
==== Front
Radiat Oncol
Radiat Oncol
Radiation Oncology (London, England)
1748-717X
BioMed Central London

39272128
2514
10.1186/s13014-024-02514-6
Research
Spatially fractionated GRID radiation potentiates immune-mediated tumor control
Bekker Rebecca A. 14
Obertopp Nina 24
Redler Gage 3
Penagaricano José 3
Caudell Jimmy J. 3
Yamoah Kosj 3
Pilon-Thomas Shari 2
Moros Eduardo G. 3
Enderling Heiko henderling@mdanderson.org

56
1 https://ror.org/01xf75524 grid.468198.a 0000 0000 9891 5233 Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL 33612 USA
2 https://ror.org/01xf75524 grid.468198.a 0000 0000 9891 5233 Department of Immunology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL 33612 USA
3 https://ror.org/01xf75524 grid.468198.a 0000 0000 9891 5233 Department of Radiation Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL 33612 USA
4 https://ror.org/032db5x82 grid.170693.a 0000 0001 2353 285X Cancer Biology Ph.D. Program, University of South Florida, Tampa, FL 33612 USA
5 https://ror.org/04twxam07 grid.240145.6 0000 0001 2291 4776 Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, TX 77030 USA
6 https://ror.org/04twxam07 grid.240145.6 0000 0001 2291 4776 Institute for Data Science in Oncology, The University of Texas MD Anderson Cancer Center, Houston, TX 77030 USA
13 9 2024
13 9 2024
2024
19 1216 2 2024
26 8 2024
© The Author(s) 2024
2024
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Background

Tumor-immune interactions shape a developing tumor and its tumor immune microenvironment (TIME) resulting in either well-infiltrated, immunologically inflamed tumor beds, or immune deserts with low levels of infiltration. The pre-treatment immune make-up of the TIME is associated with treatment outcome; immunologically inflamed tumors generally exhibit better responses to radio- and immunotherapy than non-inflamed tumors. However, radiotherapy is known to induce opposing immunological consequences, resulting in both immunostimulatory and inhibitory responses. In fact, it is thought that the radiation-induced tumoricidal immune response is curtailed by subsequent applications of radiation. It is thus conceivable that spatially fractionated radiotherapy (SFRT), administered through GRID blocks (SFRT-GRID) or lattice radiotherapy to create areas of low or high dose exposure, may create protective reservoirs of the tumor immune microenvironment, thereby preserving anti-tumor immune responses that are pivotal for radiation success.

Methods

We have developed an agent-based model (ABM) of tumor-immune interactions to investigate the immunological consequences and clinical outcomes after 2Gy×35 whole tumor radiation therapy (WTRT) and SFRT-GRID. The ABM is conceptually calibrated such that untreated tumors escape immune surveillance and grow to clinical detection. Individual ABM simulations are initialized from four distinct multiplex immunohistochemistry (mIHC) slides, and immune related parameter rates are generated using Latin Hypercube Sampling.

Results

In silico simulations suggest that radiation-induced cancer cell death alone is insufficient to clear a tumor with WTRT. However, explicit consideration of radiation-induced anti-tumor immunity synergizes with radiation cytotoxicity to eradicate tumors. Similarly, SFRT-GRID is successful with radiation-induced anti-tumor immunity, and, for some pre-treatment TIME compositions and modeling parameters, SFRT-GRID might be superior to WTRT in providing tumor control.

Conclusion

This study demonstrates the pivotal role of the radiation-induced anti-tumor immunity. Prolonged fractionated treatment schedules may counteract early immune recruitment, which may be protected by SFRT-facilitated immune reservoirs. Different biological responses and treatment outcomes are observed based on pre-treatment TIME composition and model parameters. A rigorous analysis and model calibration for different tumor types and immune infiltration states is required before any conclusions can be drawn for clinical translation.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13014-024-02514-6.

Keywords

Tumor immune interactions
Spatially fractionated radiotherapy
Mathematical model
Personalized oncology
http://dx.doi.org/10.13039/100000002 National Institutes of Health U01CA244100 issue-copyright-statement© BioMed Central Ltd., part of Springer Nature 2024
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pmcBackground

Head and neck cancer (HNC) is one of the most prevalent cancer types globally, with cases rising in incidence [1]. Head and neck squamous cell carcinomas (HNSCC) represent 90% of HNC, for which treatment (Tx) options include radiotherapy (RT), surgical resection, and chemotherapy. Traditionally, RT was thought to be only genotoxic: inducing irreparable DNA damage leading to cell death. However, an extensive body of work now exists describing the interplay between radiotherapy and the immune system. RT-induced DNA damage leads to cell death and the release of tumor antigens and damage associated molecular patterns (DAMPs). These so-called danger signals initiate and potentiate innate and adaptive immune responses. For instance, calreticulin binds with CD91 on macrophages to promote phagocytosis, while HMGB1 binds with certain toll-like receptors (TLR2, TLR3, TLR4 and TLR9) to promote dendritic cell activation and the expression of pro-inflammatory cytokines such as NF-κB, TNF-α, and IL-6. Activated dendritic cells take up and process the released tumor antigens, before migrating to the lymph nodes to prime and activate tumor specific T cells, including cytotoxic CD8+ T cells [2–4]. Paradoxically, radiotherapy can also provoke immunosuppressive effects, by killing radiosensitive immune cells and inducing the downregulation of immune cell activation pathways while promoting the recruitment of immunosuppressive cell-types such as FOXP3 + CD4+ regulatory T cells and upregulating the PD-1–PD-L1 axis [5, 6]. The presence of CD8+ T cells has been positively correlated with response in multiple solid cancers, including HNC [7–9]. However, research into the relationships between other immune cells within the tumor-immune microenvironment (TIME) is not conclusive [10]. Thus, it is conceivable that patient response to RT may benefit from protecting the existing and/or induced anti-tumor immune subpopulations within the TIME.

One potential method of eradicating immunosuppressive populations whilst preserving and promoting immune effector cells is spatially fractionated radiotherapy (SFRT), developed in the early twentieth century to deliver high dose levels to deep tumors while minimizing the skin toxicity generally associated with the kilovoltage energy X-ray equipment of that time [11–13]. Since the 1950’s, SFRT has been used primarily in the palliative setting [14], or for debulking large tumors prior to conventional radiation, concomitant chemoradiotherapy, or surgery [15–18]. Current clinical use of SFRT focuses on single ablative doses (>15Gy) prior to conventional whole tumor/whole field RT (WTRT) [19, 20], which may obliterate the immune-activating features of SFRT. Recent insights into both pro- and anti-tumor immunological consequences of radiation warrant a novel look at SFRT: radiation-shielded areas may create immune reservoirs that are additionally promoted by the release of immune-stimulatory cytokines in adjacent unshielded sites. In fact, murine models of SFRT demonstrate increased systemic anti-tumor immunity [21], and indicate that tumor response correlates to radiation dosimetry parameters and the specific SFRT geometry (number of unshielded areas and distance between them) [22]. Other preclinical studies demonstrate that RT applied to only half of a tumor delays tumor growth longer than expected in immunocompetent but not immunodeficient mice, indicating a critical role of the immune system. This study further demonstrated CD8+ T-cell migration between the tumor periphery, the irradiated area, and the unirradiated tumor area [23]. To improve the clinical application of SFRT a deeper understanding of the immunological consequences of SFRT as a function of dose, dose fractionation, and SFRT geometry is required.

To exhaustively evaluate every such combination in even the pre-clinical setting is, however, infeasible [24]. Integrating mathematical modeling with experimental approaches and clinical data may circumvent these restrictions [25–34], while further elucidating relationships between the dose, dose fractionation, SFRT geometry and tumor response. Mathematical oncology models have been used in various contexts, from generating hypotheses of novel tumor biology to predicting treatment response [35]. The ultimate goal of modeling—hypothesis generation or prediction – generally informs methodological approaches. Models used for the latter should be rigorously calibrated with existing data, prior to being validated on unseen data, and the predictive power evaluated. Only then can the model be used to predict alternative treatments [36]. In contrast, models used for hypothesis generation only need to qualitatively recapitulate the system or phenomenon being studied.

Furthermore, the scientific question and available data inform the mathematical approach: deterministic modeling methods such as ordinary differential equations are ideal when working with temporal data on a population scale. However, stochastic modeling methods such as agent-based models (ABMs) are more suited to highly granular data such as tumor-immune cell interactions. ABMs are considered “bottom-up”, incorporating biological mechanism via individual autonomous agents which follow predetermined rules based on the underlying biology. These models facilitate investigations into how perturbations of the system or changes to the agent rules impact the emergent behavior of the model.

In this work, we developed such an ABM to explore relationships between SFRT GRID-block geometry, pre-treatment TIME states, and tumor response. Specifically, we investigated whether SFRT-GRID exhibits improved, or comparable efficacy compared to WTRT when administered to specific pre-Tx TIMEs.

Methods

Herein we present a 2D on-lattice ABM of three populations, cancer cell agents (C), anti-tumor effector cell agents (E) and pro-tumor regulatory cell agents (R). This ABM is initialized from digitized fluorescent multiplex immunohistochemistry (mIHC) slides obtained from biopsies of primary HNC tumors. In silico treatment simulations using WTRT or two SFRT geometries are analyzed using MATLAB 2022, and the mechanisms of response and outcome are investigated (Fig. 1).Fig. 1 From patient biopsy to agent-based model. A Fluorescent Multiplex Immunohistochemistry (mIHC) is performed on biopsies of head and neck cancer to identify and quantify cellular populations within the tumor-immune microenvironment (TIME). B Digitized mIHC slides are used to generate in silico tumors, consisting of cancer cells (C), effector immune cells (E), and regulatory immune cells (R). See Methods for in-depth discussion of agent rules. C We treat in silico tumors from B with either WTRT or SFRT, and asses the treatment efficacy for each therapy

Patient data

Patients with oropharyngeal cancer were identified via two IRB approved studies: Total Cancer Care (MCC#14690) with a diagnosis of head and neck cancer and obtained written consent, and Using Radiotherapy to Perturb the Tumor-Immune Ecosystem for Immune-Modulated Tumor Control (MCC#19233). After Institutional IRB approval was obtained, we selected four patients with different tumor immune ecosystem compositions for this study.

Fluorescent multiplex immunohistochemistry (IHC) panel procedure

Formalin-fixed and paraffin-embedded (FFPE) tissue samples were immunostained using the AKOAYA Biosciences OPAL TM 7-Color Automation IHC kit (Waltham, MA) on the BOND RX autostainer (Leica Biosystems, Vista, CA). The OPAL 7-color kit uses tyramide signal amplification (TSA)-conjugated to individual fluorophores to detect various targets within the multiplex assay. Sections were baked at 65 °C for one hour then transferred to the BOND RX (Leica Biosystems). All subsequent steps (ex., deparaffinization, antigen retrieval) were performed using an automated OPAL IHC procedure (AKOYA). OPAL staining of each antigen occurred as follows: heat induced epitope retrieval (HIER) was achieved with Citrate pH 6.0 buffer for 20 min at 95 °C before the slides were blocked with AKOYA blocking buffer for 10 min. Then slides were incubated with primary antibody, CD68 (CST, D4BAC, 1:300, dye 520) at RT for 60 min followed by OPAL HRP polymer and one of the OPAL fluorophores during the final TSA step. Individual antibody complexes are stripped after each round of antigen detection. This was repeated five more times using the following antibodies; CD8 (DAKO, C8/144B, HIER-EDTA pH 9.0, 1:100, dye540), CD4 (CM, EP204, HIER- EDTA pH 9.0, 1:100, dye570), CD3 (Thermofisher, SP7, HIER-EDTA pH 9.0, 1:500, dye 570), FOXP3 (ABCAM, 236A/E7, HIER- EDTA pH 9.0, 1:500, dye650), and PCK (DAKO, AE1/AE3, HIER- Citrate pH 6.0, 1:200, dye690). After the final stripping step, DAPI counterstain is applied to the multiplexed slide and is removed from BOND RX for coverslipping with ProLong Diamond Antifade Mountant (ThermoFisher Scientific). All slides were imaged with the Vectra®3 Automated Quantitative Pathology Imaging System. See Table S1 for an overview of the stains used in the multiplex immunohistochemistry panel.

Quantitative image analysis

Multi-layer TIFF images are exported from InForm (AKOYA) and loaded into HALO (Indica Labs, New Mexico) for quantitative image analysis. A classifier is trained to identify areas of tumor, stroma or non-tissue regions. Pan-cytokeratin is used to train tumor regions because it is a masking marker for tumor cells. The classifier is created and tested on various images in the image set. The tissue is segmented into individual cells using the DAPI marker which stains cell nuclei. For each marker, a positivity threshold within the nucleus or cytoplasm are determined per marker based on published staining patterns and intensity for that specific antibody. After setting a positive fluorescent threshold for each staining marker, the entire image set is analyzed with the created algorithm. The generated data includes positive cell counts for each fluorescent marker in cytoplasm or nucleus, and percent of cells positive for the marker. Along with the summary output, a per-cell analysis can be exported to provide the marker status, classification, and fluorescent intensities of every individual cell within an image.

Agent-based model of tumor-immune interactions

The ABM was implemented in Java 1.8, using the Java library HAL (Hybrid Automata Library) [37], and is initialized from multiplex immunohistochemistry slides of head and neck cancer as detailed in the following section. The ABM domain represents an area of approximately 1.38mm2, and consists of 68×51 nodes, with a domain constant of 20μm × 20μm, corresponding to the assumption of an average cell diameter of 20μm (see following subsection and [38, 39]). The ABM timestep is Δt=1h. Each agent is autonomous, with their behavior being determined by cell-type specific rules based on the underlying biology. The specific rules are discussed in-depth in the following subsections. Due to the stochasticity of agent-based modeling, 50 independent replicates are run.

ABM Initialization

HALO post processed files containing cellular locations (xMin,yMin,xMax and yMax coordinates) and types (see above) were imported into MATLAB. Next, we compute the cell center coordinates:xcomputed,ycomputed=xMin+xMax2,yMin+yMax2

which are mapped onto a 2D lattice by using the formula:x,ymapped=floorxcomputedκ,ycomputedκ,

where κ is a conversion factor. We select κ=20, which corresponds to the assumption of an average cellular diameter of 20μm. The range 10,100 for κ was investigated and an inverse relationship between κ and the fraction of retained cells within each in silico tumor can be observed (Fig. S1).

The mapped cell centers for each discretized mIHC slide are used to create the corresponding in silico tumor which is used as the initial condition of the ABM. Certain properties of individual agents are initialized by sampling from the corresponding distributions. For example, cancer cell agents keep track of their own cell cycle length, as well as their temporal position in their cell cycle. When a cancer cell agent is created during the initialization of the ABM, we assign the cell cycle length (divlength) by sampling from a truncated normal distribution centered around 24 h. Then, we sample from the range 0,divlength2 to assign the cell’s position in its cell cycle. The properties for which this is done can be found in Table S2–S4.

Cellular processes and interactions

Cancer cell agent processes

Cancer cells can undergo apoptosis, proliferate, or migrate according to specific probabilities, and certain environmental restrictions (Fig. S2). Cancer cells progress through their cell cycle each timestep in which there is a vacant domain node in their Moore neighborhood. Once a cancer cell has reached the end of their cell cycle, mitosis may occur, and the daughter cell is placed in a randomly chosen vacant node within the Moore neighborhood. Cancer cells that are surrounded by neighbors are considered quiescent during that timestep, due to space inhibition. Cancer cells have a probability of apoptosis of pa=3×10-3per timestep, which translates to a lifespan of approximately 14 days [40]. Cells that undergo apoptosis are removed from the simulation and the domain node becomes vacant immediately. The probability of migration of cancer cells is assumed to be pm=0.9per timestep (i.e., 1/h) and we assume a migration speed of 2.3μm/min, this translates to a migration potential of 6 domain nodes per timestep. Thus, the migration of cancer cells is implemented as an iterative process, with cells moving up to 6 times per timestep [41, 42].

Immune recruitment parameter rates

The ABM contains four immune recruitment related parameters. We estimate plausible values for these by generating 15 parameter sets using Latin Hypercube Sampling. Each set consists of a rate of (i) recruitment of effector-immune cells due to cancer cell apoptosis (ζapoptosis), (ii) recruitment of effector-immune cells due to effector-cell induced cancer cell death (ζeffector), (iii) the probability of placing an effector cell (recruited in (ii)) near the location of cancer cell death (μ), and (iv) recruitment of regulatory cells due to cancer cell proliferation (ζregulatory) (see Table S5).

Immune cell dynamics

Recruitment of Effector agents

Effector cell are recruited by the death of cancer cell agents, and so we record the number of apoptotic cancer cell deaths Capoptosis(ti), and the number of cancer cell deaths due to interaction with effector immune cells Ceffector(ti) that occur in timestep ti. Then, the number of effector cells recruited in the next timestepti+1, is:Eapoptosisti+1=ζapoptosis∗Capoptosisti,Eeffectorti+1=ζeffector∗Ceffectorti,

where ζapoptosis and ζeffector are the rates at which the different types of cancer cell death recruit effector immune cells. Effector cell agents that are recruited due to apoptosis of cancer cells are placed randomly, following the assumption of a uniform distribution of blood vessels in the ABM domain. However, effector cell agents that are recruited due to the killing of cancer cells by effector immune cells are placed near locations of such death with probability μ (in an empty lattice node within a radius of 10 lattice points of the cell-death location). This is in line with the so-called “post-code” hypothesis, which explains the multi-step, tissue-selective homing of T cells [43, 44].

Recruitment of regulatory agents

Regulatory cells are recruited by cancer cell proliferation events, and so for each timestep ti we record the number of proliferation events Cmitosis(ti). Then, the number of regulatory cells recruited in the next timestep ti+1 is:Rti+1=ζregulatory∗Cmitosisti,

where ζregulatory is the rate of recruitment. Regulatory cells are placed in empty lattice nodes, randomly throughout the ABM domain.

Migration

Immune cells migrate into, and infiltrate tumors by following specific biochemical gradients [44, 45], before interacting with their target cells (effector immune cells target cancer cells and regulatory immune cells target effector immune cells). We assume immune cell migration to be either entirely random or a combination of random- and directed motion towards their respective target cells. Similar methods of migration can be found elsewhere [46–48]. Below is the migration process for any immune cell p.Find q the nearest target cell(s) to p within a radius of r=50 domain nodes.If no target cells are found, immune cell p undergoes random motion, moving into an open node within its Moore neighborhood.

If target cells are found: i. Calculate the normalized vector u¯ from the location of cell p to the location of cell q:u¯=pq→pq.

ii. Calculate a random unit vector v¯.

iii. Calculate direction vector w¯: w¯=ηrndv¯+ηdirectedu¯, where ηrnd and ηdirected are weights for random migration and directed migration respectively. (Note: ηrnd=1-ηdirected so that if ηrnd=0 immune cells undergo purely directed motion, while if ηdirected=0 immune cells exhibit Brownian motion).

iv. Find all the vacant lattice node(s) x within the Moore neighborhood of p that minimize the angle θ between the vectors px→ and w¯.

v. Randomly select one such node for p to move into.

Immune cells are assumed to have a migration speed of 5μm/min [49–51], which translates to 15 lattice nodes per timestep, and we fix ηdirected=0.19. Thus, the above process is repeated multiple times per immune cell per timestep.

Cell–cell interactions

Following attempted or successful migration by an immune cell p, it can interact with other cells. Recent studies have shown support for the “multiple hit” hypothesis, in which target cells require multiple contacts from cytotoxic lymphocytes before death [52]. It has also been shown that cells can recover from sublethal damage caused by interactions with cytotoxic lymphocytes, with those receiving two or more “hits” displaying accelerated apoptosis induction [53]. Thus, we assume that target cells require three “hits” with cells of the appropriate immune sub-type, and that the damage from these hits is repaired within a time step. That is, interaction with effector cells or regulatory cells will lead to the death of a cancer cell or effector cell respectively if three such interactions occur within a single timestep. However, we assume that each immune cell can only deliver a single hit during one timestep, with a maximum of 10 hits before becoming exhausted and being removed from the simulation (Fig. S2).

Effects of radiation on cells

We calculate the probability that a cell of type i survives a radiation dose of dGy using the linear quadratic equation (54, 55):SFid=exp-αidξ-βidξ2,

where αiGy-1andβi(Gy-2) are cell type specific radiosensitivity parameters [54]. For the purposes of this study we use SFC2Gy=0.49,SFE2Gy=0.60 and SFR2Gy=0.77 in line with those used previously [56]. As discussed elsewhere, proliferating cells are more sensitive to radiation than quiescent cells which we model by scaling the dose by ξ=1 if the cell is actively cycling, and ξ=3 if the cell is not [57, 58].

Radiation induces DNA damage [59, 60], the attempted repair of which may lead to temporary cell cycle arrest and successful repair or delayed cell death after failed repair. Studies show that these delays are dose dependent, and we assume a cell cycle lengthening of 2h/Gy [61], and an 8h delay between the administration of radiation and cell death in the case of irreparable DNA damage [62]. Thus, cancer cell killing via radiation is not immediate in this model.

Radiation-induced effector immune cell recruitment

As previously mentioned, radiation-induced cancer cell death can be immunogenic, the level of which is determined by a range of factors (levels of tumor antigenicity, release of DAMPs, maturation of dendritic cells and other antigen presenting cells etc.) [6]. We collapse this biology into a single rate and assume that radiation-induced cancer cell death recruits effector immune cells at a rate of ζTx immune effector cells per Tx-induced cancer cell death in the preceding timestep. Thus, radiation-induced cancer cell death recruits effector-immune cells at a rateETxti+1=ζTx∗CTxti.

For the purposes of this study, we assume radiation-induced cancer cell death is either non-, low- or highly immunogenic: ζTx∈(0;0.01;0.1). That is, if ζTx=0.1, ten Tx-induced cancer cell deaths are required in timestep ti to recruit one effector immune cell in timestep ti+1. Effector cells recruited in this manner are seeded randomly in the domain.

Treatment with whole tumor radiotherapy

When treating with whole tumor radiotherapy (WTRT), a uniform dose of 2Gy radiation per weekday fraction is administered throughout the ABM domain, for a total dose of 70Gy.

Generation of in silico SFRT-GRID geometries

Commercially available SFRT collimator geometries have openings with diameters between 0.6–1 cm and center-to-center spacings of 1.15–1.4 cm, and generally result in approximately 50% of the tissue being shielded from the RT beam. These dimensions are not suited for the spatial scale of our agent-based model, and we scale the SFRT-GRID geometries appropriately. Two SFRT GRID block geometries are investigated here. The first has openings with a diameter of 11 lattice nodes and a center-to-center distance of 30 lattice nodes (200μm and 600μm respectively), and the second block has openings with a diameter of 11 lattice nodes and a center-to-center distance of 35 lattice nodes (200μm and 700μm respectively) (Fig. 2A,B). The first SFRT geometry results in shielding of approximately 70% of tissue, with the other 30% receiving the peak dose. The second SFRT geometry is in line with clinical practice and results in sparing of approximately 50% of the tissue, with the remaining 50% receiving the peak dose (Fig. 2C). For the rest of the manuscript, we refer to treatment using each geometry as SFRT-GRID (30:70) and SFRT-GRID (50:50) respectively. In line with published peak to valley dose ratios (PVDR) used in pre-clinical studies [22, 63, 64], we assume a PVDR of 15. That is, tissues within the dose valleys receive 15% of the peak dose per treatment fraction. For an administered radiation dose of 2Gy, the average dose delivered to the entire domain for SFRT-GRID(30:70) and SFRT-GRID(50:50) is 0.81Gy and 1.15Gy, respectively.Fig. 2 Characterization of the architectures of the in silico GRID blocks. A, B In silico SFRT-GRID blocks overlayed on mIHC slide 12, showing “peak” regions of the domain that appear under the openings of the GRID block and receive the full administered dose vs the areas in the shielded / “valley” regions which receive 15% of the administered dose. C Open to Shielded regions for both SFRT-GRID blocks. Approximately 30% of the ABM domain is in the “peak” areas, with approximately 70% being in the “valley” regions for the first geometry, while the second is an approximately even split of peak to valley areas

Assessment of treatment success

The success of a treatment administered for a specific duration with the assumption of a specific level of immunogenicity of radiation-induced cell death ζTx, is described via the probability of tumor eradication of fifty independent simulations:TETx=numberofsimulationsthathaveC=0atendofsimulation50.

Each ABM initial condition was either left untreated and followed for 15 weeks or 2Gy weekday fractions were administered for 7 weeks and followed post-Tx for 8 weeks (for a possible total simulated time of 15 weeks). Simulations stopped at end the of week 15, or when the cancer population was entirely eradicated, whichever occurred first.

Determining the primary mechanism of cancer cell death

For each timestep, the ABM output includes the number of cancer cells that undergo a specific type of cell death: effector cell cytotoxicity, direct radiation cell-kill, or apoptosis. These data are used to determine the primary mechanism of cancer cell death during the 7-day and 1-day periods immediately prior to and including the timestep in which tumor eradication occurs. Specifically, we calculate the total number of cancer cells which have undergone each type of death within the specific period.

Results

Agent-based model simulations without treatment exhibit distinct outcomes as a function of model parameters

We generated 15 parameter sets using Latin Hypercube Sampling, each consisting of a rate of (i) recruitment of effector-immune cells due to cancer cell apoptosis (ζapoptosis), (ii) recruitment of effector-immune cells due to effector-cell induced cancer cell death (ζeffector), (iii) the probability of placing an effector cell (recruited in (ii)) near the location of cancer cell death (μ), and (iv) recruitment of regulatory cells due to cancer cell proliferation (ζregulatory) (see table S4). To select plausible parameter sets, simulations without treatment were performed using each digitized mIHC slide as initial condition for the ABM (Fig. S1). Two distinct outcomes were observed: tumor elimination (e.g. parameter set 6, Fig. 3A–E) and immune escape (e.g. parameter set 13, Fig. 3F–J). These dynamics can also be visualized by plotting the cancer and effector populations against each other, highlighting the two observed behaviors (Fig. 3E, J). Despite initial tumor growth, in the case of tumor elimination the cancer-effector trajectories shift ever rightwards, indicating increases in the effector populations leading to tumor eradication (Fig. 3E). However, the same phenomenon is not observed in the case of tumor escape, suggesting that the observed tumor clearance is immune mediated. Thus, the ABM simulated immune-mediated tumor elimination and immune escape as described in literature [65]. These results suggest that there may be two distinct basins of attraction in the tumor immune ecosystem, which consist of all TIME compositions that lead to the described outcome—either immune-mediated tumor eradication (IMTE) or tumor escape. Furthermore, the existence, shape and size of these regions depend on the immune recruitment parameters [66]. Two of the 15 generated parameter sets result in moderate to complete clearance of replicates for each mIHC slide (Fig S3). Cursory analysis of the parameter space reveals no clear separation for the behavior observed (Fig. S4). In line with literature [67], we assume clinically detectable tumors have evaded the immune system, and so we discard parameter sets that lead to tumor elimination without therapy. For the rest of the manuscript, we investigate how we might use WTRT or SFRT-GRID to shift tumor trajectories from the region of immune escape to that of IMTE and elucidate the mechanisms of success for each therapy.Fig. 3 ABM recapitulates distinct tumor outcomes without treatment. Temporal dynamics of i. cancer population, ii. effector population, and iii. regulatory population, for mIHC slides A 12, B 28, C 63, and D 93, using parameter set 6. E Representative trajectories for A-D on the cancer-effector plane. Temporal dynamics of i. cancer population, ii. effector population, and iii. regulatory population, for mIHC slides F 12, G 28, H 63 and I 93, using parameter set 13. J. Representative trajectories for F-I on the cancer-effector plane. See Fig. S1 for details of mIHC slides

WTRT does not lead to clearance with solely radiation-induced cytotoxicity

We simulated radiation treatment on the digitized mIHC slides with 2Gy×35 whole tumor radiotherapy (WTRT) using two of the 15 previously generated parameter sets (sets 13 and 15). Here, the effect of WTRT is solely lethal DNA damage. Despite early reductions in tumor burden, no tumor eradication was observed (Fig. 4A). During treatment, effector immune populations remain at or below baseline levels, and do not recover even after treatment has ended (Fig. 4B). Snapshots of a representative replicate of each tissue are shown at the end of treatment (week 7), and the end of the simulation (week 15) (Fig. 4D). It is clear that for parameter set 13, treatment with 2Gy×35 WTRT fails to shift either of the four tissues into the region of attraction for IMTE (Fig. 4E). The immune parameter rates of set 15 lead to more intra-replicate heterogeneity of each mIHC slide, as well as higher immune populations post-treatment (Fig. 4F–I). However, despite higher effector populations, treatment again fails to shift trajectories into the region of IMTE (Fig. 4J). Thus, WTRT with solely radiation-induced cytotoxicity does not lead to clearance. However, head and neck cancers report five-year local response rates of 70–100% [68], which motivates the analysis of additional biological consequences, such as immune activation, after radiation.Fig. 4 WTRT does not lead to clearance with solely radiation-induced cytotoxicity. For parameter set 13: A–C Temporal dynamics of each cell population of mIHC slides 12, 28, 63 and 93, when treated with 2 Gy × 35. D Snapshots of representative simulations of all mIHC slides at the end of weeks 7 and 15. E Cancer-effector cell plane of all mIHC slides treated with 2 Gy × 35 WTRT. For parameter set 15: F–H Temporal dynamics of each cell population of mIHC slides 12, 28, 63 and 93, when treated with 2 Gy × 35. I Snapshots of representative simulations of all mIHC slides at the end of weeks 7 and 15. J. Cancer-effector cell plane of all mIHC slides treated with 2 Gy × 35 WTRT using parameter set 15. See Fig. S1 for details of mIHC slides

WTRT needs interaction with immune system for success

We investigate whether a low- or highly immunogenic response to lethal DNA-damage is sufficient to obtain 70–100% tumor control (see Methods). Low immunogenicity of lethal DNA damage does not result in tumor eradication for either parameter set (Fig. S5). A highly immunogenic response to lethal DNA damage leads to eradication of the majority of trajectories of mIHC slides 12 and 28 (TE12 = 84% and TE28 = 98%), but not mIHC slides 63 and 93 (TE63 = 0% and TE93 = 0%) (Fig. 5A). Representative snapshots of the mIHC slides at the end of the first week of treatment (Fig. 5B top row) and the end of simulation (Fig. 5B bottom row) highlight the differential responses to WTRT (Fig. 5B first two columns: clearance vs Fig. 5B last two columns: recurrence). In the latter cases, WTRT shifts trajectories leftwards, indicating the induction of treatment related suppression of the effector populations. This phenomenon and its association with poor prognoses was recently reported in literature [69]. Parameter set 15 results in similar outcomes (TE12 = 82%, TE28 = 96%, TE63 = 0%, TE93 = 2%), but results in higher effector populations and increases intra-trajectory heterogeneity (Fig. 5C, D). Thus, 2Gy×35 WTRT can shift trajectories of mIHC slides 12 and 28 into the IMTE region for parameter sets 13 and 15 when treatment-induced cell death is sufficiently immunogenic. However, it is insufficient to shift trajectories of mIHC slides 63 and 93 into the IMTE region.Fig. 5 WTRT leads to clearance when Tx is sufficiently immunogenic. Parameter set 13: A Cancer-effector plane dynamics of mIHC slides 12, 28, 63, 93 treated with 2 Gy × 35 WTRT. B Snapshots of mIHC slides 12, 28, 63, 93 at the end of the first week of treatment (top row) and at the end of simulation (bottom row). Parameter set 15: C Cancer-effector plane dynamics of mIHC slides 12, 28, 63, 93 treated with 2 Gy × 35 WTRT. D Snapshots of mIHC slides 12, 28, 63, 93 at the end of the first week of treatment (top row) and at the end of simulation (bottom row)

SFRT can be successful in contexts of high immunogenicity of DNA damage

We next asked whether SFRT could recapitulate the response rates of mIHC slide 12 and 28 above, while improving response rates of those tumors for which WTRT was unsuccessful. To this end, we administered 2Gy×35 of either SFRT-GRID (30:70) or SFRT-GRID (50:50) to all four mIHC slides, with the assumption that Tx is immunogenic. For parameter set 13, treatment with either SFRT-GRID geometry is sufficient to shift all trajectories of mIHC slides 12, 28, 63 and 93 into the immune-mediated tumor eradication region (Fig. 6A, B, Fig. S7A, B). Interestingly we see that the first week of treatment induces an upwards and right shift for slides 12 and 28, indicating early increases in both effector and cancer populations, but slides 63 and 93 experience an initial upwards and left shift indicating an increase in cancer cells and a decrease in effector cells. Subsequent weeks of treatment generally shift the tumor trajectories downwards and to the right, indicating an increasing effector population. However, when using parameter set 15 no models exhibit notable tumor eradication. Instead, trajectories shift within the tumor escape region, remaining at high levels of cancer cells (Fig. 6C, D, Fig. S7C, D). Thus, for certain pre-treatment state and parameter set combinations SFRT-GRID successfully shifts trajectories into the tumor-eradication region, and is equally or more effective than WTRT despite delivering less total average dose (0.81Gy and 1.15Gy average dose per fraction for SFRT-GRID(30:70) and SFRT-GRID (50:50) respectively vs 2Gy for WTRT).Fig. 6 SFRT-GRID leads to clearance when Tx is sufficiently immunogenic. Parameter set 13: A.i. Cancer-effector plane dynamics and snapshots of mIHC slides 12 and 63 treated with 2 Gy × 35 SFRT-GRID (30:70). A.ii. Snapshots of representative simulations of mIHC slides 12 and 63 at the end of week 1 (top row), and tumor clearance (bottom row). B.i. Cancer-effector plane dynamics and snapshots of mIHC slides 12 and 63 treated with 2 Gy × 35 SFRT-GRID (50:50). B.ii. Snapshots of representative simulations of mIHC slides 12 and 63 at the end of week 1 (top row), and tumor clearance (bottom row). Parameter set 15: C.i. Cancer-effector plane dynamics and snapshots of mIHC slides 12 and 63 treated with 2 Gy × 35 SFRT-GRID (30:70). C.ii. Snapshots of representative simulations of mIHC slides 12 and 63 at the end of week 1 (top row), and week 15 (bottom row). D.i. Cancer-effector plane dynamics and snapshots of mIHC slides 12 and 63 treated with 2 Gy × 35 SFRT-GRID (50:50). D.ii. Snapshots of representative simulations of mIHC slides 12 and 63 at the end of week 1 (top row), and week 15 (bottom row). See Fig. S7 for snapshots of mIHC slides 28 and 93

Elucidating the biological mechanism of tumor response

In the following subsections we interrogate the mechanisms of the observed outcomes following treatment with WTRT and SFRT-GRID, using representative slide-parameter set pairs for each treatment type. Specifically, for WTRT we use mIHC slide 12 and parameter set 15, while we use mIHC slide 63 and parameter set 13 for SFRT-GRID.

Treatment-induced DNA damage is the primary mechanism of tumor response to WTRT

When using parameter set 15, the first week of treatment with WTRT results in notable increases in the average effector population for mIHC slide 12. Subsequent applications of WTRT lead to sustained effector suppression, which only wears off weeks after treatment has ended (Fig. 7A). Interestingly, the average effector population of responding simulations are higher than non-responders following the first week of treatment, but lower than non-responders during subsequent weeks (Fig. 7A, solid vs dashed curves). This initial difference corresponds to the time-period in which most clearances occur (Fig. 7B), suggesting that WTRT reduces the tumor burden either completely or to such a degree that the suppressed effector population can eliminate the remaining cancer cells. The dominant mechanism of cancer cell death within the 7-day period leading up to and including tumor eradication is treatment induced DNA damage (Fig. 7C, Table S7, p < 0.005), while effector-mediated cell death is the primary mechanism during the 24-h period leading up to tumor clearance (Fig. 7D, Table S7, p < 0.005). Thus, DNA damage contributes more to tumor clearance during WTRT than effector mediated cancer cell death.Fig. 7 WTRT success relies on maximizing log-cell kill. A Average fold change of effector population in responding or non-responding mIHC slide 12 tumors treated with 2 Gy × 35 of WTRT. B Distribution of clearance times for responding tumors in A. C, D Contribution of effector-mediated cancer cell death, treatment, and apoptosis in the 7 day or 1 day period leading up to and including clearance of tumors treated with WTRT respectively. Error bars are mean ± SEM. (*** p < 0.001, two-sided Wilcoxon rank sum test, Table S7)

SFRT-GRID promotes an accumulation of effector cells

Different effector cell dynamics are observed when we use parameter set 13. During the first week of treatment with either SFRT-GRID geometry we see a large decline in the average fold change of the effector population of mIHC slide 63. However, subsequent weeks of treatment result in a cumulative increase in the effector population (Fig. 8A, dashed curves).. The distribution of clearance times of tumors treated with SFRT-GRID(30:70) or SFRT-GRID (50:50) suggest that the observed accumulation of effector cells may be responsible for tumor eradication (Fig. 8B).

Cumulative immunogenic cell death during SFRT-GRID drives cancer cell clearance

To confirm this, we determined the dominant mechanism of cancer cell death (effector-cell mediated, treatment-induced, or apoptosis) within the 7 day and 24-h periods leading up to and including the timestep in which tumor clearance occurred for mIHC slide 63. For tumors treated with either of the SFRT-GRID geometries, effector cell mediated cancer cell death is the primary mechanism (Fig. 8C-F, Table S8, S9, p < 0.005). Taken together, these data suggest that cumulative immunogenic cell death during SFRT-GRID drives cancer cell clearance, and thus SFRT-GRID, but not WTRT, may potentiate immune-mediated tumor control (Fig. 8).Fig. 8 SFRT potentiates immune mediated tumor clearance. A Average fold change of effector population in responding or non-responding mIHC slide 63 tumors treated with 2 Gy × 35 of WTRT, SFRT-GRID(30:70) or SFRT-GRID(50:50). B Distribution of clearance times for responding tumors in (A). C, D Contribution of effector-mediated cancer cell death, treatment, and apoptosis in the 7 day or 1 day leading up to and including clearance of tumors treated with SFRT-GRID(30:70). E, F Contribution of effector-mediated cancer cell death, treatment, and apoptosis in the 7 day or 1 day leading up to and including clearance of tumors treated with SFRT-GRID(50:50). Error bars are mean ± SEM. (**p < 0.01, ***p < 0.001, two-sided Wilcoxon rank sum test, Table S8–S9)

Discussion

We developed an ABM to study the biological and immunological consequences of radiation therapy as a function of pre-irradiation TIME composition using immunohistochemistry slides, spatial radiation distribution, and model parameters. The goal of this study was to explore the immunological consequences of whole tumor and spatially fractionated radiotherapy. In this hypothesis-generating approach, we explored the parameter space to arrive at parameter combinations that yield biologically and clinically feasible population-level dynamics. While we focus on HNC, the model is not calibrated nor validated for a specific cancer type.

Unrepairable, lethal DNA damage was long thought to be the only driving factor of the tumoricidal effect of radiotherapy. In the described model, all simulations of whole tumor radiation with generic radiosensitivity parameters did not lead to tumor extinction despite the very low number of cancer cells at simulation initialization compared to clinical tumors (we only consider the cells counted in the biopsy tissue, not the entire clinical target volume). While there is a significant loss of cancer cells early during radiation, cancer cell repopulation appears to outcompete radiation-induced cell death in later stages of therapy. This is a visualization of accelerated repopulation during radiation therapy, and one motivation for hyperfractionated radiation accelerated treatment, which is most helpful later in treatment [70].

Of importance here, whole tumor radiation also wipes out nearly all immune cells. The addition of immunologic cell death and radiation-induced recruitment of additional immune cells was able to simulate tumor control comparable to clinical observations. This adds to the growing body of literature that stresses the immune-related effect of radiation and warrants further exploration into the biological and especially immunological consequences of radiation, and how to best tailor radiation towards immune activation compared to historical log-cell kill maximization. In the setting of strong radiation-induced anti-tumor immunity, we see that spatially fractionated radiation synergizes with the immune system, and may create areas of low dose radiation where immune cells are sheltered and can amount a robust attack on cancer cells outside of the radiation fields. While these results confirm our tested hypothesis, other herein untested parameter combinations and biological and radiobiological mechanisms may also be at play in providing whole tumor radiation control, such as re-oxygenation and re-sensitization of cancer cells to subsequent radiation fractions. The plethora of nonlinear radiation response mechanisms motivates a rigorous analysis of this biological complexity to guide future pre-clinical and clinical experimentation to fully decipher the importance of radiation-induced antitumor immunity.

In our study, we set out to test the immunological consequences of spatially fractionated radiation compared whole tumor radiation over a seven-weeks course of radiotherapy. In the clinic, SFRT-GRID is currently applied as an upfront ablative fraction of 15Gy×1 followed by whole tumor radiation with 2Gy×25 [19, 20]. Comparison of the treatment efficacy for each mIHC slide when parameter set 13 is used shows that the clinical ablative SFRT-GRID schedule is less effective for mIHC slides 63 and 93 than the fractionated SFRT-GRID schedules. However, for parameter set 15, we observe that the ablative schedules are more effective for certain mIHC slides (Table S10). Analysis of the underlying mechanism highlights the differences in underlying mechanisms of action: fractionated SFRT-GRID synergizes with the immune effector population, while ablative SFRT-GRID debulks the tumor population, and suppresses the immune effector population (Fig. S10, Table S11).

These results offer a novel approach of SFRT as a sole treatment plan without subsequent whole tumor radiation as currently done in clinical practice. Of note, however, the success of SFRT is crucially dependent on pre-treatment TIME composition and model parameters. It is therefore crucial to take the findings herein and rigorously calibrate and validate the ABM for specific cancer types and clinical immune infiltration scenarios before clinical translation.

Central to developing in silico models is the need for simplifying assumptions. Through these we condense current biological knowledge, with the aim of retaining the most critical components while minimizing the complexity and inherent variability of in vitro or in vivo experiments. Here, we have assumed that the SFRT-GRID block is always positioned such that the placement of the openings aligns perfectly throughout the course of treatment, thereby conserving the initial heterogeneous dose distribution. In reality, tumor motion due to respiratory or other physiological movements, may cause intra-fraction dose smearing. In addition, slight differences in patient alignment or tumor size and shape may result in inter-fraction changes of the dose distribution. This blurring could conceivably lead to higher cumulative valley doses, and less contrast between peaks and valleys. The immune activation / enhancement seen during SFRT may consequently be curbed. While accurate tumor tracking and patient alignment are essential to maintain the integrity of the peak and valley dose distributions, research suggests that dose smearing may be minimized by selecting appropriate SFRT-GRID block designs and orienting the blocks according to the path of tumor motion [71].

Prior to experimental validation of the hypotheses presented here, murine scale SFRT-GRID must be manufactured. While replicating the SFRT-GRID geometries used in this study may not be feasible, replicating the open-to-shielded ratios is easily feasible. Of note, the focus of this work is not to design SFRT-GRID blocks for translation into preclinical experimentation; rather, we aimed to investigate if such experimentation is theoretically warranted.

We used multiplex immunohistochemistry (mIHC) stained tissue samples as initial conditions for the ABM to simulate radiation on realistic TIME states. While pre-treatment mIHC tissues allow us to visualize the cellular TIME makeup, tissues are unavailable in a longitudinal manner, and little to no information is available regarding the dynamics that give rise to the TIME state at that point in time. In the future, novel machine learning approaches may be able to help decipher ABM parameters that lead to specific TIME compositions as seen in patient biopsies [72].

Conclusion

Radiation-induced anti-tumor immunity seems pivotal in eradicating tumors. Thus, radiation should be tailored to each patient’s tumor immune ecosystem to eradicate cancer cells, protect immune cells, and harness the synergy with the immune system. For some patients, spatially fractionated radiation rather than whole tumor radiation may be a promising approach. To prospectively identify who would benefit from SFRT, further research must be dedicated to rigorous calibration and validation of the presented modeling approach.

Supplementary Information

Supplementary Material 1

Abbreviations

ABM Agent-based model

DAMPS Damage associated molecular patterns

HMGB1 HIGH mobility group box 1

HNC Head and neck cancer

HNSCC Head and neck squamous cell carcinoma

IL-6 Interleukin 6

IMTE Immune-mediated tumor elimination

mIHC Multiple immunohistochemistry

NF-κB Nuclear factor kappa-light-chain-enhancer of activated B cells

PD-1 Programmed cell death protein 1

PDL1 Programmed death ligand 1

PVDR Peak-valley dose ratio

RT Radiotherapy/radiation

SF Survival fraction

SFRT Spatially fractionated radiotherapy

SFRT-GRID Spatially fractionated radiotherapy administered using GRID blocks

TIME Tumor immune microenvironment

TLR2 Toll-like receptor 2

TLR3 Toll-like receptor 3

TLR4 Toll-like receptor 4

TLR9 Toll-like receptor 9

TNF-α Tumor-necrosis factor-alpha

Tx Treatment

WTRT Whole tumor radiotherapy

Acknowledgements

We would like to thank the Advanced Analytical and Digital Pathology laboratory within the Pathology Department at H. Lee Moffitt Cancer Center and Research Institute for their contribution to this work. In addition, we would like to acknowledge the University of South Florida Medical Engineering Capstone Program and thank Dr. Souheil Zekri, Alejandro Acosta, Melissa Chau, Daniel Morejon, and Michael Diaz. Finally, the authors would also like to thank Dr. Renee Brady-Nicholls, Dr. Stefano Pasetto, Dr. Daniel Glazar, Dr. Mohammad Zahid, Dr. Thomas Dombrowski and Jacob Yarinsky for helpful discussions and feedback.

Author contributions

R.A.B. developed and implemented the model, generated, and analyzed the data, and contributed to project conceptualization, and writing and revising the manuscript. N.O., G.R. and J.P. contributed to model development and to revising the manuscript. J.J.C. performed data collection and curation and contributed to revising the manuscript. S.PT. contributed to project conceptualization, model development and revising the manuscript. K.Y. and E.G.M. contributed to project conceptualization and revising the manuscript. H.E. contributed project conceptualization, model development and writing and revising the manuscript. All authors read and approved the final manuscript.

Funding

This work was supported in part by the National Institutes of Health U01CA244100.

Availability of data and materials

All de-identified post-processed clinical data, as well as simulation code (Java in HAL environment: link https://halloworld.org/) and statistical analysis code (MATLAB) will be deposited in a github repository.

Declarations

Ethics approval and consent to participate

All tissues used in this study were collected as part of two IRB approved studies: Total Cancer Care (MCC#14690) and Using Radiotherapy to Perturb the Tumor-Immune Ecosystem for Immune-Modulated Tumor Control (MCC#19233), with patients providing written informed consent.

Consent for publication

Not applicable.

Competing interests

Moffitt Cancer Center has licensed Intellectual Property (IP) related to the proliferation and expansion of tumor infiltrating lymphocytes (TILs) to Iovance Biotherapeutics. Moffitt has also licensed IP to Tuhura Biopharma. SPT is an inventor on such Intellectual Property. SPT is listed as a co-inventor on a patent application with Provectus Biopharmaceuticals. SPT participates in sponsored research agreements with Provectus Biopharmaceuticals, Iovance Biotherapeutics, Intellia Therapeutics, Dyve Biosciences, Turnstone Biologics, and Celgene that are not related to this research. SPT has received consulting fees from Seagen Inc., Morphogenesis, Inc., and KSQ Therapeutics. RAB, NO, GR, JP, KY, EGM and HE declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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References

1. Ferlay J Colombet M Soerjomataram I Mathers C Parkin DM Pineros M Estimating the global cancer incidence and mortality in 2018: GLOBOCAN sources and methods Int J Cancer 2019 144 8 1941 1953 10.1002/ijc.31937 30350310
Ferlay J, Colombet M, Soerjomataram I, Mathers C, Parkin DM, Pineros M, et al. Estimating the global cancer incidence and mortality in 2018: GLOBOCAN sources and methods. Int J Cancer. 2019;144(8):1941–53.30350310 10.1002/ijc.31937
2. Ren W Zhao L Sun Y Wang X Shi X HMGB1 and Toll-like receptors: potential therapeutic targets in autoimmune diseases Mol Med 2023 29 1 117 10.1186/s10020-023-00717-3 37667233
Ren W, Zhao L, Sun Y, Wang X, Shi X. HMGB1 and Toll-like receptors: potential therapeutic targets in autoimmune diseases. Mol Med. 2023;29(1):117.37667233 10.1186/s10020-023-00717-3
3. Barker HE Paget JT Khan AA Harrington KJ The tumour microenvironment after radiotherapy: mechanisms of resistance and recurrence Nat Rev Cancer 2015 15 7 409 425 10.1038/nrc3958 26105538
Barker HE, Paget JT, Khan AA, Harrington KJ. The tumour microenvironment after radiotherapy: mechanisms of resistance and recurrence. Nat Rev Cancer. 2015;15(7):409–25.26105538 10.1038/nrc3958
4. Galluzzi L Aryankalayil MJ Coleman CN Formenti SC Emerging evidence for adapting radiotherapy to immunotherapy Nat Rev Clin Oncol 2023 20 8 543 557 10.1038/s41571-023-00782-x 37280366
Galluzzi L, Aryankalayil MJ, Coleman CN, Formenti SC. Emerging evidence for adapting radiotherapy to immunotherapy. Nat Rev Clin Oncol. 2023;20(8):543–57.37280366 10.1038/s41571-023-00782-x
5. Jarosz-Biej M Smolarczyk R Cichon T Kulach N Tumor microenvironment as a "game changer" in cancer radiotherapy Int J Mol Sci 2019 20 13 3212 10.3390/ijms20133212 31261963
Jarosz-Biej M, Smolarczyk R, Cichon T, Kulach N. Tumor microenvironment as a “game changer” in cancer radiotherapy. Int J Mol Sci. 2019;20(13):3212.31261963 10.3390/ijms20133212
6. Arnold KM Flynn NJ Raben A Romak L Yu Y Dicker AP The impact of radiation on the tumor microenvironment: effect of dose and fractionation schedules Cancer Growth Metastasis 2018 11 1 17 10.1177/1179064418761639
Arnold KM, Flynn NJ, Raben A, Romak L, Yu Y, Dicker AP, et al. The impact of radiation on the tumor microenvironment: effect of dose and fractionation schedules. Cancer Growth Metastasis. 2018;11:1–17.10.1177/1179064418761639
7. Reichert TE Scheuer C Day R Wagner W Whiteside TL The number of intratumoral dendritic cells and zeta-chain expression in T cells as prognostic and survival biomarkers in patients with oral carcinoma Cancer 2001 91 11 2136 2147 10.1002/1097-0142(20010601)91:11<2136::AID-CNCR1242>3.0.CO;2-Q 11391595
Reichert TE, Scheuer C, Day R, Wagner W, Whiteside TL. The number of intratumoral dendritic cells and zeta-chain expression in T cells as prognostic and survival biomarkers in patients with oral carcinoma. Cancer. 2001;91(11):2136–47.11391595 10.1002/1097-0142(20010601)91:11<2136::AID-CNCR1242>3.0.CO;2-Q
8. Shibuya TY Nugyen N McLaren CE Li KT Wei WZ Kim S Clinical significance of poor CD3 response in head and neck cancer Clin Cancer Res 2002 8 3 745 751 11895904
Shibuya TY, Nugyen N, McLaren CE, Li KT, Wei WZ, Kim S, et al. Clinical significance of poor CD3 response in head and neck cancer. Clin Cancer Res. 2002;8(3):745–51.11895904
9. Badoual C Hans S Rodriguez J Peyrard S Klein C Agueznay Nel H Prognostic value of tumor-infiltrating CD4+ T-cell subpopulations in head and neck cancers Clin Cancer Res 2006 12 2 465 472 10.1158/1078-0432.CCR-05-1886 16428488
Badoual C, Hans S, Rodriguez J, Peyrard S, Klein C, Agueznay Nel H, et al. Prognostic value of tumor-infiltrating CD4+ T-cell subpopulations in head and neck cancers. Clin Cancer Res. 2006;12(2):465–72.16428488 10.1158/1078-0432.CCR-05-1886
10. Liu Y Liu Z Yang Y Cui J Sun J Liu Y The prognostic and biology of tumour-infiltrating lymphocytes in the immunotherapy of cancer Br J Cancer 2023 129 7 1041 1049 10.1038/s41416-023-02321-y 37452117
Liu Y, Liu Z, Yang Y, Cui J, Sun J, Liu Y. The prognostic and biology of tumour-infiltrating lymphocytes in the immunotherapy of cancer. Br J Cancer. 2023;129(7):1041–9.37452117 10.1038/s41416-023-02321-y
11. Johnson TR Bassil AM Williams NT Brundage S Kent CL Palmer G An investigation of kV mini-GRID spatially fractionated radiation therapy: dosimetry and preclinical trial Phys Med Biol 2022 67 4 045017 10.1088/1361-6560/ac508c
Johnson TR, Bassil AM, Williams NT, Brundage S, Kent CL, Palmer G, et al. An investigation of kV mini-GRID spatially fractionated radiation therapy: dosimetry and preclinical trial. Phys Med Biol. 2022;67(4):045017.10.1088/1361-6560/ac508c
12. Kohler A Zur Roentgentiefentherapie mit Massendosen Muecnchener Med Wochenschr 1909 56 2314 2316
Kohler A. Zur Roentgentiefentherapie mit Massendosen. Muecnchener Med Wochenschr. 1909;56:2314–6.
13. Yan W Khan MK Wu X Simone CB 2nd Fan J Gressen E Spatially fractionated radiation therapy: history, present and the future Clin Transl Radiat Oncol 2020 20 30 38 31768424
Yan W, Khan MK, Wu X, Simone CB 2nd, Fan J, Gressen E, et al. Spatially fractionated radiation therapy: history, present and the future. Clin Transl Radiat Oncol. 2020;20:30–8.31768424
14. Mohiuddin M Fujita M Regine WF Megooni AS Ibbott GS Ahmed MM High-dose spatially-fractionated radiation (grid): a new paradigm in the management of advanced cancers Int J Radiat Oncol Biol Phys 1999 45 3 721 727 10.1016/S0360-3016(99)00170-4 10524428
Mohiuddin M, Fujita M, Regine WF, Megooni AS, Ibbott GS, Ahmed MM. High-dose spatially-fractionated radiation (grid): a new paradigm in the management of advanced cancers. Int J Radiat Oncol Biol Phys. 1999;45(3):721–7.10524428 10.1016/S0360-3016(99)00170-4
15. Huhn JL Regine WF Valentino JP Meigooni AS Kudrimoti M Mohiuddin M Spatially fractionated GRID radiation treatment of advanced neck disease associated with head and neck cancer Technol Cancer Res Treat 2006 5 6 607 612 10.1177/153303460600500608 17121437
Huhn JL, Regine WF, Valentino JP, Meigooni AS, Kudrimoti M, Mohiuddin M. Spatially fractionated GRID radiation treatment of advanced neck disease associated with head and neck cancer. Technol Cancer Res Treat. 2006;5(6):607–12.17121437 10.1177/153303460600500608
16. Griffin RJ Prise KM McMahon SJ Zhang X Penagaricano J Butterworth KT History and current perspectives on the biological effects of high-dose spatial fractionation and high dose-rate approaches: GRID, Microbeam & FLASH radiotherapy Br J Radiol 2020 93 1113 20200217 10.1259/bjr.20200217 32706989
Griffin RJ, Prise KM, McMahon SJ, Zhang X, Penagaricano J, Butterworth KT. History and current perspectives on the biological effects of high-dose spatial fractionation and high dose-rate approaches: GRID, Microbeam & FLASH radiotherapy. Br J Radiol. 2020;93(1113):20200217.32706989 10.1259/bjr.20200217
17. Peñagarícano JA Griffin R Corry P Moros E Yan Y Ratanatharathorn V Spatially fractionated (GRID) therapy for large and bulky tumors J Ark Med Soc 2009 105 11 263 265 19475814
Peñagarícano JA, Griffin R, Corry P, Moros E, Yan Y, Ratanatharathorn V. Spatially fractionated (GRID) therapy for large and bulky tumors. J Ark Med Soc. 2009;105(11):263–5.19475814
18. Peñagarícano JA Moros EG Ratanatharathorn V Yan Y Corry P Evaluation of spatially fractionated radiotherapy (GRID) and definitive chemoradiotherapy with curative intent for locally advanced squamous cell carcinoma of the head and neck: initial response rates and toxicity Int J Radiat Oncol Biol Phys 2010 76 5 1369 1375 10.1016/j.ijrobp.2009.03.030 19625138
Peñagarícano JA, Moros EG, Ratanatharathorn V, Yan Y, Corry P. Evaluation of spatially fractionated radiotherapy (GRID) and definitive chemoradiotherapy with curative intent for locally advanced squamous cell carcinoma of the head and neck: initial response rates and toxicity. Int J Radiat Oncol Biol Phys. 2010;76(5):1369–75.19625138 10.1016/j.ijrobp.2009.03.030
19. Amendola BE Mahadevan A Blanco Suarez JM Griffin RJ Wu X Perez NC An international consensus on the design of prospective clinical-translational trials in spatially fractionated radiation therapy for advanced gynecologic cancer Cancers 2022 14 17 4267 10.3390/cancers14174267 36077802
Amendola BE, Mahadevan A, Blanco Suarez JM, Griffin RJ, Wu X, Perez NC, et al. An international consensus on the design of prospective clinical-translational trials in spatially fractionated radiation therapy for advanced gynecologic cancer. Cancers. 2022;14(17):4267.36077802 10.3390/cancers14174267
20. Mayr NA Snider JW Regine WF Mohiuddin M Hippe DS Peñagarícano J An international consensus on the design of prospective clinical-translational trials in spatially fractionated radiation therapy Adv Radiat Oncol 2022 7 2 100866 10.1016/j.adro.2021.100866 35198833
Mayr NA, Snider JW, Regine WF, Mohiuddin M, Hippe DS, Peñagarícano J, et al. An international consensus on the design of prospective clinical-translational trials in spatially fractionated radiation therapy. Adv Radiat Oncol. 2022;7(2):100866.35198833 10.1016/j.adro.2021.100866
21. Zagurovskaya-Sultanov M Shareef MM Gupta S Mohiuddin MM Ahmed MM Abscopal tumor regression effects of high-dose spatially fractionated GRID radiation Cancer Res 2005 65 9_Supplement 1341
Zagurovskaya-Sultanov M, Shareef MM, Gupta S, Mohiuddin MM, Ahmed MM. Abscopal tumor regression effects of high-dose spatially fractionated GRID radiation. Cancer Res. 2005;65(9_Supplement):1341.
22. Rivera JN Kierski TM Kasoji SK Abrantes AS Dayton PA Chang SX Conventional dose rate spatially-fractionated radiation therapy (SFRT) treatment response and its association with dosimetric parameters-A preclinical study in a Fischer 344 rat model PLoS ONE 2020 15 6 e0229053 10.1371/journal.pone.0229053 32569277
Rivera JN, Kierski TM, Kasoji SK, Abrantes AS, Dayton PA, Chang SX. Conventional dose rate spatially-fractionated radiation therapy (SFRT) treatment response and its association with dosimetric parameters-A preclinical study in a Fischer 344 rat model. PLoS ONE. 2020;15(6):e0229053.32569277 10.1371/journal.pone.0229053
23. Markovsky E Budhu S Samstein RM Li H Russell J Zhang Z An antitumor immune response is evoked by partial-volume single-dose radiation in 2 murine models Int J Radiat Oncol Biol Phys 2019 103 3 697 708 10.1016/j.ijrobp.2018.10.009 30342090
Markovsky E, Budhu S, Samstein RM, Li H, Russell J, Zhang Z, et al. An antitumor immune response is evoked by partial-volume single-dose radiation in 2 murine models. Int J Radiat Oncol Biol Phys. 2019;103(3):697–708.30342090 10.1016/j.ijrobp.2018.10.009
24. Enderling H Kim S Pilon-Thomas S The accelerating quest for optimal radiation and immunotherapy combinations for local and systemic tumor control Therapeutic Radiology and Oncology. 2018 2 33 10.21037/tro.2018.08.04
Enderling H, Kim S, Pilon-Thomas S. The accelerating quest for optimal radiation and immunotherapy combinations for local and systemic tumor control. Therapeutic Radiology and Oncology. 2018;2:33.10.21037/tro.2018.08.04
25. Poleszczuk J Enderling H The optimal radiation dose to induce robust systemic anti-tumor immunity Int J Mol Sci 2018 19 11 3377 10.3390/ijms19113377 30380596
Poleszczuk J, Enderling H. The optimal radiation dose to induce robust systemic anti-tumor immunity. Int J Mol Sci. 2018;19(11):3377.30380596 10.3390/ijms19113377
26. Walker R Enderling H From concept to clinic: mathematically informed immunotherapy Curr Probl Cancer 2016 40 1 68 83 10.1016/j.currproblcancer.2015.10.004 26645497
Walker R, Enderling H. From concept to clinic: mathematically informed immunotherapy. Curr Probl Cancer. 2016;40(1):68–83.26645497 10.1016/j.currproblcancer.2015.10.004
27. Walker R Poleszczuk J Pilon-Thomas S Kim S Anderson AARA Czerniecki BJ Immune interconnectivity of anatomically distant tumors as a potential mediator of systemic responses to local therapy Sci Rep 2018 8 1 9474 10.1038/s41598-018-27718-1 29930290
Walker R, Poleszczuk J, Pilon-Thomas S, Kim S, Anderson AARA, Czerniecki BJ, et al. Immune interconnectivity of anatomically distant tumors as a potential mediator of systemic responses to local therapy. Sci Rep. 2018;8(1):9474.29930290 10.1038/s41598-018-27718-1
28. Dullens HF Van der Tol MW De Weger RA Den Otter W A survey of some formal models in tumor immunology Cancer Immunol Immunother CII 1986 23 3 159 164 10.1007/BF00205644 3491679
Dullens HF, Van der Tol MW, De Weger RA, Den Otter W. A survey of some formal models in tumor immunology. Cancer Immunol Immunother CII. 1986;23(3):159–64.3491679 10.1007/BF00205644
29. Eftimie R Gillard JJ Cantrell DA Mathematical models for immunology: current state of the art and future research directions Bull Math Biol 2016 78 10 2091 2134 10.1007/s11538-016-0214-9 27714570
Eftimie R, Gillard JJ, Cantrell DA. Mathematical models for immunology: current state of the art and future research directions. Bull Math Biol. 2016;78(10):2091–134.27714570 10.1007/s11538-016-0214-9
30. de Pillis LG Radunskaya AE Wiseman CL A validated mathematical model of cell-mediated immune response to tumor growth Cancer Res 2005 65 17 7950 7958 10.1158/0008-5472.CAN-05-0564 16140967
de Pillis LG, Radunskaya AE, Wiseman CL. A validated mathematical model of cell-mediated immune response to tumor growth. Cancer Res. 2005;65(17):7950–8.16140967 10.1158/0008-5472.CAN-05-0564
31. Barbolosi D, Summer I, Meille C, Serre R, Kelly A, Zerdoud S, et al. Modeling therapeutic response to radioiodine in metastatic thyroid cancer: a proof-of-concept study for individualized medicine. Oncotarget. 2014 (1949–2553 (Electronic)).
32. Serre R Benzekry S Padovani L Meille C Andre N Ciccolini J Mathematical modeling of cancer immunotherapy and its synergy with radiotherapy Cancer Res 2016 76 17 4931 4940 10.1158/0008-5472.CAN-15-3567 27302167
Serre R, Benzekry S, Padovani L, Meille C, Andre N, Ciccolini J, et al. Mathematical modeling of cancer immunotherapy and its synergy with radiotherapy. Cancer Res. 2016;76(17):4931–40.27302167 10.1158/0008-5472.CAN-15-3567
33. Alfonso JC Poleszczuk J Walker R Kim S Pilon-Thomas S Conejo-Garcia J Immunologic consequences of sequencing cancer radiotherapy and surgery JCO Clin Cancer Inf 2019 3 1 16
Alfonso JC, Poleszczuk J, Walker R, Kim S, Pilon-Thomas S, Conejo-Garcia J, et al. Immunologic consequences of sequencing cancer radiotherapy and surgery. JCO Clin Cancer Inf. 2019;3:1–16.
34. Enderling H Hlatky L Hahnfeldt P Immunoediting: evidence of the multifaceted role of the immune system in self-metastatic tumor growth Theor Biol Med Model 2012 9 1 31 10.1186/1742-4682-9-31 22838395
Enderling H, Hlatky L, Hahnfeldt P. Immunoediting: evidence of the multifaceted role of the immune system in self-metastatic tumor growth. Theor Biol Med Model. 2012;9(1):31.22838395 10.1186/1742-4682-9-31
35. Bekker RA Kim S Pilon-Thomas S Enderling H Mathematical modeling of radiotherapy and its impact on tumor interactions with the immune system Neoplasia 2022 28 100796 10.1016/j.neo.2022.100796 35447601
Bekker RA, Kim S, Pilon-Thomas S, Enderling H. Mathematical modeling of radiotherapy and its impact on tumor interactions with the immune system. Neoplasia. 2022;28:100796.35447601 10.1016/j.neo.2022.100796
36. Brady R Enderling H Mathematical models of cancer: when to predict novel therapies, and when not to Bull Math Biol 2019 81 10 3722 3731 10.1007/s11538-019-00640-x 31338741
Brady R, Enderling H. Mathematical models of cancer: when to predict novel therapies, and when not to. Bull Math Biol. 2019;81(10):3722–31.31338741 10.1007/s11538-019-00640-x
37. Bravo R Baratchart E West J Schenck R Miller A Gallaher J Hybrid Automata Library: a flexible platform for hybrid modeling with real-time visualization PLoS Comput Biol 2020 16 3 e1007635 10.1371/journal.pcbi.1007635 32155140
Bravo R, Baratchart E, West J, Schenck R, Miller A, Gallaher J, et al. Hybrid Automata Library: a flexible platform for hybrid modeling with real-time visualization. PLoS Comput Biol. 2020;16(3):e1007635.32155140 10.1371/journal.pcbi.1007635
38. Chaffer CL Weinberg RA A perspective on cancer cell metastasis Science 2011 331 6024 1559 1564 10.1126/science.1203543 21436443
Chaffer CL, Weinberg RA. A perspective on cancer cell metastasis. Science. 2011;331(6024):1559–64.21436443 10.1126/science.1203543
39. Chambers AF Groom AC MacDonald IC Dissemination and growth of cancer cells in metastatic sites Nat Rev Cancer 2002 2 8 563 572 10.1038/nrc865 12154349
Chambers AF, Groom AC, MacDonald IC. Dissemination and growth of cancer cells in metastatic sites. Nat Rev Cancer. 2002;2(8):563–72.12154349 10.1038/nrc865
40. Chaplain MAJ Graziano L Preziosi L Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development Math Med Biol J IMA 2006 23 3 197 229 10.1093/imammb/dql009
Chaplain MAJ, Graziano L, Preziosi L. Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development. Math Med Biol J IMA. 2006;23(3):197–229.10.1093/imammb/dql009
41. Enderling H, Anderson Ar Fau - Chaplain MAJ, Chaplain Ma Fau - Beheshti A, Beheshti A Fau - Hlatky L, Hlatky L Fau - Hahnfeldt P, Hahnfeldt P. Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics. 2009(1538–7445 (Electronic)).
42. Enderling H, Hlatky L Fau - Hahnfeldt P, Hahnfeldt P. Migration rules: tumours are conglomerates of self-metastases. 2009 (1532–1827 (Electronic)).
43. Butcher EC, Picker LJ. Lymphocyte homing and homeostasis. 1996 (0036–8075 (Print)).
44. Masopust D Schenkel JM The integration of T cell migration, differentiation and function Nat Rev Immunol 2013 13 5 309 320 10.1038/nri3442 23598650
Masopust D, Schenkel JM. The integration of T cell migration, differentiation and function. Nat Rev Immunol. 2013;13(5):309–20.23598650 10.1038/nri3442
45. Kohli K Pillarisetty VG Kim TS Key chemokines direct migration of immune cells in solid tumors Cancer Gene Ther 2022 29 1 10 21 10.1038/s41417-021-00303-x 33603130
Kohli K, Pillarisetty VG, Kim TS. Key chemokines direct migration of immune cells in solid tumors. Cancer Gene Ther. 2022;29(1):10–21.33603130 10.1038/s41417-021-00303-x
46. Enderling H Hlatky L Hahnfeldt P Tumor morphological evolution: directed migration and gain and loss of the self-metastatic phenotype Biol Direct 2010 5 1 23 10.1186/1745-6150-5-23 20406441
Enderling H, Hlatky L, Hahnfeldt P. Tumor morphological evolution: directed migration and gain and loss of the self-metastatic phenotype. Biol Direct. 2010;5(1):23.20406441 10.1186/1745-6150-5-23
47. Ghaffarizadeh A Heiland R Friedman SH Mumenthaler SM Macklin P PhysiCell: an open source physics-based cell simulator for 3-D multicellular systems PLoS Comput Biol 2018 14 2 e1005991 10.1371/journal.pcbi.1005991 29474446
Ghaffarizadeh A, Heiland R, Friedman SH, Mumenthaler SM, Macklin P. PhysiCell: an open source physics-based cell simulator for 3-D multicellular systems. PLoS Comput Biol. 2018;14(2):e1005991.29474446 10.1371/journal.pcbi.1005991
48. Enderling H Hlatky L Hahnfeldt P The promoting role of a tumour-secreted chemorepellent in self-metastatic tumour progression Math Med Biol J IMA 2012 29 1 21 29 10.1093/imammb/dqq015
Enderling H, Hlatky L, Hahnfeldt P. The promoting role of a tumour-secreted chemorepellent in self-metastatic tumour progression. Math Med Biol J IMA. 2012;29(1):21–9.10.1093/imammb/dqq015
49. Miller MJ Wei SH Parker I Cahalan MD Two-photon imaging of lymphocyte motility and antigen response in intact lymph node Science 2002 296 5574 1869 1873 10.1126/science.1070051 12016203
Miller MJ, Wei SH, Parker I, Cahalan MD. Two-photon imaging of lymphocyte motility and antigen response in intact lymph node. Science. 2002;296(5574):1869–73.12016203 10.1126/science.1070051
50. Mueller SN Effector T-cell responses in non-lymphoid tissues: insights from in vivo imaging Immunol Cell Biol 2013 91 4 290 296 10.1038/icb.2012.75 23295362
Mueller SN. Effector T-cell responses in non-lymphoid tissues: insights from in vivo imaging. Immunol Cell Biol. 2013;91(4):290–6.23295362 10.1038/icb.2012.75
51. Bougherara H Mansuet-Lupo A Alifano M Ngô C Damotte D Le Frère-Belda M-A Real-time imaging of resident T cells in human lung and ovarian carcinomas reveals how different tumor microenvironments control T lymphocyte migration Front Immunol 2015 6 500 10.3389/fimmu.2015.00500 26528284
Bougherara H, Mansuet-Lupo A, Alifano M, Ngô C, Damotte D, Le Frère-Belda M-A, et al. Real-time imaging of resident T cells in human lung and ovarian carcinomas reveals how different tumor microenvironments control T lymphocyte migration. Front Immunol. 2015;6:500.26528284 10.3389/fimmu.2015.00500
52. Beck RJ Bijker DI Beltman JB Heterogeneous, delayed-onset killing by multiple-hitting T cells: stochastic simulations to assess methods for analysis of imaging data PLoS Comput Biol 2020 16 7 e1007972 10.1371/journal.pcbi.1007972 32658891
Beck RJ, Bijker DI, Beltman JB. Heterogeneous, delayed-onset killing by multiple-hitting T cells: stochastic simulations to assess methods for analysis of imaging data. PLoS Comput Biol. 2020;16(7):e1007972.32658891 10.1371/journal.pcbi.1007972
53. Weigelin B den Boer AT Wagena E Broen K Dolstra H de Boer RJ Cytotoxic T cells are able to efficiently eliminate cancer cells by additive cytotoxicity Nat Commun 2021 12 1 5217 10.1038/s41467-021-25282-3 34471116
Weigelin B, den Boer AT, Wagena E, Broen K, Dolstra H, de Boer RJ, et al. Cytotoxic T cells are able to efficiently eliminate cancer cells by additive cytotoxicity. Nat Commun. 2021;12(1):5217.34471116 10.1038/s41467-021-25282-3
54. McMahon SJ The linear quadratic model: usage, interpretation and challenges Phys Med Biol 2018 64 1 01TR01 10.1088/1361-6560/aaf26a 30523903
McMahon SJ. The linear quadratic model: usage, interpretation and challenges. Phys Med Biol. 2018;64(1):01TR01.30523903 10.1088/1361-6560/aaf26a
55. Jones L Hoban P Metcalfe P The use of the linear quadratic model in radiotherapy: a review Australas Phys Eng Sci Med 2001 24 3 132 146 10.1007/BF03178355 11764395
Jones L, Hoban P, Metcalfe P. The use of the linear quadratic model in radiotherapy: a review. Australas Phys Eng Sci Med. 2001;24(3):132–46.11764395 10.1007/BF03178355
56. Alfonso JCL Grass GD Welsh E Ahmed KA Teer JK Pilon-Thomas S Tumor-immune ecosystem dynamics define an individual Radiation Immune Score to predict pan-cancer radiocurability Neoplasia (New York, NY) 2021 23 11 1110 1122 10.1016/j.neo.2021.09.003
Alfonso JCL, Grass GD, Welsh E, Ahmed KA, Teer JK, Pilon-Thomas S, et al. Tumor-immune ecosystem dynamics define an individual Radiation Immune Score to predict pan-cancer radiocurability. Neoplasia (New York, NY). 2021;23(11):1110–22.10.1016/j.neo.2021.09.003
57. Enderling H Park D Hlatky L Hahnfeldt P The importance of spatial distribution of stemness and proliferation state in determining tumor radioresponse Math Model Nat Phenom 2009 4 3 117 133 10.1051/mmnp/20094305
Enderling H, Park D, Hlatky L, Hahnfeldt P. The importance of spatial distribution of stemness and proliferation state in determining tumor radioresponse. Math Model Nat Phenom. 2009;4(3):117–33.10.1051/mmnp/20094305
58. Hill RP Bristow RG Fyles A Koritzinsky M Milosevic M Wouters BG Hypoxia and predicting radiation response Semin Radiat Oncol 2015 25 4 260 272 10.1016/j.semradonc.2015.05.004 26384274
Hill RP, Bristow RG, Fyles A, Koritzinsky M, Milosevic M, Wouters BG. Hypoxia and predicting radiation response. Semin Radiat Oncol. 2015;25(4):260–72.26384274 10.1016/j.semradonc.2015.05.004
59. Jeggo P, Löbrich M. Radiation-induced DNA damage responses. (0144–8420 (Print)).
60. Santivasi WL, Xia F. Ionizing radiation-induced DNA damage, response, and repair. (1557–7716 (Electronic)).
61. Endlich B Radford IR Forrester HB Dewey WC Computerized video time-lapse microscopy studies of ionizing radiation-induced rapid-interphase and mitosis-related apoptosis in lymphoid cells Radiat Res 2000 153 1 36 48 10.1667/0033-7587(2000)153[0036:CVTLMS]2.0.CO;2 10630976
Endlich B, Radford IR, Forrester HB, Dewey WC. Computerized video time-lapse microscopy studies of ionizing radiation-induced rapid-interphase and mitosis-related apoptosis in lymphoid cells. Radiat Res. 2000;153(1):36–48.10630976 10.1667/0033-7587(2000)153[0036:CVTLMS]2.0.CO;2
62. Gilbreath C Ma S Yu L Sonavane R Roggero CM Devineni A Dynamic differences between DNA damage repair responses in primary tumors and cell lines Transl Oncol 2021 14 1 100898 10.1016/j.tranon.2020.100898 33096336
Gilbreath C, Ma S, Yu L, Sonavane R, Roggero CM, Devineni A, et al. Dynamic differences between DNA damage repair responses in primary tumors and cell lines. Transl Oncol. 2021;14(1):100898.33096336 10.1016/j.tranon.2020.100898
63. Johnsrud AJ Jenkins SV Jamshidi-Parsian A Quick CM Galhardo EP Dings RPM Evidence for early stage anti-tumor immunity elicited by spatially fractionated radiotherapy-immunotherapy combinations Radiat Res 2020 194 6 688 697 10.1667/RADE-20-00065.1 33348372
Johnsrud AJ, Jenkins SV, Jamshidi-Parsian A, Quick CM, Galhardo EP, Dings RPM, et al. Evidence for early stage anti-tumor immunity elicited by spatially fractionated radiotherapy-immunotherapy combinations. Radiat Res. 2020;194(6):688–97.33348372 10.1667/RADE-20-00065.1
64. Ahmed M Bicher S Stewart RD Bartzsch S Schmid TE Combs SE Dosimetric quantities and cell survival for spatially fractionated radiation therapy Front Phys 2023 10 1064860 10.3389/fphy.2022.1064860
Ahmed M, Bicher S, Stewart RD, Bartzsch S, Schmid TE, Combs SE, et al. Dosimetric quantities and cell survival for spatially fractionated radiation therapy. Front Phys. 2023;10:1064860.10.3389/fphy.2022.1064860
65. Dunn GP Old LJ Schreiber RD The three Es of cancer immunoediting Annu Rev Immunol 2004 22 329 360 10.1146/annurev.immunol.22.012703.104803 15032581
Dunn GP, Old LJ, Schreiber RD. The three Es of cancer immunoediting. Annu Rev Immunol. 2004;22:329–60.15032581 10.1146/annurev.immunol.22.012703.104803
66. Bekker RA Zahid MU Binning JM Spring BQ Hwu P Pilon-Thomas S Rethinking the immunotherapy numbers game J Immunother Cancer 2022 10 7 e005107 10.1136/jitc-2022-005107 35793871
Bekker RA, Zahid MU, Binning JM, Spring BQ, Hwu P, Pilon-Thomas S, et al. Rethinking the immunotherapy numbers game. J Immunother Cancer. 2022;10(7):e005107.35793871 10.1136/jitc-2022-005107
67. Hanahan D Weinberg RA Hallmarks of cancer: the next generation Cell 2011 144 5 646 674 10.1016/j.cell.2011.02.013 21376230
Hanahan D, Weinberg RA. Hallmarks of cancer: the next generation. Cell. 2011;144(5):646–74.21376230 10.1016/j.cell.2011.02.013
68. Yeh SA Radiotherapy for head and neck cancer Semin Plast Surg 2010 24 2 127 136 10.1055/s-0030-1255330 22550433
Yeh SA. Radiotherapy for head and neck cancer. Semin Plast Surg. 2010;24(2):127–36.22550433 10.1055/s-0030-1255330
69. Wang X Zhao Z Wang P Geng X Zhu L Li M Low lymphocyte count is associated with radiotherapy parameters and affects the outcomes of esophageal squamous cell carcinoma patients Front Oncol 2020 10 997 10.3389/fonc.2020.00997 32656085
Wang X, Zhao Z, Wang P, Geng X, Zhu L, Li M. Low lymphocyte count is associated with radiotherapy parameters and affects the outcomes of esophageal squamous cell carcinoma patients. Front Oncol. 2020;10:997.32656085 10.3389/fonc.2020.00997
70. Marks LB Dewhirst M Accelerated repopulation: friend or foe? Exploiting changes in tumor growth characteristics to improve the “efficiency” of radiotherapy Int J Radiat Oncol Biol Phys 1991 21 5 1377 1383 10.1016/0360-3016(91)90301-J 1938539
Marks LB, Dewhirst M. Accelerated repopulation: friend or foe? Exploiting changes in tumor growth characteristics to improve the “efficiency” of radiotherapy. Int J Radiat Oncol Biol Phys. 1991;21(5):1377–83.1938539 10.1016/0360-3016(91)90301-J
71. Naqvi SA Mohiuddin MM Ha JK Regine WF Effects of tumor motion in GRID therapy Med Phys 2008 35 10 4435 4442 10.1118/1.2977538 18975690
Naqvi SA, Mohiuddin MM, Ha JK, Regine WF. Effects of tumor motion in GRID therapy. Med Phys. 2008;35(10):4435–42.18975690 10.1118/1.2977538
72. Cess CG Finley SD Calibrating agent-based models to tumor images using representation learning PLoS Comput Biol 2023 19 4 e1011070 10.1371/journal.pcbi.1011070 37083821
Cess CG, Finley SD. Calibrating agent-based models to tumor images using representation learning. PLoS Comput Biol. 2023;19(4):e1011070.37083821 10.1371/journal.pcbi.1011070
