Reinforcement learning informs optimal treatment strategies to limit antibiotic resistance.

Antimicrobial resistance was estimated to be associated with 4.95 million deaths worldwide in 2019. It is possible to frame the antimicrobial resistance problem as a feedback-control problem. If we could optimize this feedback-control problem and translate our findings to the clinic, we could slow, prevent, or reverse the development of high-level drug resistance. Prior work on this topic has relied on systems where the exact dynamics and parameters were known a priori. In this study, we extend this work using a reinforcement learning (RL) approach capable of learning effective drug cycling policies in a system defined by empirically measured fitness landscapes. Crucially, we show that it is possible to learn effective drug cycling policies despite the problems of noisy, limited, or delayed measurement. Given access to a panel of 15 [Formula: see text]-lactam antibiotics with which to treat the simulated Escherichia coli population, we demonstrate that RL agents outperform two naive treatment paradigms at minimizing the population fitness over time. We also show that RL agents approach the performance of the optimal drug cycling policy. Even when stochastic noise is introduced to the measurements of population fitness, we show that RL agents are capable of maintaining evolving populations at lower growth rates compared to controls. We further tested our approach in arbitrary fitness landscapes of up to 1,024 genotypes. We show that minimization of population fitness using drug cycles is not limited by increasing genome size. Our work represents a proof-of-concept for using AI to control complex evolutionary processes.

Threshold-awareness in adaptive cancer therapy.

Although adaptive cancer therapy shows promise in integrating evolutionary dynamics into treatment scheduling, the stochastic nature of cancer evolution has seldom been taken into account. Various sources of random perturbations can impact the evolution of heterogeneous tumors, making performance metrics of any treatment policy random as well. In this paper, we propose an efficient method for selecting optimal adaptive treatment policies under randomly evolving tumor dynamics. The goal is to improve the cumulative "cost" of treatment, a combination of the total amount of drugs used and the total treatment time. As this cost also becomes random in any stochastic setting, we maximize the probability of reaching the treatment goals (tumor stabilization or eradication) without exceeding a pre-specified cost threshold (or a "budget"). We use a novel Stochastic Optimal Control formulation and Dynamic Programming to find such "threshold-aware" optimal treatment policies. Our approach enables an efficient algorithm to compute these policies for a range of threshold values simultaneously. Compared to treatment plans shown to be optimal in a deterministic setting, the new "threshold-aware" policies significantly improve the chances of the therapy succeeding under the budget, which is correlated with a lower general drug usage. We illustrate this method using two specific examples, but our approach is far more general and provides a new tool for optimizing adaptive therapies based on a broad range of stochastic cancer models.

Diverse mutant selection windows shape spatial heterogeneity in evolving populations.

Mutant selection windows (MSWs), the range of drug concentrations that select for drug-resistant mutants, have long been used as a model for predicting drug resistance and designing optimal dosing strategies in infectious disease. The canonical MSW model offers comparisons between two subtypes at a time: drug-sensitive and drug-resistant. In contrast, the fitness landscape model with N alleles, which maps genotype to fitness, allows comparisons between N genotypes simultaneously, but does not encode continuous drug response data. In clinical settings, there may be a wide range of drug concentrations selecting for a variety of genotypes in both cancer and infectious diseases. Therefore, there is a need for a more robust model of the pathogen response to therapy to predict resistance and design new therapeutic approaches. Fitness seascapes, which model genotype-by-environment interactions, permit multiple MSW comparisons simultaneously by encoding genotype-specific dose-response data. By comparing dose-response curves, one can visualize the range of drug concentrations where one genotype is selected over another. In this work, we show how N-allele fitness seascapes allow for N * 2N-1 unique MSW comparisons. In spatial drug diffusion models, we demonstrate how fitness seascapes reveal spatially heterogeneous MSWs, extending the MSW model to more fully reflect the selection of drug resistant genotypes. Furthermore, using synthetic data and empirical dose-response data in cancer, we find that the spatial structure of MSWs shapes the evolution of drug resistance in an agent-based model. By simulating a tumor treated with cyclic drug therapy, we find that mutant selection windows introduced by drug diffusion promote the proliferation of drug resistant cells. Our work highlights the importance and utility of considering dose-dependent fitness seascapes in evolutionary medicine.

Habitat escalated adaptive therapy (HEAT): a phase 2 trial utilizing radiomic habitat-directed and genomic-adjusted radiation dose (GARD) optimization for high-grade soft tissue sarcoma.

BACKGROUND: Soft tissue sarcomas (STS), have significant inter- and intra-tumoral heterogeneity, with poor response to standard neoadjuvant radiotherapy (RT). Achieving a favorable pathologic response (FPR ≥ 95%) from RT is associated with improved patient outcome. Genomic adjusted radiation dose (GARD), a radiation-specific metric that quantifies the expected RT treatment effect as a function of tumor dose and genomics, proposed that STS is significantly underdosed. STS have significant radiomic heterogeneity, where radiomic habitats can delineate regions of intra-tumoral hypoxia and radioresistance. We designed a novel clinical trial, Habitat Escalated Adaptive Therapy (HEAT), utilizing radiomic habitats to identify areas of radioresistance within the tumor and targeting them with GARD-optimized doses, to improve FPR in high-grade STS. METHODS: Phase 2 non-randomized single-arm clinical trial includes non-metastatic, resectable high-grade STS patients. Pre-treatment multiparametric MRIs (mpMRI) delineate three distinct intra-tumoral habitats based on apparent diffusion coefficient (ADC) and dynamic contrast enhanced (DCE) sequences. GARD estimates that simultaneous integrated boost (SIB) doses of 70 and 60 Gy in 25 fractions to the highest and intermediate radioresistant habitats, while the remaining volume receives standard 50 Gy, would lead to a > 3 fold FPR increase to 24%. Pre-treatment CT guided biopsies of each habitat along with clip placement will be performed for pathologic evaluation, future genomic studies, and response assessment. An mpMRI taken between weeks two and three of treatment will be used for biological plan adaptation to account for tumor response, in addition to an mpMRI after the completion of radiotherapy in addition to pathologic response, toxicity, radiomic response, disease control, and survival will be evaluated as secondary endpoints. Furthermore, liquid biopsy will be performed with mpMRI for future ancillary studies. DISCUSSION: This is the first clinical trial to test a novel genomic-based RT dose optimization (GARD) and to utilize radiomic habitats to identify and target radioresistance regions, as a strategy to improve the outcome of RT-treated STS patients. Its success could usher in a new phase in radiation oncology, integrating genomic and radiomic insights into clinical practice and trial designs, and may reveal new radiomic and genomic biomarkers, refining personalized treatment strategies for STS. TRIAL REGISTRATION: NCT05301283. TRIAL STATUS: The trial started recruitment on March 17, 2022.

Inferring density-dependent population dynamics mechanisms through rate disambiguation for logistic birth-death processes.

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can manifest in birth processes, death processes, or both. Therefore, we utilize the mean and variance of cell number fluctuations to separately identify birth and death rates from time series that follow stochastic birth-death processes with logistic growth. Our nonparametric method provides a novel perspective on stochastic parameter identifiability, which we validate by analyzing the accuracy in terms of the discretization bin size. We apply our method to the scenario where a homogeneous cell population goes through three stages: (1) grows naturally to its carrying capacity, (2) is treated with a drug that reduces its carrying capacity, and (3) overcomes the drug effect to restore its original carrying capacity. In each stage, we disambiguate whether the dynamics occur through the birth process, death process, or some combination of the two, which contributes to understanding drug resistance mechanisms. In the case of limited sample sizes, we provide an alternative method based on maximum likelihood and solve a constrained nonlinear optimization problem to identify the most likely density dependence parameter for a given cell number time series. Our methods can be applied to other biological systems at different scales to disambiguate density-dependent mechanisms underlying the same net growth rate.

Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems.

Theoretical and applied cancer studies that use individual-based models (IBMs) have been limited by the lack of a mathematical formulation that enables rigorous analysis of these models. However, spatial cumulant models (SCMs), which have arisen from theoretical ecology, describe population dynamics generated by a specific family of IBMs, namely spatio-temporal point processes (STPPs). SCMs are spatially resolved population models formulated by a system of differential equations that approximate the dynamics of two STPP-generated summary statistics: first-order spatial cumulants (densities), and second-order spatial cumulants (spatial covariances). We exemplify how SCMs can be used in mathematical oncology by modelling theoretical cancer cell populations comprising interacting growth factor-producing and non-producing cells. To formulate model equations, we use computational tools that enable the generation of STPPs, SCMs and mean-field population models (MFPMs) from user-defined model descriptions (Cornell et al. Nat Commun 10:4716, 2019). To calculate and compare STPP, SCM and MFPM-generated summary statistics, we develop an application-agnostic computational pipeline. Our results demonstrate that SCMs can capture STPP-generated population density dynamics, even when MFPMs fail to do so. From both MFPM and SCM equations, we derive treatment-induced death rates required to achieve non-growing cell populations. When testing these treatment strategies in STPP-generated cell populations, our results demonstrate that SCM-informed strategies outperform MFPM-informed strategies in terms of inhibiting population growths. We thus demonstrate that SCMs provide a new framework in which to study cell-cell interactions, and can be used to describe and perturb STPP-generated cell population dynamics. We, therefore, argue that SCMs can be used to increase IBMs' applicability in cancer research.

Evolution-Informed Strategies for Combating Drug Resistance in Cancer.

The ever-changing nature of cancer poses the most difficult challenge oncologists face today. Cancer's remarkable adaptability has inspired many to work toward understanding the evolutionary dynamics that underlie this disease in hopes of learning new ways to fight it. Eco-evolutionary dynamics of a tumor are not accounted for in most standard treatment regimens, but exploiting them would help us combat treatment-resistant effectively. Here, we outline several notable efforts to exploit these dynamics and circumvent drug resistance in cancer.

Machine learning demonstrates that somatic mutations imprint invariant morphologic features in myelodysplastic syndromes.

Morphologic interpretation is the standard in diagnosing myelodysplastic syndrome (MDS), but it has limitations, such as varying reliability in pathologic evaluation and lack of integration with genetic data. Somatic events shape morphologic features, but the complexity of morphologic and genetic changes makes clear associations challenging. This article interrogates novel clinical subtypes of MDS using a machine-learning technique devised to identify patterns of cooccurrence among morphologic features and genomic events. We sequenced 1079 MDS patients and analyzed bone marrow morphologic alterations and other clinical features. A total of 1929 somatic mutations were identified. Five distinct morphologic profiles with unique clinical characteristics were defined. Seventy-seven percent of higher-risk patients clustered in profile 1. All lower-risk (LR) patients clustered into the remaining 4 profiles: profile 2 was characterized by pancytopenia, profile 3 by monocytosis, profile 4 by elevated megakaryocytes, and profile 5 by erythroid dysplasia. These profiles could also separate patients with different prognoses. LR MDS patients were classified into 8 genetic signatures (eg, signature A had TET2 mutations, signature B had both TET2 and SRSF2 mutations, and signature G had SF3B1 mutations), demonstrating association with specific morphologic profiles. Six morphologic profiles/genetic signature associations were confirmed in a separate analysis of an independent cohort. Our study demonstrates that nonrandom or even pathognomonic relationships between morphology and genotype to define clinical features can be identified. This is the first comprehensive implementation of machine-learning algorithms to elucidate potential intrinsic interdependencies among genetic lesions, morphologies, and clinical prognostic in attributes of MDS.

Network potential identifies therapeutic miRNA cocktails in Ewing sarcoma.

MicroRNA (miRNA)-based therapies are an emerging class of targeted therapeutics with many potential applications. Ewing Sarcoma patients could benefit dramatically from personalized miRNA therapy due to inter-patient heterogeneity and a lack of druggable (to this point) targets. However, because of the broad effects miRNAs may have on different cells and tissues, trials of miRNA therapies have struggled due to severe toxicity and unanticipated immune response. In order to overcome this hurdle, a network science-based approach is well-equipped to evaluate and identify miRNA candidates and combinations of candidates for the repression of key oncogenic targets while avoiding repression of essential housekeeping genes. We first characterized 6 Ewing sarcoma cell lines using mRNA sequencing. We then estimated a measure of tumor state, which we term network potential, based on both the mRNA gene expression and the underlying protein-protein interaction network in the tumor. Next, we ranked mRNA targets based on their contribution to network potential. We then identified miRNAs and combinations of miRNAs that preferentially act to repress mRNA targets with the greatest influence on network potential. Our analysis identified TRIM25, APP, ELAV1, RNF4, and HNRNPL as ideal mRNA targets for Ewing sarcoma therapy. Using predicted miRNA-mRNA target mappings, we identified miR-3613-3p, let-7a-3p, miR-300, miR-424-5p, and let-7b-3p as candidate optimal miRNAs for preferential repression of these targets. Ultimately, our work, as exemplified in the case of Ewing sarcoma, describes a novel pipeline by which personalized miRNA cocktails can be designed to maximally perturb gene networks contributing to cancer progression.

Pan-cancer prediction of radiotherapy benefit using genomic-adjusted radiation dose (GARD): a cohort-based pooled analysis.

BACKGROUND: Despite advances in cancer genomics, radiotherapy is still prescribed on the basis of an empirical one-size-fits-all paradigm. Previously, we proposed a novel algorithm using the genomic-adjusted radiation dose (GARD) model to personalise prescription of radiation dose on the basis of the biological effect of a given physical dose of radiation, calculated using individual tumour genomics. We hypothesise that GARD will reveal interpatient heterogeneity associated with opportunities to improve outcomes compared with physical dose of radiotherapy alone. We aimed to test this hypothesis and investigate the GARD-based radiotherapy dosing paradigm. METHODS: We did a pooled, pan-cancer analysis of 11 previously published clinical cohorts of unique patients with seven different types of cancer, which are all available cohorts with the data required to calculate GARD, together with clinical outcome. The included cancers were breast cancer, head and neck cancer, non-small-cell lung cancer, pancreatic cancer, endometrial cancer, melanoma, and glioma. Our dataset comprised 1615 unique patients, of whom 1298 (982 with radiotherapy, 316 without radiotherapy) were assessed for time to first recurrence and 677 patients (424 with radiotherapy and 253 without radiotherapy) were assessed for overall survival. We analysed two clinical outcomes of interest: time to first recurrence and overall survival. We used Cox regression, stratified by cohort, to test the association between GARD and outcome with separate models using dose of radiation and sham-GARD (ie, patients treated without radiotherapy, but modelled as having a standard-of-care dose of radiotherapy) for comparison. We did interaction tests between GARD and treatment (with or without radiotherapy) using the Wald statistic. FINDINGS: Pooled analysis of all available data showed that GARD as a continuous variable is associated with time to first recurrence (hazard ratio [HR] 0·98 [95% CI 0·97-0·99]; p=0·0017) and overall survival (0·97 [0·95-0·99]; p=0·0007). The interaction test showed the effect of GARD on overall survival depends on whether or not that patient received radiotherapy (Wald statistic p=0·011). The interaction test for GARD and radiotherapy was not significant for time to first recurrence (Wald statistic p=0·22). The HR for physical dose of radiation was 0·99 (95% CI 0·97-1·01; p=0·53) for time to first recurrence and 1·00 (0·96-1·04; p=0·95) for overall survival. The HR for sham-GARD was 1·00 (0·97-1·03; p=1·00) for time to first recurrence and 1·00 (0·98-1·02; p=0·87) for overall survival. INTERPRETATION: The biological effect of radiotherapy, as quantified by GARD, is significantly associated with time to first recurrence and overall survival for patients with cancer treated with radiation. It is predictive of radiotherapy benefit, and physical dose of radiation is not. We propose integration of genomics into radiation dosing decisions, using a GARD-based framework, as the new paradigm for personalising radiotherapy prescription dose. FUNDING: None. VIDEO ABSTRACT.

Impact of immediate cryopreservation on the establishment of patient derived xenografts from head and neck cancer patients.

BACKGROUND: Patient-derived xenografts established from human cancers are important tools for investigating novel anti-cancer therapies. Establishing PDXs requires a significant investment and many PDXs may be used infrequently due to their similarity to existing models, their growth rate, or the lack of relevant mutations. We performed this study to determine whether we could efficiently establish PDXs after cryopreservation to allow molecular profiling to be completed prior to implanting the human cancer. METHODS: Fresh tumor was split with half used to establish a PDX immediately and half cryopreserved for later implantation. Resulting tumors were assessed histologically and tumors established from fresh or cryopreserved tissues compared as to the growth rate, extent of tumor necrosis, mitotic activity, keratinization, and grade. All PDXs were subjected to short tandem repeat testing to confirm identity and assess similarity between methods. RESULTS: Tumor growth was seen in 70% of implanted cases. No growth in either condition was seen in 30% of tumors. One developed a SCC from the immediate implant but a lymphoproliferative mass without SCC from the cryopreserved specimen. No difference in growth rate was seen. No difference between histologic parameters was seen between the two approaches. CONCLUSIONS: Fresh human cancer tissue can be immediately cryopreserved and later thawed and implanted to establish PDXs. This resource saving approach allows for tumor profiling prior to implantation into animals thus maximizing the probability that the tumor will be utilized for future research.

Inferring Tumor Proliferative Organization from Phylogenetic Tree Measures in a Computational Model.

We use a computational modeling approach to explore whether it is possible to infer a solid tumor's cellular proliferative hierarchy under the assumptions of the cancer stem cell hypothesis and neutral evolution. We work towards inferring the symmetric division probability for cancer stem cells, since this is believed to be a key driver of progression and therapeutic response. Motivated by the advent of multiregion sampling and resulting opportunities to infer tumor evolutionary history, we focus on a suite of statistical measures of the phylogenetic trees resulting from the tumor's evolution in different regions of parameter space and through time. We find strikingly different patterns in these measures for changing symmetric division probability which hinge on the inclusion of spatial constraints. These results give us a starting point to begin stratifying tumors by this biological parameter and also generate a number of actionable clinical and biological hypotheses regarding changes during therapy, and through tumor evolutionary time. [Cancer; evolution; phylogenetics.].

Evidence for hypoxia increasing the tempo of evolution in glioblastoma.

BACKGROUND: Tumour hypoxia is associated with metastatic disease, and while there have been many mechanisms proposed for why tumour hypoxia is associated with metastatic disease, it remains unclear whether one precise mechanism is the key reason or several in concert. Somatic evolution drives cancer progression and treatment resistance, fuelled not only by genetic and epigenetic mutation but also by selection from interactions between tumour cells, normal cells and physical micro-environment. Ecological habitats influence evolutionary dynamics, but the impact on tempo of evolution is less clear. METHODS: We explored this complex dialogue with a combined clinical-theoretical approach by simulating a proliferative hierarchy under heterogeneous oxygen availability with an agent-based model. Predictions were compared against histology samples taken from glioblastoma patients, stained to elucidate areas of necrosis and TP53 expression heterogeneity. RESULTS: Results indicate that cell division in hypoxic environments is effectively upregulated, with low-oxygen niches providing avenues for tumour cells to spread. Analysis of human data indicates that cell division is not decreased under hypoxia, consistent with our results. CONCLUSIONS: Our results suggest that hypoxia could be a crucible that effectively warps evolutionary velocity, making key mutations more likely. Thus, key tumour ecological niches such as hypoxic regions may alter the evolutionary tempo, driving mutations fuelling tumour heterogeneity.

Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory.

Recent clinical trials have shown that adaptive drug therapies can be more efficient than a standard cancer treatment based on a continuous use of maximum tolerated doses (MTD). The adaptive therapy paradigm is not based on a preset schedule; instead, the doses are administered based on the current state of tumour. But the adaptive treatment policies examined so far have been largely ad hoc. We propose a method for systematically optimizing adaptive policies based on an evolutionary game theory model of cancer dynamics. Given a set of treatment objectives, we use the framework of dynamic programming to find the optimal treatment strategies. In particular, we optimize the total drug usage and time to recovery by solving a Hamilton-Jacobi-Bellman equation. We compare MTD-based treatment strategy with optimal adaptive treatment policies and show that the latter can significantly decrease the total amount of drugs prescribed while also increasing the fraction of initial tumour states from which the recovery is possible. We conclude that the use of optimal control theory to improve adaptive policies is a promising concept in cancer treatment and should be integrated into clinical trial design.

Technical Note: A step-by-step guide to Temporally Feathered Radiation Therapy planning for head and neck cancer.

PURPOSE: Prior in silico simulations propose that Temporally Feathered Radiation Therapy (TFRT) may reduce toxicity related to head and neck radiation therapy. In this study we demonstrate a step-by-step guide to TFRT planning with modern treatment planning systems. METHODS: One patient with oropharyngeal cancer planned for definitive radiation therapy using intensity-modulated radiation therapy (IMRT) techniques was replanned using the TFRT technique. Five organs at risk (OAR) were identified to be feathered. A "base plan" was first created based on desired planning target volumes (PTV) coverage, plan conformality, and OAR constraints. The base plan was then re-optimized by modifying planning objectives, to generate five subplans. All beams from each subplan were imported onto one trial to create the composite TFRT plan. The composite TFRT plan was directly compared with the non-TFRT IMRT plan. During plan assessment, the composite TFRT was first evaluated followed by each subplan to meet preset compliance criteria. RESULTS: The following organs were feathered: oral cavity, right submandibular gland, left submandibular gland, supraglottis, and OAR Pharynx. Prescription dose PTV coverage (>95%) was met in each subplan and the composite TFRT plan. Expected small variations in dose were observed among the plans. The percent variation between the high fractional dose and average low fractional dose was 29%, 28%, 24%, 19%, and 10% for the oral cavity, right submandibular, left submandibular, supraglottis, and OAR pharynx nonoverlapping with the PTV. CONCLUSIONS: Temporally Feathered Radiation Therapy planning is possible with modern treatment planning systems. Modest dosimetric changes are observed with TFRT planning compared with non-TFRT IMRT planning. We await the results of the current prospective trial to seeking to demonstrate the feasibility of TFRT in the modern clinical workflow (NCT03768856). Further studies will be required to demonstrate the potential benefit of TFRT over non-TFRT IMRT Planning.

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.

Endogenous miRNA sponges mediate the generation of oscillatory dynamics for a non-coding RNA network.

Oscillations are crucial to the normal function of living organisms, across a wide variety of biological processes. In eukaryotes, oscillatory dynamics are thought to arise from interactions at the protein and RNA levels; however, the role of non-coding RNA in regulating these dynamics remains understudied. In this work, we show how non-coding RNA acting as microRNA (miRNA) sponges in a conserved miRNA - transcription factor feedback motif, can give rise to oscillatory behaviour, and how to test for this experimentally. Control of these non-coding RNA can dynamically create oscillations or stability, and we show how this behaviour predisposes to oscillations in the stochastic limit. These results, supported by emerging evidence for the role of miRNA sponges in development, point towards key roles of different species of miRNA sponges, such as circular RNA, potentially in the maintenance of yet unexplained oscillatory behaviour. These results help to provide a paradigm for understanding functional differences between the many redundant, but distinct RNA species thought to act as miRNA sponges in nature, such as long non-coding RNA, pseudogenes, competing mRNA, circular RNA, and3' UTRs.

Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs.

Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. The optimal timing of drug switching in these situations, however, remains unknown. To study this, we developed a dynamical model of sequential therapy on heterogeneous tumors comprised of resistant and sensitive cells. A pair of drugs (DrugA, DrugB) are utilized and are periodically switched during therapy. Assuming resistant cells to one drug are collaterally sensitive to the opposing drug, we classified cancer cells into two groups, [Formula: see text] and [Formula: see text], each of which is a subpopulation of cells resistant to the indicated drug and concurrently sensitive to the other, and we subsequently explored the resulting population dynamics. Specifically, based on a system of ordinary differential equations for [Formula: see text] and [Formula: see text], we determined that the optimal treatment strategy consists of two stages: an initial stage in which a chosen effective drug is utilized until a specific time point, T, and a second stage in which drugs are switched repeatedly, during which each drug is used for a relative duration (i.e., [Formula: see text]-long for DrugA and [Formula: see text]-long for DrugB with [Formula: see text] and [Formula: see text]). We prove that the optimal duration of the initial stage, in which the first drug is administered, T, is shorter than the period in which it remains effective in decreasing the total population, contrary to current clinical intuition. We further analyzed the relationship between population makeup, [Formula: see text], and the effect of each drug. We determine a critical ratio, which we term [Formula: see text], at which the two drugs are equally effective. As the first stage of the optimal strategy is applied, [Formula: see text] changes monotonically to [Formula: see text] and then, during the second stage, remains at [Formula: see text] thereafter. Beyond our analytic results, we explored an individual-based stochastic model and presented the distribution of extinction times for the classes of solutions found. Taken together, our results suggest opportunities to improve therapy scheduling in clinical oncology.

A genome-based model for adjusting radiotherapy dose (GARD): a retrospective, cohort-based study.

BACKGROUND: Despite its common use in cancer treatment, radiotherapy has not yet entered the era of precision medicine, and there have been no approaches to adjust dose based on biological differences between or within tumours. We aimed to assess whether a patient-specific molecular signature of radiation sensitivity could be used to identify the optimum radiotherapy dose. METHODS: We used the gene-expression-based radiation-sensitivity index and the linear quadratic model to derive the genomic-adjusted radiation dose (GARD). A high GARD value predicts for high therapeutic effect for radiotherapy; which we postulate would relate to clinical outcome. Using data from the prospective, observational Total Cancer Care (TCC) protocol, we calculated GARD for primary tumours from 20 disease sites treated using standard radiotherapy doses for each disease type. We also used multivariable Cox modelling to assess whether GARD was independently associated with clinical outcome in five clinical cohorts: Erasmus Breast Cancer Cohort (n=263); Karolinska Breast Cancer Cohort (n=77); Moffitt Lung Cancer Cohort (n=60); Moffitt Pancreas Cancer Cohort (n=40); and The Cancer Genome Atlas Glioblastoma Patient Cohort (n=98). FINDINGS: We calculated GARD for 8271 tissue samples from the TCC cohort. There was a wide range of GARD values (range 1·66-172·4) across the TCC cohort despite assignment of uniform radiotherapy doses within disease types. Median GARD values were lowest for gliomas and sarcomas and highest for cervical cancer and oropharyngeal head and neck cancer. There was a wide range of GARD values within tumour type groups. GARD independently predicted clinical outcome in breast cancer, lung cancer, glioblastoma, and pancreatic cancer. In the Erasmus Breast Cancer Cohort, 5-year distant-metastasis-free survival was longer in patients with high GARD values than in those with low GARD values (hazard ratio 2·11, 95% 1·13-3·94, p=0·018). INTERPRETATION: A GARD-based clinical model could allow the individualisation of radiotherapy dose to tumour radiosensitivity and could provide a framework to design genomically-guided clinical trials in radiation oncology. FUNDING: None.