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Hami R, Apeke S, Redou P, Gaubert L, Dubois LJ, Lambin P, Visvikis D, Boussion N. Predicting the Tumour Response to Radiation by Modelling the Five Rs of Radiotherapy Using PET Images. J Imaging 2023; 9:124. [PMID: 37367472 DOI: 10.3390/jimaging9060124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Revised: 06/10/2023] [Accepted: 06/13/2023] [Indexed: 06/28/2023] Open
Abstract
Despite the intensive use of radiotherapy in clinical practice, its effectiveness depends on several factors. Several studies showed that the tumour response to radiation differs from one patient to another. The non-uniform response of the tumour is mainly caused by multiple interactions between the tumour microenvironment and healthy cells. To understand these interactions, five major biologic concepts called the "5 Rs" have emerged. These concepts include reoxygenation, DNA damage repair, cell cycle redistribution, cellular radiosensitivity and cellular repopulation. In this study, we used a multi-scale model, which included the five Rs of radiotherapy, to predict the effects of radiation on tumour growth. In this model, the oxygen level was varied in both time and space. When radiotherapy was given, the sensitivity of cells depending on their location in the cell cycle was taken in account. This model also considered the repair of cells by giving a different probability of survival after radiation for tumour and normal cells. Here, we developed four fractionation protocol schemes. We used simulated and positron emission tomography (PET) imaging with the hypoxia tracer 18F-flortanidazole (18F-HX4) images as input data of our model. In addition, tumour control probability curves were simulated. The result showed the evolution of tumours and normal cells. The increase in the cell number after radiation was seen in both normal and malignant cells, which proves that repopulation was included in this model. The proposed model predicts the tumour response to radiation and forms the basis for a more patient-specific clinical tool where related biological data will be included.
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Affiliation(s)
- Rihab Hami
- INSERM UMR 1101 "LaTIM", CEDEX 3, 29238 Brest, France
| | - Sena Apeke
- INSERM UMR 1101 "LaTIM", CEDEX 3, 29238 Brest, France
- CERV, European Center for Virtual Reality, ENIB, CEDEX 3, 29238 Brest, France
| | - Pascal Redou
- INSERM UMR 1101 "LaTIM", CEDEX 3, 29238 Brest, France
- CERV, European Center for Virtual Reality, ENIB, CEDEX 3, 29238 Brest, France
| | - Laurent Gaubert
- INSERM UMR 1101 "LaTIM", CEDEX 3, 29238 Brest, France
- CERV, European Center for Virtual Reality, ENIB, CEDEX 3, 29238 Brest, France
| | - Ludwig J Dubois
- The D-Lab, Department of Precision Medicine, GROW-School for Oncology, Maastricht University, 6211 LK Maastricht, The Netherlands
| | - Philippe Lambin
- The D-Lab, Department of Precision Medicine, GROW-School for Oncology, Maastricht University, 6211 LK Maastricht, The Netherlands
| | - Dimitris Visvikis
- INSERM UMR 1101 "LaTIM", CEDEX 3, 29238 Brest, France
- CHRU BREST, 29200 Brest, France
| | - Nicolas Boussion
- INSERM UMR 1101 "LaTIM", CEDEX 3, 29238 Brest, France
- CHRU BREST, 29200 Brest, France
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Böhlen TT, Germond JF, Bourhis J, Vozenin MC, Bailat C, Bochud F, Moeckli R. Technical Note: Break-even dose level for hypofractionated treatment schedules. Med Phys 2021; 48:7534-7540. [PMID: 34609744 PMCID: PMC9298418 DOI: 10.1002/mp.15267] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2021] [Revised: 09/03/2021] [Accepted: 09/24/2021] [Indexed: 01/10/2023] Open
Abstract
PURPOSE To derive the isodose line R relative to the prescription dose below which irradiated normal tissue (NT) regions benefit from a hypofractionated schedule with an isoeffective dose to the tumor. To apply the formalism to clinical case examples. METHODS From the standard biologically effective dose (BED) equation based on the linear-quadratic (LQ) model, the BED of an NT that receives a relative proportion r of the prescribed dose per fraction for a given α/β-ratio of the tumor, (α/β)T , and NT, (α/β)NT , is derived for different treatment schedules while keeping the BED to the tumor constant. Based on this, the "break-even" isodose line R is then derived. The BED of NT regions that receive doses below R decreases for more hypofractionated treatment schedules, and hence a lower risk for NT injury is predicted in these regions. To assess the impact of a linear behavior of BED for high doses per fraction (>6 Gy), we evaluated BED also using the LQ-linear (LQ-L) model. RESULTS The formalism provides the equations to derive the BED of an NT as function of dose per fraction for an isoeffective dose to the tumor and the corresponding break-even isodose line R. For generic α/β-ratios of (α/β)T = 10 Gy and (α/β)NT = 3 Gy and homogeneous dose in the target, R is 30%. R is doubling for stereotactic treatments for which tumor control correlates with the maximum dose of 100% instead of the encompassing isodose line of 50%. When using the LQ-L model, the notion of a break-even dose level R remains valid up to about 20 Gy per fraction for generic α/β-ratios and D T = 2 ( α / β ) . CONCLUSIONS The formalism may be used to estimate below which relative isodose line R there will be a differential sparing of NT when increasing hypofractionation. More generally, it allows to assess changes of the therapeutic index for sets of isoeffective treatment schedules at different relative dose levels compared to a reference schedule in a compact manner.
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Affiliation(s)
- Till Tobias Böhlen
- Institute of Radiation Physics, Lausanne University Hospital and Lausanne University, Lausanne, Switzerland
| | - Jean-François Germond
- Institute of Radiation Physics, Lausanne University Hospital and Lausanne University, Lausanne, Switzerland
| | - Jean Bourhis
- Radiation-Oncology Department, Lausanne University Hospital and University of Lausanne, Lausanne, Switzerland
| | - Marie-Catherine Vozenin
- Radiation-Oncology Department, Lausanne University Hospital and University of Lausanne, Lausanne, Switzerland
| | - Claude Bailat
- Institute of Radiation Physics, Lausanne University Hospital and Lausanne University, Lausanne, Switzerland
| | - François Bochud
- Institute of Radiation Physics, Lausanne University Hospital and Lausanne University, Lausanne, Switzerland
| | - Raphaël Moeckli
- Institute of Radiation Physics, Lausanne University Hospital and Lausanne University, Lausanne, Switzerland
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Ghate A. Imputing radiobiological parameters of the linear-quadratic dose-response model from a radiotherapy fractionation plan. Phys Med Biol 2020; 65:225009. [PMID: 32937610 DOI: 10.1088/1361-6560/abb935] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
The objective in cancer radiotherapy is to maximize tumor-kill while limiting toxic effects of radiation dose on nearby organs-at-risk (OAR). Given a fixed number of treatment sessions, planners thus face the problem of finding a dosing sequence that achieves this goal. This is called the fractionation problem, and has received steady attention over a long history in the clinical literature. Mathematical formulations of the resulting optimization problem utilize the linear-quadratic (LQ) framework to characterize radiation dose-response of tumors and OAR. This yields a nonconvex quadratically constrained quadratic program. The optimal dosing plan in this forward problem crucially depends on the parameters of the LQ model. Unfortunately, these parameters are difficult to estimate via in vitro or in vivo studies, and as such, their values are unknown to treatment planners. The clinical literature is thus replete with debates about what parameter values will make specific dosing plans effective. This paper formulates this as an inverse optimization problem. The LQ dose-response parameters appear in the objective function, the left hand side, and the right hand side of the forward problem, and none of the existing generic methods can provide an exact solution of the inverse problem. This paper exploits the structure of the problem and identifies all possible parameter values that render the given dosing plan optimal, in closed-form. This closed-form formula is applied to dosing-plans from three clinical studies published within the last two years.
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Affiliation(s)
- Archis Ghate
- Industrial & Systems Engineering, University of Washington, Seattle, United States of America
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Tien CJ, Bond JE, Chen ZJ. Associating dose-volume characteristics with theoretical radiobiological metrics for rapid Gamma Knife stereotactic radiosurgery plan evaluation. J Appl Clin Med Phys 2020; 21:132-140. [PMID: 32910543 PMCID: PMC7592963 DOI: 10.1002/acm2.13018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2020] [Revised: 07/17/2020] [Accepted: 07/30/2020] [Indexed: 12/03/2022] Open
Abstract
Purpose To examine general dose–volume characteristics in Gamma Knife (GK) plans which may be associated with higher tumor control probability (TCP) and equivalent uniform dose (EUD) using characteristic curve sets. Methods Two sets of dose–volume histograms (DVHs) were exported alongside an analytical purpose‐generated DVH: (a) single‐shot large collimator (8 or 16 mm) emulated with multiple shots of 4 mm collimator. (b) shot‐within‐shot (SWS) technique with isodose lines (IDLs) of 40–75%. TCP, average dose, EUD in single‐fraction (EUDT) and 2 Gy fractionated regimens (EUDR) were examined for trends with cumulative DVH (cDVH) shape as calculated using a linear‐quadratic cell survival model (α/β = 10.0 Gy, N0 = 1 × 106) with both α = 0.20 Gy−1 and α = 0.23 Gy−1. Results Using α = 0.20 Gy−1 (α = 0.23 Gy−1), plans in the analytical set with higher shoulder regions had TCP, EUDT, EUDR increased by 180%, 5.9%, 10.7% (11.2%, 6.3%, 10.0%), respectively. With α = 0.20 Gy−1 (α = 0.23 Gy−1), plans with higher heels had TCP, EUDT, EUDR increased by 4.0%, <1%, <1% (0.6%, <1%, <1%), respectively. In emulating a 16 (8) mm collimator, 64 (12) shots of the small collimators were used. Plans based on small collimators had higher shoulder regions and, with α = 0.20 Gy−1 (α = 0.23 Gy−1), TCP, EUDT, EUDR was increased up to 351.4%, 5.0%, 8.8% (270.4%, 5.0%, 6.8%) compared with the single‐shot large collimator. Delivery times ranged from 10.2 to 130.3 min. The SWS technique used 16:8 mm collimator weightings ranging from 1:2 to 9.2:1 for 40–75% IDL. With α = 0.20 Gy−1 (α = 0.23 Gy−1), the 40% IDL plan had the highest shoulder with increased TCP, EUDT, EUDR by 130.7%, 9.6%, 17.1% (12.9%, 9.1%, 16.4%) over the 75% IDL plan. Delivery times ranged 6.9–13.8 min. Conclusions The magnitude of the shoulder region characteristic to GK cDVHs may be used to rapidly identify superior plan among candidates. Practical issues such as delivery time may require further consideration.
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Affiliation(s)
- Christopher J Tien
- Department of Therapeutic Radiology, Yale School of Medicine, New Haven, CT, USA
| | - James E Bond
- Department of Therapeutic Radiology, Yale School of Medicine, New Haven, CT, USA
| | - Zhe Jay Chen
- Department of Therapeutic Radiology, Yale School of Medicine, New Haven, CT, USA
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Applications of Nonlinear Programming to the Optimization of Fractionated Protocols in Cancer Radiotherapy. INFORMATION 2020. [DOI: 10.3390/info11060313] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The present work of review collects and evidences the main results of our previous papers on the optimization of fractionated radiotherapy protocols. The problem under investigation is presented here in a unitary framework as a nonlinear programming application that aims to determine the optimal schemes of dose fractionation commonly used in external beam radiotherapy. The radiation responses of tumor and normal tissues are described by means of the linear quadratic model. We formulate a nonlinear, non-convex optimization problem including two quadratic constraints to limit the collateral normal tissue damages and linear box constraints on the fractional dose sizes. The general problem is decomposed into two subproblems: (1) analytical determination of the optimal fraction dose sizes as a function of the model parameters for arbitrarily fixed treatment lengths; and (2) numerical determination of the optimal fraction number, and of the optimal treatment time, in different parameter settings. After establishing the boundedness of the optimal number of fractions, we investigate by numerical simulation the optimal solution behavior for experimentally meaningful parameter ranges, recognizing the crucial role of some parameters, such as the radiosensitivity ratio, in determining the optimality of hypo- or equi-fractionated treatments. Our results agree with findings of the theoretical and clinical literature.
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Nourollahi S, Ghate A, Kim M. Optimal modality selection in external beam radiotherapy. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2019; 36:361-380. [PMID: 30192934 DOI: 10.1093/imammb/dqy013] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2017] [Revised: 08/07/2018] [Accepted: 08/13/2018] [Indexed: 12/25/2022]
Abstract
The goal in external beam radiotherapy (EBRT) for cancer is to maximize damage to the tumour while limiting toxic effects on the organs-at-risk. EBRT can be delivered via different modalities such as photons, protons and neutrons. The choice of an optimal modality depends on the anatomy of the irradiated area and the relative physical and biological properties of the modalities under consideration. There is no single universally dominant modality. We present the first-ever mathematical formulation of the optimal modality selection problem. We show that this problem can be tackled by solving the Karush-Kuhn-Tucker conditions of optimality, which reduce to an analytically tractable quartic equation. We perform numerical experiments to gain insights into the effect of biological and physical properties on the choice of an optimal modality or combination of modalities.
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Affiliation(s)
- Sevnaz Nourollahi
- Department of Industrial & Systems Engineering, University of Washington, Seattle, USA
| | - Archis Ghate
- Department of Industrial & Systems Engineering, University of Washington, Seattle, USA
| | - Minsun Kim
- Department of Radiation Oncology, University of Washington, Seattle, USA
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ten Eikelder SCM, den Hertog D, Bortfeld T, Perkó Z. Optimal combined proton–photon therapy schemes based on the standard BED model. ACTA ACUST UNITED AC 2019; 64:065011. [DOI: 10.1088/1361-6560/aafe52] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
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Ajdari A, Ghate A, Kim M. Adaptive treatment-length optimization in spatiobiologically integrated radiotherapy. ACTA ACUST UNITED AC 2018; 63:075009. [DOI: 10.1088/1361-6560/aab4b6] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
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Adibi A, Salari E. Spatiotemporal radiotherapy planning using a global optimization approach. ACTA ACUST UNITED AC 2018; 63:035040. [DOI: 10.1088/1361-6560/aaa729] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
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Bruni C, Conte F, Papa F, Sinisgalli C. Optimal number and sizes of the doses in fractionated radiotherapy according to the LQ model. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2018; 36:1-53. [DOI: 10.1093/imammb/dqx020] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2017] [Accepted: 12/10/2017] [Indexed: 01/18/2023]
Affiliation(s)
- C Bruni
- Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti” – CNR, Via dei Taurini 19, Rome, Italy
| | - F Conte
- Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti” – CNR, Via dei Taurini 19, Rome, Italy
| | - F Papa
- Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti” – CNR, Via dei Taurini 19, Rome, Italy
| | - C Sinisgalli
- Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti” – CNR, Via dei Taurini 19, Rome, Italy
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Zhu J, Badri H, Leder K. A Robust Optimization Approach to Cancer Treatment under Toxicity Uncertainty. Methods Mol Biol 2018; 1711:297-331. [PMID: 29344896 DOI: 10.1007/978-1-4939-7493-1_15] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The design of optimal protocols plays an important role in cancer treatment. However, in clinical applications, the outcomes under the optimal protocols are sensitive to variations of parameter settings such as drug effects and the attributes of age, weight, and health conditions in human subjects. One approach to overcoming this challenge is to formulate the problem of finding an optimal treatment protocol as a robust optimization problem (ROP) that takes parameter uncertainty into account. In this chapter, we describe a method to model toxicity uncertainty. We then apply a mixed integer ROP to derive the optimal protocols that minimize the cumulative tumor size. While our method may be applied to other cancers, in this work we focus on the treatment of chronic myeloid leukemia (CML) with tyrosine kinase inhibitors (TKI). For simplicity, we focus on one particular mode of toxicity arising from TKI therapy, low blood cell counts, in particular low absolute neutrophil count (ANC). We develop optimization methods for locating optimal treatment protocols assuming that the rate of decrease of ANC varies within a given interval. We further investigated the relationship between parameter uncertainty and optimal protocols. Our results suggest that the dosing schedule can significantly reduce tumor size without recurrence in 360 weeks while insuring that toxicity constraints are satisfied for all realizations of uncertain parameters.
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Affiliation(s)
- Junfeng Zhu
- Industrial and Systems Engineering, University of Minnesota, 111 Church street SE, Minneapolis, MN, 55455, USA
| | - Hamidreza Badri
- Industrial and Systems Engineering, University of Minnesota, 111 Church street SE, Minneapolis, MN, 55455, USA
| | - Kevin Leder
- Industrial and Systems Engineering, University of Minnesota, 111 Church street SE, Minneapolis, MN, 55455, USA.
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Evaluating optimal therapy robustness by virtual expansion of a sample population, with a case study in cancer immunotherapy. Proc Natl Acad Sci U S A 2017; 114:E6277-E6286. [PMID: 28716945 DOI: 10.1073/pnas.1703355114] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Cancer is a highly heterogeneous disease, exhibiting spatial and temporal variations that pose challenges for designing robust therapies. Here, we propose the VEPART (Virtual Expansion of Populations for Analyzing Robustness of Therapies) technique as a platform that integrates experimental data, mathematical modeling, and statistical analyses for identifying robust optimal treatment protocols. VEPART begins with time course experimental data for a sample population, and a mathematical model fit to aggregate data from that sample population. Using nonparametric statistics, the sample population is amplified and used to create a large number of virtual populations. At the final step of VEPART, robustness is assessed by identifying and analyzing the optimal therapy (perhaps restricted to a set of clinically realizable protocols) across each virtual population. As proof of concept, we have applied the VEPART method to study the robustness of treatment response in a mouse model of melanoma subject to treatment with immunostimulatory oncolytic viruses and dendritic cell vaccines. Our analysis (i) showed that every scheduling variant of the experimentally used treatment protocol is fragile (nonrobust) and (ii) discovered an alternative region of dosing space (lower oncolytic virus dose, higher dendritic cell dose) for which a robust optimal protocol exists.
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Badri H, Leder K. Optimal treatment and stochastic modeling of heterogeneous tumors. Biol Direct 2016; 11:40. [PMID: 27549860 PMCID: PMC4994177 DOI: 10.1186/s13062-016-0142-5] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2016] [Accepted: 07/07/2016] [Indexed: 12/24/2022] Open
Abstract
UNLABELLED In this work we review past articles that have mathematically studied cancer heterogeneity and the impact of this heterogeneity on the structure of optimal therapy. We look at past works on modeling how heterogeneous tumors respond to radiotherapy, and take a particularly close look at how the optimal radiotherapy schedule is modified by the presence of heterogeneity. In addition, we review past works on the study of optimal chemotherapy when dealing with heterogeneous tumors. REVIEWERS This article was reviewed by Thomas McDonald, David Axelrod, and Leonid Hanin.
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Affiliation(s)
- Hamidreza Badri
- Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN 55455 USA
| | - Kevin Leder
- Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN 55455 USA
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