Time-dependent cell disintegration kinetics in lung tumors after irradiation

A Multidisciplinary Hyper-Modeling Scheme in Personalized In Silico Oncology: Coupling Cell Kinetics with Metabolism, Signaling Networks, and Biomechanics as Plug-In Component Models of a Cancer Digital Twin

The massive amount of human biological, imaging, and clinical data produced by multiple and diverse sources necessitates integrative modeling approaches able to summarize all this information into answers to specific clinical questions. In this paper, we present a hypermodeling scheme able to combine models of diverse cancer aspects regardless of their underlying method or scale. Describing tissue-scale cancer cell proliferation, biomechanical tumor growth, nutrient transport, genomic-scale aberrant cancer cell metabolism, and cell-signaling pathways that regulate the cellular response to therapy, the hypermodel integrates mutation, miRNA expression, imaging, and clinical data. The constituting hypomodels, as well as their orchestration and links, are described. Two specific cancer types, Wilms tumor (nephroblastoma) and non-small cell lung cancer, are addressed as proof-of-concept study cases. Personalized simulations of the actual anatomy of a patient have been conducted. The hypermodel has also been applied to predict tumor control after radiotherapy and the relationship between tumor proliferative activity and response to neoadjuvant chemotherapy. Our innovative hypermodel holds promise as a digital twin-based clinical decision support system and as the core of future in silico trial platforms, although additional retrospective adaptation and validation are necessary.

A mathematical model for predicting the changes of non-small cell lung cancer based on tumor mass during radiotherapy

This study aims to build a feasible mathematical model to analyze the mass evolution of NSCLC during standard fractionated radiotherapy. Seventy-three cases of NSCLC who were received radiotherapy with prescription dose of 2 Gy  ×  30 fx were selected retrospectively and divided into adenocarcinoma (ADC) group and squamous cell carcinoma (SCC) group according to the pathological type. A total of six sets of CT/CBCT images were collected. The tumor masses were measured according to each set of images. We build a mathematical model (Linear Quadratic_Repopulation&Reoxygenation& Dissolution model, LQ_RRD model), which was used to fit the first five sets of measured mass into a smooth curve. By adjusting the model parameters (λ, ν and µ), the optimal fitting results can be obtained. In order to verify the accuracy of model prediction, we measured the mass of the review images (MV, measured values), and found out the estimate point of the corresponding time (EV, estimated value) on the fitting curve. The difference and correlation between MV and EV were compared. It was found that the model could substantially simulate the tumor mass changes during radiotherapy, and it had a good fit to the clinical data (%RMSE-Median  =  5.52, %RMSE-Range  =  [3.19, 10.73]). Comparing the differences of model parameters between ADC and SCC group, there was no significant difference in λ (t  =  1.622, p   =  0.109), but the difference was significant in ν and µ (z  =  -7.270, p   =  0.000 and t  =  -10.205, p   =  0.000). Moreover, linear correlation analysis showed that there was a linear correlation between MV and EV no matter mass or volume (r  =  0.960, p   =  0.000 versus r  =  0.926, p   =  0.000). Nevertheless, the deviation between MV and EV of volume was larger than that of mass (z  =  -1.897, p   =  0.058 versus z  =  -3.387, p   =  0.001), and the deviation was more pronounced in larger tumors. We suggest that this mathematical model is more suitable to predict the tumor mass than volume for NSCLC during radiotherapy.

Modeling the Cellular Response of Lung Cancer to Radiation Therapy for a Broad Range of Fractionation Schedules

Purpose: To demonstrate that a mathematical model can be used to quantitatively understand tumor cellular dynamics during a course of radiotherapy and to predict the likelihood of local control as a function of dose and treatment fractions.Experimental Design: We model outcomes for early-stage, localized non-small cell lung cancer (NSCLC), by fitting a mechanistic, cellular dynamics-based tumor control probability that assumes a constant local supply of oxygen and glucose. In addition to standard radiobiological effects such as repair of sub-lethal damage and the impact of hypoxia, we also accounted for proliferation as well as radiosensitivity variability within the cell cycle. We applied the model to 36 published and two unpublished early-stage patient cohorts, totaling 2,701 patients.Results: Precise likelihood best-fit values were derived for the radiobiological parameters: α [0.305 Gy^-1; 95% confidence interval (CI), 0.120-0.365], the α/β ratio (2.80 Gy; 95% CI, 0.40-4.40), and the oxygen enhancement ratio (OER) value for intermediately hypoxic cells receiving glucose but not oxygen (1.70; 95% CI, 1.55-2.25). All fractionation groups are well fitted by a single dose-response curve with a high χ² P value, indicating consistency with the fitted model. The analysis was further validated with an additional 23 patient cohorts (n = 1,628). The model indicates that hypofractionation regimens overcome hypoxia (and cell-cycle radiosensitivity variations) by the sheer impact of high doses per fraction, whereas lower dose-per-fraction regimens allow for reoxygenation and corresponding sensitization, but lose effectiveness for prolonged treatments due to proliferation.Conclusions: This proposed mechanistic tumor-response model can accurately predict overtreatment or undertreatment for various treatment regimens. Clin Cancer Res; 23(18); 5469-79. ©2017 AACR.

Theoretical effectiveness of cell survival in fractionated radiotherapy with hypoxia-targeted dose escalation

PURPOSE

The goal of this article is to compute the cell survival during fractionated radiotherapy with non-uniform hypoxia-targeted dose distribution relative to cell survival for a uniform dose distribution with equal integral tumor dose. The analysis is performed for different parameters of radiotherapy with conventional and hypofractionated dose regimens.

METHODS

Our analysis is done using a parsimonious tumor response model that describes the major components of tumor response to radiotherapy such as radiosensitivity, cell proliferation, and hypoxia using as few variables as possible. Two levels of oxygenated and hypoxic cells with the survival curves described by the linear quadratic (LQ) model are implemented in the model. The model allows for analytical solutions for relative cell survival in a single fraction simulation which can be used for additional validation of our numerical simulations. The relative cell survival was computed for conventional and hypofractionated dose regimens in a model problem with radiobiological parameters for the non-small-cell lung cancer. Sensitivity of cell survival to different parameters of radiotherapy such as the relative volume of hypoxic fraction, boost dose ratio, re-oxygenation rate, and delivery errors was investigated.

RESULTS

Our computational and analytical results show that relative cell survival for non-uniform and uniform dose distributions is larger than 1.0 during the first few fractions of radiotherapy with conventional fractionation. This indicates that the uniform dose distribution produces a higher cell killing effect for the equal integral dose. This may stem from domination of linear contribution to the cell killing effect seen in the dose range of 1-2 Gy and a steeper slope of survival curve in the oxygenated tumor region. This effect can only happen if the distribution of clonogens is nearly uniform; therefore, after the first few fractions, the non-uniform dose distributions outperform the uniform dose distribution and relative cell survival becomes less than 1.0. However, re-oxygenation and delivery errors can also reduce the effectiveness of hypoxia-targeted non-uniform dose distributions toward the end of treatment. For hypofractionated radiotherapy with fractional dose >3 Gy, the relative cell survival was always below 1.0, which means the non-uniform dose distributions produced higher cell killing effect than the uniform dose distribution during the entire treatment.

CONCLUSION

The data obtained in this work suggest that non-uniform hypoxia-targeted dose distributions are less effective at cell killing than uniform dose distributions at the beginning of radiotherapy with conventional fractionation. However; non-uniform dose distributions can outperform uniform dose distribution by the end of the treatment if the effects of re-oxygenation and delivery errors are reduced. In hypofractionated radiotherapy, non-uniform hypoxia-targeted dose distributions are more efficient than uniform dose distributions during the entire treatment.

Modelling and Bayesian adaptive prediction of individual patients' tumour volume change during radiotherapy

The aim of this study is to develop a mathematical modelling method that can predict individual patients’ response to radiotherapy, in terms of tumour volume change during the treatment. The main concept is to start from a population-average model, which is subsequently updated from an individual’s tumour volume measurement. The model becomes increasingly personalized and so too does the prediction it produces. This idea of adaptive prediction was realised by using a Bayesian approach for updating the model parameters. The feasibility of the developed method was demonstrated on the data from 25 non-small cell lung cancer patients treated with helical tomotherapy, during which tumour volume was measured from daily imaging as part of the image-guided radiotherapy. The method could provide useful information for adaptive treatment planning and dose scheduling based on the patient’s personalised response.

Mathematical modelling of tumour volume dynamics in response to stereotactic ablative radiotherapy for non-small cell lung cancer

This paper reports a modelling study of tumour volume dynamics in response to stereotactic ablative radiotherapy (SABR). The main objective was to develop a model that is adequate to describe tumour volume change measured during SABR, and at the same time is not excessively complex as lacking support from clinical data. To this end, various modelling options were explored, and a rigorous statistical method, the Akaike information criterion, was used to help determine a trade-off between model accuracy and complexity. The models were calibrated to the data from 11 non-small cell lung cancer patients treated with SABR. The results showed that it is feasible to model the tumour volume dynamics during SABR, opening up the potential for using such models in a clinical environment in the future.

Kinetic Models for Predicting Cervical Cancer Response to Radiation Therapy on Individual Basis Using Tumor Regression Measured In Vivo With Volumetric Imaging

This article describes a macroscopic mathematical modeling approach to capture the interplay between solid tumor evolution and cell damage during radiotherapy. Volume regression profiles of 15 patients with uterine cervical cancer were reconstructed from serial cone-beam computed tomography data sets, acquired for image-guided radiotherapy, and used for model parameter learning by means of a genetic-based optimization. Patients, diagnosed with either squamous cell carcinoma or adenocarcinoma, underwent different treatment modalities (image-guided radiotherapy and image-guided chemo-radiotherapy). The mean volume at the beginning of radiotherapy and the end of radiotherapy was on average 23.7 cm(3) (range: 12.7-44.4 cm(3)) and 8.6 cm(3) (range: 3.6-17.1 cm(3)), respectively. Two different tumor dynamics were taken into account in the model: the viable (active) and the necrotic cancer cells. However, according to the results of a preliminary volume regression analysis, we assumed a short dead cell resolving time and the model was simplified to the active tumor volume. Model learning was performed both on the complete patient cohort (cohort-based model learning) and on each single patient (patient-specific model learning). The fitting results (mean error: ∼ 16% and ∼ 6% for the cohort-based model and patient-specific model, respectively) highlighted the model ability to quantitatively reproduce tumor regression. Volume prediction errors of about 18% on average were obtained using cohort-based model computed on all but 1 patient at a time (leave-one-out technique). Finally, a sensitivity analysis was performed and the data uncertainty effects evaluated by simulating an average volume perturbation of about 1.5 cm(3) obtaining an error increase within 0.2%. In conclusion, we showed that simple time-continuous models can represent tumor regression curves both on a patient cohort and patient-specific basis; this discloses the opportunity in the future to exploit such models to predict how changes in the treatment schedule (number of fractions, doses, intervals among fractions) might affect the tumor regression on an individual basis.

Modeling the Interplay Between Tumor Volume Regression and Oxygenation in Uterine Cervical Cancer During Radiotherapy Treatment

This paper describes a patient-specific mathematical model to predict the evolution of uterine cervical tumors at a macroscopic scale, during fractionated external radiotherapy. The model provides estimates of tumor regrowth and dead-cell reabsorption, incorporating the interplay between tumor regression rate and radiosensitivity, as a function of the tumor oxygenation level. Model parameters were estimated by minimizing the difference between predicted and measured tumor volumes, these latter being obtained from a set of 154 serial cone-beam computed tomography scans acquired on 16 patients along the course of the therapy. The model stratified patients according to two different estimated dynamics of dead-cell removal and to the predicted initial value of the tumor oxygenation. The comparison with a simpler model demonstrated an improvement in fitting properties of this approach (fitting error average value <5%, p < 0.01), especially in case of tumor late responses, which can hardly be handled by models entailing a constant radiosensitivity, failing to model changes from initial severe hypoxia to aerobic conditions during the treatment course. The model predictive capabilities suggest the need of clustering patients accounting for cancer cell line, tumor staging, as well as microenvironment conditions (e.g., oxygenation level).

Assessment of interpatient heterogeneity in tumor radiosensitivity for nonsmall cell lung cancer using tumor-volume variation data

PURPOSE

In our previous work, the authors showed that a distribution of cell surviving fractions S2 in a heterogeneous group of patients could be derived from tumor-volume variation curves during radiotherapy for head and neck cancer. In this research study, the authors show that this algorithm can be applied to other tumors, specifically in nonsmall cell lung cancer. This new application includes larger patient volumes and includes comparison of data sets obtained at independent institutions.

METHODS

Our analysis was based on two data sets of tumor-volume variation curves for heterogeneous groups of 17 patients treated for nonsmall cell lung cancer with conventional dose fractionation. The data sets were obtained previously at two independent institutions by using megavoltage computed tomography. Statistical distributions of cell surviving fractions S2 and clearance half-lives of lethally damaged cells T(1/2) have been reconstructed in each patient group by using a version of the two-level cell population model of tumor response and a simulated annealing algorithm. The reconstructed statistical distributions of the cell surviving fractions have been compared to the distributions measured using predictive assays in vitro.

RESULTS

Nonsmall cell lung cancer presents certain difficulties for modeling surviving fractions using tumor-volume variation curves because of relatively large fractional hypoxic volume, low gradient of tumor-volume response, and possible uncertainties due to breathing motion. Despite these difficulties, cell surviving fractions S2 for nonsmall cell lung cancer derived from tumor-volume variation measured at different institutions have similar probability density functions (PDFs) with mean values of 0.30 and 0.43 and standard deviations of 0.13 and 0.18, respectively. The PDFs for cell surviving fractions S2 reconstructed from tumor volume variation agree with the PDF measured in vitro.

CONCLUSIONS

The data obtained in this work, when taken together with the data obtained previously for head and neck cancer, suggests that the cell surviving fractions S2 can be reconstructed from the tumor volume variation curves measured during radiotherapy with conventional fractionation. The proposed method can be used for treatment evaluation and adaptation.

Modelling the interplay between hypoxia and proliferation in radiotherapy tumour response

A tumour control probability computational model for fractionated radiotherapy was developed, with the goal of incorporating the fundamental interplay between hypoxia and proliferation, including reoxygenation over a course of radiotherapy. The fundamental idea is that the local delivery of oxygen and glucose limits the amount of proliferation and metabolically-supported cell survival a tumour sub-volume can support. The model has three compartments: a proliferating compartment of cells receiving oxygen and glucose; an intermediate, metabolically-active compartment receiving glucose; and a highly hypoxic compartment of starving cells. Following the post-mitotic cell death of proliferating cells, intermediate cells move into the proliferative compartment and hypoxic cells move into the intermediate compartment. A key advantage of the proposed model is that the initial compartmental cell distribution is uniquely determined from the assumed local growth fraction (GF) and volume doubling time (TD) values. Varying initial cell state distributions, based on the local (voxel) GF and TD, were simulated. Tumour response was simulated for head and neck squamous cell carcinoma using relevant parameter values based on published sources. The tumour dose required to achieve a 50% local control rate (TCD50) was found for various GFs and TD's, and the effect of fraction size on TCD50 was also evaluated. Due to the advantage of reoxygenation over a course of radiotherapy, conventional fraction sizes (2-2.4 Gy fx(-1)) were predicted to result in smaller TCD50's than larger fraction sizes (4-5 Gy fx(-1)) for a 10 cc tumour with GFs of around 0.15. The time to eliminate hypoxic cells (the reoxygenation time) was estimated for a given GF and decreased as GF increased. The extra dose required to overcome accelerated stem cell accumulation in longer treatment schedules was estimated to be 0.68 Gy/day (in EQD26.6), similar to published values derived from clinical data. The model predicts, for a 2 Gy/weekday fractionation, that increased initial proliferation (high GF) should, surprisingly, lead to moderately higher local control values. Tumour hypoxia is predicted to increase the required dose for local control by approximately 30%. Predicted tumour regression patterns are consistent with clinical observations. This simple yet flexible model shows how the local competition for chemical resources might impact local control rates under varying fractionation conditions.

Classifying geometric variability by dominant eigenmodes of deformation in regressing tumours during active breath-hold lung cancer radiotherapy

The purpose of this study is to develop and evaluate a lung tumour interfraction geometric variability classification scheme as a means to guide adaptive radiotherapy and improve measurement of treatment response. Principal component analysis (PCA) was used to generate statistical shape models of the gross tumour volume (GTV) for 12 patients with weekly breath hold CT scans. Each eigenmode of the PCA model was classified as 'trending' or 'non-trending' depending on whether its contribution to the overall GTV variability included a time trend over the treatment course. Trending eigenmodes were used to reconstruct the original semi-automatically delineated GTVs into a reduced model containing only time trends. Reduced models were compared to the original GTVs by analyzing the reconstruction error in the GTV and position. Both retrospective (all weekly images) and prospective (only the first four weekly images) were evaluated. The average volume difference from the original GTV was 4.3% ± 2.4% for the trending model. The positional variability of the GTV over the treatment course, as measured by the standard deviation of the GTV centroid, was 1.9 ± 1.4 mm for the original GTVs, which was reduced to 1.2 ± 0.6 mm for the trending-only model. In 3/13 cases, the dominant eigenmode changed class between the prospective and retrospective models. The trending-only model preserved GTV and shape relative to the original GTVs, while reducing spurious positional variability. The classification scheme appears feasible for separating types of geometric variability by time trend.

Localization accuracy of the clinical target volume during image-guided radiotherapy of lung cancer

PURPOSE

To evaluate the position and shape of the originally defined clinical target volume (CTV) over the treatment course, and to assess the impact of gross tumor volume (GTV)-based online computed tomography (CT) guidance on CTV localization accuracy.

METHODS AND MATERIALS

Weekly breath-hold CT scans were acquired in 17 patients undergoing radiotherapy. Deformable registration was used to propagate the GTV and CTV from the first weekly CT image to all other weekly CT images. The on-treatment CT scans were registered rigidly to the planning CT scan based on the GTV location to simulate online guidance, and residual error in the CTV centroids and borders was calculated.

RESULTS

The mean GTV after 5 weeks relative to volume at the beginning of treatment was 77% ± 20%, whereas for the prescribed CTV, it was 92% ± 10%. The mean absolute residual error magnitude in the CTV centroid position after a GTV-based localization was 2.9 ± 3.0 mm, and it varied from 0.3 to 20.0 mm over all patients. Residual error of the CTV centroid was associated with GTV regression and anisotropy of regression during treatment (p = 0.02 and p = 0.03, respectively; Spearman rank correlation). A residual error in CTV border position greater than 2 mm was present in 77% of patients and 50% of fractions. Among these fractions, residual error of the CTV borders was 3.5 ± 1.6 mm (left-right), 3.1 ± 0.9 mm (anterior-posterior), and 6.4 ± 7.5 mm (superior-inferior).

CONCLUSIONS

Online guidance based on the visible GTV produces substantial error in CTV localization, particularly for highly regressing tumors. The results of this study will be useful in designing margins for CTV localization or for developing new online CTV localization strategies.

Tumor-volume simulation during radiotherapy for head-and-neck cancer using a four-level cell population model

PURPOSE

To develop a fast computational radiobiologic model for quantitative analysis of tumor volume during fractionated radiotherapy. The tumor-volume model can be useful for optimizing image-guidance protocols and four-dimensional treatment simulations in proton therapy that is highly sensitive to physiologic changes.

METHODS

The analysis is performed using two approximations: (1) tumor volume is a linear function of total cell number and (2) tumor-cell population is separated into four subpopulations: oxygenated viable cells, oxygenated lethally damaged cells, hypoxic viable cells, and hypoxic lethally damaged cells. An exponential decay model is used for disintegration and removal of oxygenated lethally damaged cells from the tumor.

RESULTS

We tested our model on daily volumetric imaging data available for 14 head-and-neck cancer patients treated with an integrated computed tomography/linear accelerator system. A simulation based on the averaged values of radiobiologic parameters was able to describe eight cases during the entire treatment and four cases partially (50% of treatment time) with a maximum 20% error. The largest discrepancies between the model and clinical data were obtained for small tumors, which may be explained by larger errors in the manual tumor volume delineation procedure.

CONCLUSIONS

Our results indicate that the change in gross tumor volume for head-and-neck cancer can be adequately described by a relatively simple radiobiologic model. In future research, we propose to study the variation of model parameters by fitting to clinical data for a cohort of patients with head-and-neck cancer and other tumors. The potential impact of other processes, like concurrent chemotherapy, on tumor volume should be evaluated.