases. Compared to currently used computer-aided planning methods, plans derived via the MIP approach use fewer seeds (20–30 fewer) and needles, and provide better coverage and conformity – measures commonly used to assess the quality of treatment plans. Good treatment plans are returned in 15 CPU minutes, suggesting that incorporation of this MIP-based optimization module into a real-time comprehensive treatment planning system is feasible.     

Detection and localization of hidden radioactive sources with spatial statistical method

The detection of radioactive materials has become a critical issue for environmental services, public health, and national security. This paper proposes a spatial statistical method to detect and localize a hidden radioactive source. Based on a detection system of multiple radiation detectors, the statistical model assumes that the counts of radiation particles received by those detectors are spatially distributed of Poisson distribution, and each comprises a signal and a background. By considering the physical law of signal degradation with distance, the paper provides a numerical method to compute the maximum likelihood estimates of the strength and location of the source. Based on these estimates, a likelihood ratio statistic is used to test the existence of the source. Because of the special properties of the model, the test statistic does not converge asymptotically to the standard chi-square distribution. Thus a bootstrap method is proposed to compute the p-value in the test. The simulation results show that the proposed method is efficient for detecting and localizing the hidden radioactive source.     

Scheduling the adjuvant endocrine therapy for early stage breast cancer

Based on the data available through published trial results, we build a mixed integer nonlinear programming (MINLP) model in order to find an optimal treatment plan for a given HR+ early stage breast cancer patient who is postmenopausal. The objective is to maximize the disease-free survival percentage at the end of the treatment period subject to the constraints on the risk of contralateral breast cancer and the risks of several side effects, including endometrial cancer, thromboembolic events, cardiovascular diseases, bone fractures, hot flushes, and vaginal bleeding. The results of numerical experiments suggest the effectiveness of some of the schedules currently used in practice, as well as suggest some attractive alternative treatment plans.     

Solitary solutions to an androgen-deprivation prostate cancer treatment model

A model of androgen deprivation treatment for prostate cancer is considered in this paper. Bright/dark solitary solutions to the model are constructed using inverse balancing and generalized differential operator techniques. It is shown that solitary solutions correspond to biomedically relevant sets of model parameters. Dynamical properties of solitary solutions are analyzed in the phase plane. It is demonstrated that such solutions closely reflect the real-world phenomena observed during androgen deprivation treatment. Computational experiments are used to illustrate these effects.     

Optimal design of personalized prostate cancer therapy using Infinitesimal Perturbation Analysis

The standard treatment for advanced prostate cancer is hormone therapy in the form of continuous androgen suppression (CAS), which unfortunately frequently leads to resistance and relapse. An alternative scheme is intermittent androgen suppression (IAS), in which patients are submitted to cycles of treatment (in the form of androgen deprivation) and off-treatment periods in an alternating manner. In spite of extensive recent clinical experience with IAS, the design of ideal protocols for any given patient remains a challenge. The level of prostate specific antigen (PSA) is frequently monitored to determine when patients will be taken off therapy and when therapy will resume. In this work, we propose a threshold-based policy for optimal IAS therapy design that is parameterized by lower and upper PSA threshold values and is associated with a cost metric that combines clinically relevant measures of therapy success. We use a Stochastic Hybrid Automaton (SHA) model of prostate cancer evolution under IAS and perform Infinitesimal Perturbation Analysis (IPA) to adaptively adjust PSA threshold values so as to improve therapy outcomes. We also apply this methodology to clinical data from real patients, and obtain promising results and valuable insights for personalized IAS therapy design.     

A survey of optimization models on cancer chemotherapy treatment planning

While chemotherapy is an effective method for treating cancers such as colorectal cancer, its effectiveness may be dampened by the drug resistance and it may have significant side effects due to the destruction of normal cells during the treatment. As a result, there is a need for research on choosing an optimal chemotherapy treatment plan that minimizes the number of cancerous cells while ensuring that the total toxicity is below an allowable limit. In this paper, we summarize the mathematical models applied to the optimal design of the cancer chemotherapy. We first elaborate on a typical optimization model and classify relevant literature with respect to modeling methods: Optimal control model (OCM) and others. We further classify the OCM models with respect to the solution method used. We discuss the limitations of the existing research and provide several directions for further research in optimizing chemotherapy treatment planning.     

Optimal Biopsy Protocols for Prostate Cancer

Prostate cancer is the second leading cause of cancer-related death among American men. Biopsy for prostate cancer is a procedure known as transrectal ultrasound-guided needle biopsy. Because of the low resolution of ultrasound, the urologist cannot usually distinguish between cancerous and healthy tissue. For this reason, most biopsies follow standard protocols based on long-term experience of physicians. Recent studies indicate that these protocols have a significant rate of false negative diagnoses. In this research we use real prostate specimens removed by prostatectomy to develop a 3-D distribution map of cancer in the prostate, and use this to develop optimized biopsy procedures. The new procedures have detection rates that are significantly higher than those of current procedures, and thus have the potential to increase the rate of early detection of prostate cancer.     

Multiscale cancer modeling: In the line of fast simulation and chemotherapy

Although Multiscale Cancer Modeling has a realistic view in the process of tumor growth, its numerical algorithm is time consuming. Therefore, it is problematic to run and to find the best treatment plan for chemotherapy, even in case of a small size of tissue. Using an artificial neural network, this paper simulates the multiscale cancer model faster than its numerical algorithm. In order to find the best treatment plan, it suggests applying a simpler avascular model called Gompertz. By using these proposed methods, multiscale cancer modeling may be extendable to chemotherapy for a realistic size of tissue.In order to simulate multiscale model, a hierarchical neural network called Nested Hierarchical Self Organizing Map (NHSOM) is used. The basis of the NHSOM is an enhanced version of SOM, with an adaptive vigilance parameter. Corresponding parameter and the overall bottom-up design guarantee the quality of clustering, and the embedded top-down architecture reduces computational complexity.Although by applying NHSOM, the process of simulation runs faster compared with that of the numerical algorithm, it is not possible to check a simple search space. As a result, a set containing the best treatment plans of a simpler model (Gompertz) is used. Additionally, it is assumed in this paper, that the distribution of drug in vessels has a linear relation with the blood flow rate. The technical advantage of this assumption is that by using a simple linear relation, a given diffusion of a drug dosage may be scaled to the desired one.By extracting a proper feature vector from the multiscale model and using NHSOM, applying the scaled-best treatment plans of Gompertz model is done for a small size of tissue. In addition, simulating the effect of stress reduction on normal tissue after chemotherapy is another advantage of using NHSOM, which is a kind of “emergent”.     

Dynamic optimal strategy for monitoring disease recurrence

Surveillance to detect cancer recurrence is an important part of care for cancer survivors.In this paper we discuss the design of optimal strategies for early detection of disease recurrence based on each patient’s distinct biomarker trajectory and periodically updated risk estimated in the setting of a prospective cohort study.We adopt a latent class joint model which considers a longitudinal biomarker process and an event process jointly,to address heterogeneity of patients and disease,to discover distinct biomarker trajectory patterns,to classify patients into different risk groups,and to predict the risk of disease recurrence.The model is used to develop a monitoring strategy that dynamically modifies the monitoring intervals according to patients’ current risk derived from periodically updated biomarker measurements and other indicators of disease spread.The optimal biomarker assessment time is derived using a utility function.We develop an algorithm to apply the proposed strategy to monitoring of new patients after initial treatment.We illustrate the models and the derivation of the optimal strategy using simulated data from monitoring prostate cancer recurrence over a 5-year period.     

Combinatorial optimization for an improved transition from fluence optimization to fluence delivery in IMRT treatment planning

The intensity modulated radiation therapy (IMRT) treatment planning problem is usually divided into three smaller problems that are solved sequentially: geometry problem, intensity problem and realization problem. There are many models and algorithms that address each one of the problems in a satisfactory way. However, these problems cannot be seen separately, because strong links exist between them. While the linkage between the geometry problem and the intensity problem is straightforward, the linkage between the intensity problem and the realization problem is all but simple and will determine the quality of the treatment planning. In practice, the linkage between these problems is, most of the times, done in a rather simple way, usually by rounding. This can lead to a significant deterioration of the treatment plan quality. We propose a combinatorial optimization approach to enable an improved transition from optimized to delivery fluence maps in IMRT treatment planning. Two clinical examples of head and neck cancer cases are used, both to present numerical evidences of the resulting deterioration of plan quality if a simplistic approach is used, and also to highlight a combinatorial optimization approach as a valuable alternative when linking the intensity problem and the realization problem.     

Fraction of solid angle subtended by the detector to the source

A general formula for the solid angle subtended by the detector to the radioactive source is derived.     

Poisson source localization on the plane: change-point case

We present a detection problem where several spatially distributed sensors observe Poisson signals emitted from a single radioactive source of unknown position. The measurements at each sensor are modeled by independent inhomogeneous Poisson processes. A method based on Bayesian change-point estimation is proposed to identify the location of the source’s coordinates. The asymptotic behavior of the Bayesian estimator is studied. In particular, the consistency and the asymptotic efficiency of the estimator are analyzed. The limit distribution and the convergence of the moments are also described. The similar statistical model could be used in GPS localization problems.

     

A risk-based modeling approach for radiation therapy treatment planning under tumor shrinkage uncertainty

Robust optimization approaches have been widely used to address uncertainties in radiation therapy treatment planning problems. Because of the unknown probability distribution of uncertainties, robust bounds may not be correctly chosen, and a risk of undesirable effects from worst-case realizations may exist. In this study, we developed a risk-based robust approach, embedded within the conditional value-at-risk representation of the dose-volume constraint, to deal with tumor shrinkage uncertainty during radiation therapy. The objective of our proposed model is to reduce dose variability in the worst-case scenarios as well as the total delivered dose to healthy tissues and target dose deviations from the prescribed dose, especially, in underdosed scenarios. We also took advantage of adaptive radiation therapy in our treatment planning approach. This fractionation technique considers the response of the tumor to treatment up to a particular point in time and reoptimizes the treatment plan using an estimate of tumor shrinkage. The benefits of our model were tested in a clinical lung cancer case. Four plans were generated and compared: static, nominal-adaptive, robust-adaptive, and conventional robust (worst-case) optimization. Our results showed that the robust-adaptive model, which is a risk-based model, achieved less dose variability and more control on the worst-case scenarios while delivering the prescribed dose to the tumor target and sparing organs at risk. This model also outperformed other models in terms of tumor dose homogeneity and plan robustness.     

A Mathematical Model of Intermittent Androgen Suppression for Prostate Cancer

For several decades, androgen suppression has been the principal modality for treatment of advanced prostate cancer. Although the androgen deprivation is initially effective, most patients experience a relapse within several years due to the proliferation of so-called androgen-independent tumor cells. Bruchovsky et al. suggested in animal models that intermittent androgen suppression (IAS) can prolong the time to relapse when compared with continuous androgen suppression (CAS). Therefore, IAS has been expected to enhance clinical efficacy in conjunction with reduction in adverse effects and improvement in quality of life of patients during off-treatment periods. This paper presents a mathematical model that describes the growth of a prostate tumor under IAS therapy based on monitoring of the serum prostate-specific antigen (PSA). By treating the cancer tumor as a mixed assembly of androgen-dependent and androgen-independent cells, we investigate the difference between CAS and IAS with respect to factors affecting an androgen-independent relapse. Numerical and bifurcation analyses show how the tumor growth and the relapse time are influenced by the net growth rate of the androgen-independent cells, a protocol of the IAS therapy, and the mutation rate from androgen-dependent cells to androgen-independent ones.

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The determination of optimal treatment plans for Volumetric Modulated Arc Therapy (VMAT)

The success of radiation therapy depends on the ability to deliver the proper amount of radiation to cancerous cells while protecting healthy tissues. As a natural consequence, any new treatment technology improves quality standards concerning primarily this issue. Similar to the widely used Intensity Modulated Radiation Therapy (IMRT), the radiation resource is outside of the patient’s body and the beam is shaped by a multi-leaf collimator mounted on the linear accelerator’s head during the state-of-the-art Volumetric Modulated Arc Therapy (VMAT) as well. However, unlike IMRT, the gantry of the accelerator may rotate along one or more arcs and deliver radiation continuously. This property makes VMAT powerful in obtaining high conformal plans in terms of dose distribution; but the apertures are interdependent and optimal treatment planning problem cannot be decomposed into simpler independent subproblems as a consequence. In this work, we consider optimal treatment planning problem for VMAT. First, we formulate a mixed-integer linear program minimizing total radiation dose intensity subject to clinical requirements embedded within the constraints. Then, we develop efficient solution procedures combining Benders decomposition with certain acceleration strategies. We investigate their performance on a large set of test instances obtained from an anonymous real prostate cancer data.     

Clinical decision support system for dental treatment

BackgroundIn this research, a decision making system, based on fuzzy inference mechanism as proposed by Mamdani, is presented. Literature suggests that there is a lack of consistency among dentists in choosing treatment plan(s). So, this research work aims to facilitate the dentist decide the treatment plan(s) of the broken tooth.MethodsAn expert system based on fuzzy logic has been designed to accept inaccurate and vague values of dental signs and symptoms associated with the broken tooth. We designed a knowledge base with 60 rules and used Mamdani inference algorithm to decide the possible one or more treatment(s) and suggest the same to the dentist.ResultsThe results proposed by the system are compared with the dentists’ suggestions. The Chi-square test of homogeneity is conducted on 100 randomly generated sample cases with the help of three professional dentists. It is found that the results produced by the system are consistent with the treatment plan(s) proposed by the dentists. Chi-square value of the test is 3.843565 which is less than the critical value which is 12.592. Hence, we are unable to reject the null hypothesis that assumes the two populations are homogeneous with respect to treatments.ConclusionsThe accuracy of the proposed decision support system for the treatment of broken tooth enhances the confidence level of the dentists while making decision regarding the treatment plan(s). Simple and interactive GUI makes it easy to use.     

Uniqueness for an inverse problem for a nonlinear parabolic system with an integral term by one-point Dirichlet data

We consider an inverse problem arising in laser-induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissues is destroyed by coagulation. For the dosage planning quantitatively reliable numerical simulation are indispensable. To this end the identification of the thermal growth kinetics of the coagulated zone is of crucial importance. Mathematically, this problem is a nonlinear and nonlocal parabolic inverse heat source problem. We show in this paper that the temperature dependent thermal growth parameter can be identified uniquely from a one-point measurement.