Precision Medicine with Imprecise Therapy: Computational Modeling for Chemotherapy in Breast Cancer

Medical oncology is in need of a mathematical modeling toolkit that can leverage clinically-available measurements to optimize treatment selection and schedules for patients. Just as the therapeutic choice has been optimized to match tumor genetics, the delivery of those therapeutics should be optimized based on patient-specific pharmacokinetic/pharmacodynamic properties. Under the current approach to treatment response planning and assessment, there does not exist an efficient method to consolidate biomarker changes into a holistic understanding of treatment response. While the majority of research on chemotherapies focus on cellular and genetic mechanisms of resistance, there are numerous patient-specific and tumor-specific measures that contribute to treatment response. New approaches that consolidate multimodal information into actionable data are needed. Mathematical modeling offers a solution to this problem. In this perspective, we first focus on the particular case of breast cancer to highlight how mathematical models have shaped the current approaches to treatment. Then we compare chemotherapy to radiation therapy. Finally, we identify opportunities to improve chemotherapy treatments using the model of radiation therapy. We posit that mathematical models can improve the application of anticancer therapeutics in the era of precision medicine. By highlighting a number of historical examples of the contributions of mathematical models to cancer therapy, we hope that this contribution serves to engage investigators who may not have previously considered how mathematical modeling can provide real insights into breast cancer therapy.     

Prospective image planning in radiation therapy for optimization of image quality and reduction of patient dose

IntroductionCT simulation data in image-guided radiation therapy (IGRT) provides patient-specific subject contrast. This information can be exploited to establish, a priori, a suitable imaging goal and to select patient-specific imaging acquisition parameters that optimize the similarity between reference and daily set-up images and reduce imaging dose. This study aims to describe and clinically validate a computerized algorithm designed to provide such optimization.Material and methodsAn image planning system (IPS) was developed to assist in planar kV imaging technique selection for radiation therapy. The system's patient-specific image quality and dose reduction capabilities were validated herein. Anthropomorphic phantom and clinical data were acquired. Mutual information (MI) was used to compare simulated and measured images in both phantom and clinical tests. Variations in contrast resolution resulting from imaging panel underexposure, saturation and a contrast plateau were investigated. For evaluation of patient-specific imaging dose reduction, the IPS was used to modify acquisition settings for six patients.ResultsPhantom data confirmed the IPS's predictive capability regarding image contrast. Measured and simulated images showed similar progressions from under-exposure, image quality peak, and loss of contrast due to detector saturation. Clinical data demonstrated that contrast resolution and imaging dose could be prospectively improved without loss of image contrast. The algorithm reduced imaging dose by an average of 47%, and a maximum of 80%.ConclusionsLoss of image contrast resulting from under-exposure or over-exposure, as well as a contrast plateau can be predicted by use of a prospective image planning algorithm. Image acquisition parameters can be predicted that reduce patient dose without loss of useful contrast.     

Imaging dose from cone beam computed tomography in radiation therapy

Imaging dose in radiation therapy has traditionally been ignored due to its low magnitude and frequency in comparison to therapeutic dose used to treat patients. The advent of modern, volumetric, imaging modalities, often as an integral part of linear accelerators, has facilitated the implementation of image-guided radiation therapy (IGRT), which is often accomplished by daily imaging of patients. Daily imaging results in additional dose delivered to patient that warrants new attention be given to imaging dose. This review summarizes the imaging dose delivered to patients as the result of cone beam computed tomography (CBCT) imaging performed in radiation therapy using current methods and equipment. This review also summarizes methods to calculate the imaging dose, including the use of Monte Carlo (MC) and treatment planning systems (TPS). Peripheral dose from CBCT imaging, dose reduction methods, the use of effective dose in describing imaging dose, and the measurement of CT dose index (CTDI) in CBCT systems are also reviewed.     

Addressing the dosimetric impact of bone cement and vertebroplasty in stereotactic body radiation therapy

PurposeBone cement used for vertebroplasty can affect the accuracy on the dose calculation of the radiation therapy treatment. In addition the CT values of high density objects themselves can be misrepresented in kVCT images. The aim of our study is then to propose a streamlined approach for estimating the real density of cement implants used in stereotactic body radiation therapy.MethodsSeveral samples of cement were manufactured and irradiated in order to investigate the impact of their composition on the radiation dose. The validity of the CT conversion method for a range of photon energies was investigated, for the studied samples and on six patients. Calculations and measurements were carried out with various overridden densities and dose prediction algorithms (AXB with dose-to-medium reporting or AAA) in order to find the effective density override.ResultsRelative dose differences of several percent were found between the dose measured and calculated downstream of the implant using an ion chamber and TPS or EPID dosimetry. If the correct density is assigned to the implant, calculations can provide clinically acceptable accuracy (gamma criteria of 3%/2 mm). The use of MV imaging significantly favors the attribution of a correct equivalent density to the implants compared to the use of kVCT images.ConclusionThe porosity and relative density of the various studied implants vary significantly. Bone cement density estimations can be characterized using MV imaging or planar in vivo dosimetry, which could help determining whether errors in dose calculations are due to incorrect densities.     

Simplification of head and neck volumetric modulated arc therapy patient-specific quality assurance,using a Delta4 PT

Background/AimIn many facilities, intensity-modulated radiation therapy (IMRT), and volumetric modulated arc therapy (VMAT) use intensity-modulated beams, formed by a multi-leaf collimator (MLC). In IMRT and VMAT, MLC and linear accelerator errors (both geometric and dose), can significantly affect the doses administered to patients. Therefore, IMRT and VMAT treatment plans must include the use of patient-specific quality assurance (QA) before treatment to confirm dose accuracy.Materials and methodsIn this study, we compared and analyzed the results of dose verification using a multi-dimensional dose verification system Delta4 PT, an ionization chamber dosimeter, and gafchromic film, using data from 52 patients undergoing head and neck VMAT as the test material.ResultBased on the results of the absolute dose verification for the ionization chamber dosimeter and Delta4 PT, taking an axial view, the upper limit of the 95% confidence interval was 3.13%, and the lower limit was −3.67%, indicating good agreement. These results mean that as long as absolute dose verification for the axial view does not deviate from this range, Delta4 PT can be used as an alternative to an ionization chamber dosimeter for absolute dose verification. When we then reviewed dose distribution verification, the pass rate for Delta4 PT was acceptable, and was less varied than that of gafchromic film.ConclusionThis results in that provided the pass rate result for Delta4 PT does not fall below 96%, it can be used as a substitute for gafchromic film in dose distribution verification. These results indicate that patient-specific QA could be simplified.     

Comparison of patient-specific intensity modulated radiation therapy quality assurance for the prostate across multiple institutions

AimTo evaluate the success of a patient-specific intensity modulated radiation therapy (IMRT) quality assurance (QA) practice for prostate cancer patients across multiple institutions using a questionnaire survey.BackgroundThe IMRT QA practice involves different methods of dose distribution verification and analysis at different institutions.Materials and MethodsTwo full-arc volumetric modulated arc therapy (VMAT) plan and 7 fixed-gantry IMRT plan with DMLC were used for patient specific QA across 22 institutions. The same computed tomography image and structure set were used for all plans. Each institution recalculated the dose distribution with fixed monitor units and without any modification. Single-point dose measurement with a cylindrical ionization chamber and dose distribution verification with a multi-detector or radiochromic film were performed, according to the QA process at each institution.ResultsTwenty-two institutions performed the patient-specific IMRT QA verifications. With a single-point dose measurement at the isocenter, the average difference between the calculated and measured doses was 0.5 ± 1.9%. For the comparison of dose distributions, 18 institutions used a two or three-dimensional array detector, while the others used Gafchromic film. In the γ test with dose difference/distance-to-agreement criteria of 3%?3 mm and 2%?2 mm with a 30% dose threshold, the median gamma pass rates were 99.3% (range: 41.7%–100.0%) and 96.4% (range: 29.4%–100.0%), respectively.ConclusionThis survey was an informative trial to understand the verification status of patient-specific IMRT QA measurements for prostate cancer. In most institutions, the point dose measurement and dose distribution differences met the desired criteria.     

Multiple Imputation of Missing Composite Outcomes in Longitudinal Data

In longitudinal randomised trials and observational studies within a medical context, a composite outcome—which is a function of several individual patient-specific outcomes—may be felt to best represent the outcome of interest. As in other contexts, missing data on patient outcome, due to patient drop-out or for other reasons, may pose a problem. Multiple imputation is a widely used method for handling missing data, but its use for composite outcomes has been seldom discussed. Whilst standard multiple imputation methodology can be used directly for the composite outcome, the distribution of a composite outcome may be of a complicated form and perhaps not amenable to statistical modelling. We compare direct multiple imputation of a composite outcome with separate imputation of the components of a composite outcome. We consider two imputation approaches. One approach involves modelling each component of a composite outcome using standard likelihood-based models. The other approach is to use linear increments methods. A linear increments approach can provide an appealing alternative as assumptions concerning both the missingness structure within the data and the imputation models are different from the standard likelihood-based approach. We compare both approaches using simulation studies and data from a randomised trial on early rheumatoid arthritis patients. Results suggest that both approaches are comparable and that for each, separate imputation offers some improvement on the direct imputation of a composite outcome.     

Robust Prediction of Anti-Cancer Drug Sensitivity and Sensitivity-Specific Biomarker

The personal genomics era has attracted a large amount of attention for anti-cancer therapy by patient-specific analysis. Patient-specific analysis enables discovery of individual genomic characteristics for each patient, and thus we can effectively predict individual genetic risk of disease and perform personalized anti-cancer therapy. Although the existing methods for patient-specific analysis have successfully uncovered crucial biomarkers, their performance takes a sudden turn for the worst in the presence of outliers, since the methods are based on non-robust manners. In practice, clinical and genomic alterations datasets usually contain outliers from various sources (e.g., experiment error, coding error, etc.) and the outliers may significantly affect the result of patient-specific analysis. We propose a robust methodology for patient-specific analysis in line with the NetwrokProfiler. In the proposed method, outliers in high dimensional gene expression levels and drug response datasets are simultaneously controlled by robust Mahalanobis distance in robust principal component space. Thus, we can effectively perform for predicting anti-cancer drug sensitivity and identifying sensitivity-specific biomarkers for individual patients. We observe through Monte Carlo simulations that the proposed robust method produces outstanding performances for predicting response variable in the presence of outliers. We also apply the proposed methodology to the Sanger dataset in order to uncover cancer biomarkers and predict anti-cancer drug sensitivity, and show the effectiveness of our method.     

Patient-specific modeling of dyssynchronous heart failure: A case study

The development and clinical use of patient-specific models of the heart is now a feasible goal. Models have the potential to aid in diagnosis and support decision-making in clinical cardiology. Several groups are now working on developing multi-scale models of the heart for understanding therapeutic mechanisms and better predicting clinical outcomes of interventions such as cardiac resynchronization therapy. Here we describe the methodology for generating a patient-specific model of the failing heart with a myocardial infarct and left ventricular bundle branch block. We discuss some of the remaining challenges in developing reliable patient-specific models of cardiac electromechanical activity, and identify some of the main areas for focusing future research efforts. Key challenges include: efficiently generating accurate patient-specific geometric meshes and mapping regional myofiber architecture to them; modeling electrical activation patterns based on cellular alterations in human heart failure, and estimating regional tissue conductivities based on clinically available electrocardiographic recordings; estimating unloaded ventricular reference geometry and material properties for biomechanical simulations; and parameterizing systemic models of circulatory dynamics from available hemodynamic measurements.     

A new analytical formula for neutron capture gamma dose calculations in double-bend mazes in radiation therapy

BackgroundPhotoneutrons are produced in radiation therapy with high energy photons. Also, capture gamma rays are the byproduct of neutrons interactions with wall material of radiotherapy rooms.AimIn the current study an analytical formula was proposed for capture gamma dose calculations in double bend mazes in radiation therapy rooms.Materials and methodsA total of 40 different layouts with double-bend mazes and a 18 MeV photon beam of Varian 2100 Clinac were simulated using MCNPX Monte Carlo (MC) code. Neutron capture gamma ray dose equivalent was calculated by the MC method along the maze and at the maze entrance door of all the simulated rooms. Then, all MC resulted data were fitted to an empirical formula for capture gamma dose calculations. Wu–McGinley analytical formula for capture gamma dose equivalent at the maze entrance door in single-bend mazes was also used for comparison purposes.ResultsFor capture gamma dose equivalents at the maze entrance door, the difference of 2–11% was seen between MC and the derived equation, while the difference of 36–87% was found between MC and the Wu–McGinley methods.ConclusionOur results showed that the derived formula results were consistent with the MC results for all of 40 different geometries. However, as a new formula, further evaluations are required to validate its use in practical situations. Finally, its application is recommend for capture gamma dose calculations in double-bend mazes to improve shielding calculations.     

Models for the risk of secondary cancers from radiation therapy

The interest in the induction of secondary tumours following radiotherapy has greatly increased as developments in detecting and treating the primary tumours have improved the life expectancy of cancer patients. However, most of the knowledge on the current levels of risk comes from patients treated many decades ago. As developments of irradiation techniques take place at a much faster pace than the progression of the carcinogenesis process, the earlier results could not be easily extrapolated to modern treatments. Indeed, the patterns of irradiation from historically-used orthovoltage radiotherapy and from contemporary techniques like conformal radiotherapy with megavoltage radiation, intensity modulated radiation therapy with photons or with particles are quite different. Furthermore, the increased interest in individualised treatment options raises the question of evaluating and ranking the different treatment plan options from the point of view of the risk for cancer induction, in parallel with the quantification of other long-term effects. It is therefore inevitable that models for risk assessment will have to be used to complement the knowledge from epidemiological studies and to make predictions for newer forms of treatment for which clinical evidence is not yet available. This work reviews the mathematical models that could be used to predict the risk of secondary cancers from radiotherapy-relevant dose levels, as well as the approaches and factors that have to be taken into account when including these models in the clinical evaluation process. These include the effects of heterogeneous irradiation, secondary particles production, imaging techniques, interpatient variability and other confounding factors.     

Problems of ensuring human radiation safety during interplanetary flights

The work contains the analyses and discussion of the main sources of space radiation specified for interplanetary flights, the dosimetric functionals used for describing the processes of radiation lesions and reparation of the organism in the conditions of the complex radiation impact with a broad charge composition of cosmic rays and a peculiar spatial and temporal dose behavior. It represents the results of calculations of the radiation risks during the flight and the total lifelong radiation risk with taking into account all the delayed unfavorable biological consequences. The main uncertainties in the calculated values of radiation risk leading to its undervaluation are analyzed. In addition, also provided is the range of theoretical and experimental investigations necessary for the adjustment of coefficient values used in the algorithm of radiation risk calculations, as well as in the nomenclature of experiments for estimating the individual resistance of man to the extreme influence and investigations aimed at estimating and increasing the reliability of the operator activity of cosmonauts.     

Feasibility of reducing differences in estimated doses in nuclear medicine between a patient-specific and a reference phantom

The feasibility of reducing the differences between patient-specific internal doses and doses estimated using reference phantoms was evaluated. Relatively simple adjustments to a polygon-surface ICRP adult male reference phantom were applied to fit selected individual dimensions using the software Rhinoceros®4.0. We tested this approach on two patient-specific phantoms: the biggest and the smallest phantoms from the Helmholtz Zentrum München library. These phantoms have unrelated anatomy and large differences in body-mass-index. Three models approximating each patient’s anatomy were considered: the voxel and the polygon-surface ICRP adult male reference phantoms and the adjusted polygon-surface reference phantom. The Specific Absorbed Fractions (SAFs) for internal photon and electron sources were calculated with the Monte Carlo code EGSnrc. Employing the time-integrated activity coefficients of a radiopharmaceutical (S)-4-(3-¹⁸F-fluoropropyl)-l-glutamic acid and the calculated SAFs, organ absorbed-dose coefficients were computed following the formalism promulgated by the Committee on Medical Internal Radiation Dose. We compared the absorbed-dose coefficients between each patient-specific phantom and other models considered with emphasis on the cross-fire component. The corresponding differences for most organs were notably lower for the adjusted reference models compared to the case when reference models were employed. Overall, the proposed approach provided reliable dose estimates for both tested patient-specific models despite the pronounced differences in their anatomy. To capture the full range of inter-individual anatomic variability more patient-specific phantoms are required. The results of this test study suggest a feasibility of estimating patient-specific doses within a relative uncertainty of 25% or less using adjusted reference models, when only simple phantom scaling is applied.     

Methodologies for predicting the expected combined stochastic radiobiological effects of different ionizing radiations and some applications

A methodology for predicting the expected combined stochastic radiobiological effects of sequential exposure to different ionizing radiations is used to arrive at a methodology for predicting the radiobiological effects of simultaneous exposure. Both methodologies require developing additive-damage dose-effect models. Additive-damage dose-effect models are derived assuming (a) each radiation comprised by the combined exposure produces initial damage called critical damage that could lead to the radiobiological effect of interest; (b) doses of different radiations that lead to the same level of radiobiological effect (or risk) can be viewed as producing the same amount of critical damage and being indistinguishable as far as the effects of subsequently administered radiation. Derived dose-effect functions that describe the risk per individual, conditional on radiation dose, are called risk functions. The methodologies allow the use of known radiation-specific risk functions to derive risk functions for combined effects of different radiations. The risk functions for combined exposure to different radiations are called global risk functions. For sequential exposures to different ionizing radiations, the global risk functions derived depend on how individual radiation doses are ordered. Global risk functions can also differ for sequential and simultaneous exposure. The methodologies are used to account for some previously unexplained radiobiological effects of combined exposure to high and low linear-energy-transfer radiations.     

Development of patient-specific 3D models from histopathological samples for applications in radiation therapy

The biological effects of ionizing radiation depend on the tissue, tumor type, radiation quality, and patient-specific factors. Inter-patient variation in cell/nucleus size may influence patient-specific dose response. However, this variability in dose response is not well investigated due to lack of available cell/nucleus size data. The aim of this study was to develop methods to derive cell/nucleus size distributions from digital images of 2D histopathological samples and use them to build digital 3D models for use in cellular dosimetry.Nineteen of sixty hematoxylin and eosin stained lung adenocarcinoma samples investigated passed exclusion criterion to be analyzed in the study. A difference of gaussians blob detection algorithm was used to identify nucleus centers and quantify cell spacing. Hematoxylin content was measured to determine nucleus radius. Pouring simulations were conducted to generate one-hundred 3D models containing volumes of equivalent cell spacing and nuclei radius to those in histopathological samples.The nuclei radius distributions of non-tumoral and cancerous regions appearing in the same slide were significantly different (p < 0.01) in all samples analyzed. The median nuclear-cytoplasmic ratio was 0.36 for non-tumoral cells and 0.50 for cancerous cells. The average cellular and nucleus packing densities in the 3D models generated were 65.9% (SD: 1.5%) and 13.3% (SD: 0.3%) respectively.Software to determine cell spacing and nuclei radius from histopathological samples was developed. 3D digital tissue models containing volumes with equivalent cell spacing, nucleus radius, and packing density to cancerous tissues were generated.     

Evaluation of automated statistical shape model based knee kinematics from biplane fluoroscopy

State-of-the-art fluoroscopic knee kinematic analysis methods require the patient-specific bone shapes segmented from CT or MRI. Substituting the patient-specific bone shapes with personalizable models, such as statistical shape models (SSM), could eliminate the CT/MRI acquisitions, and thereby decrease costs and radiation dose (when eliminating CT). SSM based kinematics, however, have not yet been evaluated on clinically relevant joint motion parameters.     

Using adaptive model predictive control to customize maintenance therapy chemotherapeutic dosing for childhood acute lymphoblastic leukemia

Acute lymphoblastic leukemia (ALL) is a common childhood cancer in which nearly one-quarter of patients experience a disease relapse. However, it has been shown that individualizing therapy for childhood ALL patients by adjusting doses based on the blood concentration of active drug metabolite could significantly improve treatment outcome. An adaptive model predictive control (MPC) strategy is presented in which maintenance therapy for childhood ALL is personalized using routine patient measurements of red blood cell mean corpuscular volume as a surrogate for the active drug metabolite concentration. A clinically relevant mathematical model is developed and used to describe the patient response to the chemotherapeutic drug 6-mercaptopurine, with some model parameters being patient-specific. During the course of treatment, the patient-specific parameters are adaptively identified using recurrent complete blood count measurements, which sufficiently constrain the patient parameter uncertainty to support customized adjustments of the drug dose. While this work represents only a first step toward a quantitative tool for clinical use, the simulated treatment results indicate that the proposed mathematical model and adaptive MPC approach could serve as valuable resources to the oncologist toward creating a personalized treatment strategy that is both safe and effective.     

Validation of Dolphin dosimetry in three dimensional patient-specific quality assurance programme

AimThe aim of this study is to commission and validate Dolphin-Compass dosimetry as a patient-specific Quality Assurance (QA) device.BackgroundThe advancement of radiation therapy in terms of highly conformal delivery techniques demands a novel method of patient-specific QA. Dolphin-Compass system is a dosimetry solution capable of doing different QA in radiation therapy.Materials and methodsDolphin, air-vented ionization detector array mounted on Versa-HD Linear Accelerator (LINAC) was used for measurements. The Compass is a dose computation algorithm which requires modelling of LINAC head similar to other Treatment Planning Systems (TPS). The dosimetry system was commissioned after measuring the required beam data. The validation was performed by comparison of treatment plans generated in Monaco TPS against the measurement data. Different types of simple, complex, static and dynamic radiation fields and highly conformal treatment plans of patients were used in this study.ResultsFor all field sizes, point doses obtained from Dolphin-Compass dosimetry were in good agreement with the corresponding TPS calculated values in most of the regions, except the penumbra, outside field and at build-up depth. The results of gamma passing rates of measurements by using different Multi-leaf Collimator patterns and Intensity Modulated Radiation Therapy fluence were also found to be in good correlation with the corresponding TPS values.ConclusionsThe commissioning and validation of dosimetry was performed with the help of various fields, MLC patterns and complex treatment plans. The present study also evaluated the efficiency of the 3D dosimetry system for the QA of complex treatment plans.     

Neutron, proton, and photonuclear cross-sections for radiation therapy and radiation protection

I review recent work at Los Alamos undertaken to evaluate neutron, proton, and photonuclear cross-sections up to 150 MeV (to 250 MeV for protons), based on experimental data and nuclear model calculations. These data are represented in the ENDF format and can be used in computer codes to simulate radiation transport. They permit calculations of absorbed dose in the body from therapy beams, and through use of kerma coefficients allow absorbed dose to be estimated for a given neutron energy distribution. In radiation protection, these data can be used to determine shielding requirements in accelerator environments and to calculate neutron, proton, gamma-ray, and radionuclide production. Illustrative comparisons of the evaluated cross-section and kerma coefficient data with measurements are given.