Cell kinetics and repopulation mechanisms during multifraction irradiation of spheroids

Three-Dimensional Cell Culture Systems in Radiopharmaceutical Cancer Research

In preclinical cancer research, three-dimensional (3D) cell culture systems such as multicellular spheroids and organoids are becoming increasingly important. They provide valuable information before studies on animal models begin and, in some cases, are even suitable for reducing or replacing animal experiments. Furthermore, they recapitulate microtumors, metastases, and the tumor microenvironment much better than monolayer culture systems could. Three-dimensional models show higher structural complexity and diverse cell interactions while reflecting (patho)physiological phenomena such as oxygen and nutrient gradients in the course of their growth or development. These interactions and properties are of great importance for understanding the pathophysiological importance of stromal cells and the extracellular matrix for tumor progression, treatment response, or resistance mechanisms of solid tumors. Special emphasis is placed on co-cultivation with tumor-associated cells, which further increases the predictive value of 3D models, e.g., for drug development. The aim of this overview is to shed light on selected 3D models and their advantages and disadvantages, especially from the radiopharmacist's point of view with focus on the suitability of 3D models for the radiopharmacological characterization of novel radiotracers and radiotherapeutics. Special attention is paid to pancreatic ductal adenocarcinoma (PDAC) as a predestined target for the development of new radionuclide-based theranostics.

Mathematical modeling of radiotherapy cancer treatment using Caputo fractional derivative

BACKGROUND

This paper presents a mathematical model that simulates a radiotherapy cancer treatment process. The model takes into consideration two important radiobiological factors, which are repair and repopulation of cells. The model was used to simulate the fractionated treatment process of six patients. The results gave the population changes in the cells and the final volumes of the normal and cancer cells.

METHOD

The model was formulated by integrating the Caputo fractional derivative with the previous cancer treatment model. Thereafter, the linear-quadratic with the repopulation model was coupled into the model to account for the cells' population decay due to radiation. The treatment process was then simulated with numerical variables, numerical parameters, and radiation parameters. The numerical parameters which included the proliferation coefficients of the cells, competition coefficients of the cells, and the perturbation constant of the normal cells were obtained from previous literature. The radiation and numerical parameters were obtained from reported clinical data of six patients treated with radiotherapy. The patients had tumor volumes of 24.1cm³, 17.4cm³, 28.4cm³, 18.8cm³, 30.6cm³, and 12.6cm³ with fractionated doses of 2 Gy for the first two patients and 1.8 Gy for the other four. The initial tumor volumes were used to obtain initial populations of cells after which the treatment process was simulated in MATLAB. Subsequently, a global sensitivity analysis was done to corroborate the model with clinical data. Finally, 96 radiation protocols were simulated by using the biologically effective dose formula. These protocols were used to obtain a regression equation connecting the value of the Caputo fractional derivative with the fractionated dose.

RESULTS

The final tumor volumes, from the results of the simulations, were 3.58cm³, 8.61cm³, 5.68cm³, 4.36cm³, 5.75cm³, and 6.12cm³, while those of the normal cells were 23.87cm³, 17.29cm³, 28.17cm³, 18.68cm³, 30.33cm³, and 12.55cm³. The sensitivity analysis showed that the most sensitive model factors were the value of the Caputo fractional derivative and the proliferation coefficient of the cancer cells. Lastly, the obtained regression equation accounted for 99.14% of the prediction.

CONCLUSION

The model can simulate a cancer treatment process and predict the results of other radiation protocols.

In silico analysis of cell cycle synchronisation effects in radiotherapy of tumour spheroids

Tumour cells show a varying susceptibility to radiation damage as a function of the current cell cycle phase. While this sensitivity is averaged out in an unperturbed tumour due to unsynchronised cell cycle progression, external stimuli such as radiation or drug doses can induce a resynchronisation of the cell cycle and consequently induce a collective development of radiosensitivity in tumours. Although this effect has been regularly described in experiments it is currently not exploited in clinical practice and thus a large potential for optimisation is missed. We present an agent-based model for three-dimensional tumour spheroid growth which has been combined with an irradiation damage and kinetics model. We predict the dynamic response of the overall tumour radiosensitivity to delivered radiation doses and describe corresponding time windows of increased or decreased radiation sensitivity. The degree of cell cycle resynchronisation in response to radiation delivery was identified as a main determinant of the transient periods of low and high radiosensitivity enhancement. A range of selected clinical fractionation schemes is examined and new triggered schedules are tested which aim to maximise the effect of the radiation-induced sensitivity enhancement. We find that the cell cycle resynchronisation can yield a strong increase in therapy effectiveness, if employed correctly. While the individual timing of sensitive periods will depend on the exact cell and radiation types, enhancement is a universal effect which is present in every tumour and accordingly should be the target of experimental investigation. Experimental observables which can be assessed non-invasively and with high spatio-temporal resolution have to be connected to the radiosensitivity enhancement in order to allow for a possible tumour-specific design of highly efficient treatment schedules based on induced cell cycle synchronisation.

The sensitivity of a cell to a dose of radiation is largely affected by its current position within the cell cycle. While under normal circumstances progression through the cell cycle will be asynchronous in a tumour mass, external influences such as chemo- or radiotherapy can induce a synchronisation. Such a common progression of the inner clock of the cancer cells results in the critical dependence on the effectiveness of any drug or radiation dose on a suitable timing for its administration. We analyse the exact evolution of the radiosensitivity of a sample tumour spheroid in a computer model, which enables us to predict time windows of decreased or increased radiosensitivity. Fractionated radiotherapy schedules can be tailored in order to avoid periods of high resistance and exploit the induced radiosensitivity for an increase in therapy efficiency. We show that the cell cycle effects can drastically alter the outcome of fractionated irradiation schedules in a spheroid cell system. By using the correct observables and continuous monitoring, the cell cycle sensitivity effects have the potential to be integrated into treatment planing of the future and thus to be employed for a better outcome in clinical cancer therapies.

Survival and self-renewing capacity of breast cancer initiating cells during fractionated radiation treatment

INTRODUCTION

Recent data indicate a hierarchical organization of many solid cancers, including breast cancer, with a small number of cancer initiating cells (CICs) that have the ability to self-renew and exhibit multi-lineage potency. We, and others, have demonstrated that CICs in breast cancer and glioma are relatively resistant to ionizing radiation if compared to their non-tumorigenic counterparts. However, the extent of the remaining self-renewing capacity of CICs after fractions of radiation is currently unknown. We hypothesized that CICs, in contrast to their non-tumorigenic counterparts, not only survive fractions of ionizing radiation but also retain the CIC phenotype as defined by operational means.

METHODS

We used two marker systems to identify breast CICs (CD24-/low/CD44high, or lack of proteasome activity) and performed sphere-forming assays after multiple clinical fractions of radiation. Lineage tracking was performed by membrane staining. Cell cycle distribution and RNA content were assessed by flow cytometry and senescence was assessed via beta-galactosidase staining.

RESULTS

We demonstrated that irradiated CICs survived and retained their self-renewal capacity for at least four generations. We show that fractionated radiation not only spared CICs but also mobilized them from a quiescent/G0 phase of the cell cycle into actively cycling cells, while the surviving non-tumorigenic cells were driven into senescence.

CONCLUSIONS

The breast CIC population retains increased self-renewal capacity over several generations and therefore, we conclude that increases in the number of CICs after sublethal doses of radiation have potential clinical importance. Prevention of this process may lead to improved clinical outcome.

Investigation of various growth mechanisms of solid tumour growth within the linear-quadratic model for radiotherapy

The standard linear-quadratic survival model for radiotherapy is used to investigate different schedules of radiation treatment planning to study how these may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al (1977 Br. J. Radiol. 50 681), which was concerned with the case of exponential re-growth between treatments. Here we also consider the restricted exponential model. This has been successfully used by Panetta and Adam (1995 Math. Comput. Modelling 22 67) in the case of chemotherapy treatment planning. Treatment schedules investigated include standard fractionation of daily treatments, weekday treatments, accelerated fractionation, optimized uniform schedules and variation of the dosage and alpha/beta ratio, where alpha and beta are radiobiological parameters for the tumour tissue concerned. Parameters for these treatment strategies are extracted from the literature on advanced head and neck cancer, prostate cancer, as well as radiosensitive parameters. Standardized treatment protocols are also considered. Calculations based on the present analysis indicate that even with growth laws scaled to mimic initial growth, such that growth mechanisms are comparable, variation in survival fraction to orders of magnitude emerged. Calculations show that the logistic and exponential models yield similar results in tumour eradication. By comparison the Gompertz model calculations indicate that tumours described by this law result in a significantly poorer prognosis for tumour eradication than either the exponential or logistic models. The present study also shows that the faster the tumour growth rate and the higher the repair capacity of the cell line, the greater the variation in outcome of the survival fraction. Gaps in treatment, planned or unplanned, also accentuate the differences of the survival fraction given alternative growth dynamics.

Modeling and computer simulations of tumor growth and tumor response to radiotherapy

A model of tumor growth and tumor response to radiation is introduced in which each tumor cell is taken into account individually. Each cell is assigned a set of radiobiological parameters, and the status of each cell is checked in discrete intervals. Tumor proliferation is governed by the cell cycle times of tumor cells, the growth fraction, the apoptotic capacity of the tumor, and the degree of tumor angiogenesis. The response of tumor cells to radiation is determined by the radiosensitivities and the oxygenation status. Computer simulation is performed on a 3D rigid cubic lattice, starting out from a single tumor cell. Random processes are simulated by Monte Carlo methods. Short cell cycle time, high growth fraction, and tumor angiogenesis all increase tumor proliferation rates. Accelerated time-dose patterns result in lower total doses needed for tumor control, but the extent of dose reduction depends on the kinetics and the radiosensitivities of tumor cells. Tumor angiogenesis alters fully oxygenated and hypoxic fractions within the tumor and subsequently affects the radiation response. It is demonstrated for selected radiobiological parameters that the simulation tools are suitable to quantitatively assess the total doses needed for tumor control. Using the simulation tools, it is feasible to simulate time-dependent effects during fractionated radiotherapy and to compare different time-dose patterns in terms of their tumor control.

Tumor biology and experimental therapeutics

Recent research using multicellular tumor spheroids has resulted in new insights in the regulation of invasion and metastasis, angiogenesis and cell cycle kinetics. The onset and expansion of central necrosis in tumor spheroids has been characterized to be a complex interaction of several mechanisms; in a number of cases, necrosis is not a consequence of hypoxia or anoxia, but emerges as secondary necrosis following an accumulation of apoptosis in spheroids. Recent therapeutically oriented studies have been directed towards novel hypoxic markers, targeted therapy, multicellular-mediated drug resistance, and heavy ion irradiation of spheroids. Research efforts should be enhanced mainly in the fields of tumor tissue modeling by heterotypic three-dimensional (3D) cultures and of apoptotic versus necrotic cell death. Based on the fundamental differences between monolayer and 3D cultures, spheroids should become mandatory test systems in therapeutic screening programs.

Dynamic optimization of a linear-quadratic model with incomplete repair and volume-dependent sensitivity and repopulation

PURPOSE

The linear-quadratic model typically assumes that tumor sensitivity and repopulation are constant over the time course of radiotherapy. However, evidence suggests that the growth fraction increases and the cell-loss factor decreases as the tumor shrinks. We investigate whether this evolution in tumor geometry, as well as the irregular time intervals between fractions in conventional hyperfractionation schemes, can be exploited by fractionation schedules that employ time-varying fraction sizes.

METHODS

We construct a mathematical model of a spherical tumor with a hypoxic core and a viable rim, which is most appropriate for a prevascular tumor, and is only a caricature of a vascularized tumor. This model is embedded into the traditional linear-quadratic model by assuming instantaneous reoxygenation. Dynamic programming is used to numerically compute the fractionation regimen that maximizes the tumor-control probability (TCP) subject to constraints on the biologically effective dose of the early and late tissues.

RESULTS

In several numerical examples that employ five or 10 fractions per week on a 1-cm or 5-cm diameter tumor, optimally varying the fraction sizes increases the TCP significantly. The optimal regimen incorporates large Friday (afternoon, if 10 fractions per week) fractions that are escalated throughout the course of treatment, and larger afternoon fractions than morning fractions.

CONCLUSION

Numerical results suggest that a significant increase in tumor cure can be achieved by allowing the fraction sizes to vary throughout the course of treatment. Several strategies deserve further investigation: using larger fractions before overnight and weekend breaks, and escalating the dose (particularly on Friday afternoons) throughout the course of treatment.

Changes in tumor oxygen tension during radiotherapy of uterine cervical cancer: relationships to changes in vascular density, cell density, and frequency of mitosis and apoptosis

PURPOSE

Changes in oxygen tension (pO(2)) during the early phase of fractionated radiotherapy were studied in 22 patients with uterine cervical cancer. The aims were to investigate (a) whether possible changes in pO(2) differed among and within tumors and (b) whether the changes could be attributed to changes in vascular density, cell density, and frequency of mitosis and apoptosis.

METHODS AND MATERIALS

The pO(2) was measured polarographically in four regions of the tumors before treatment and after 2 weeks of radiotherapy. The vascular density, cell density, and frequency of mitosis and apoptosis were determined from biopsies taken from the tumor regions after each pO(2) measurement.

RESULTS

The changes in pO(2) during therapy differed among the tumors and were correlated to pO(2) before treatment (p < 0.001). The direction of the changes was consistent throughout the tumors; all regions in tumors with increased oxygenation had increased or no change in pO(2) and vice versa. The tumors with increased pO(2) (n = 10) had a large decrease in cell density and a significant increase in apoptotic frequency. In contrast, the tumors with decreased pO(2) (n = 10) had a smaller decrease in cell density (p = 0.014) and no significant increase in apoptotic frequency. Vascular density and mitotic frequency showed no change during therapy; however, vascular damage other than decreased vascular density was observed.

CONCLUSION

These results indicate that the oxygenation of cervix tumors generally changes during the early phase of radiotherapy. The change depends on the balance between the factor leading to an increase and that leading to a decrease in oxygenation; i.e., decreased cell density and vascular damage, respectively. Increased apoptotic frequency may contribute to a large decrease in cell density and hence increased oxygenation during therapy.

Cell kinetics and repopulation parameters of irradiated xenograft tumours in SCID mice: comparison of two dose-fractionation regimens

The extent and mechanism(s) of repopulation were assessed in SiHa (human cervical squamous cell carcinoma) xenografts in SCID mice for two fractionated irradiation regimens. Mice in one arm of the study received 50 Gy in 20 fractions over 23 days with a 14 day split between 10 fraction, 5 day courses. The other tumours were treated with 50 Gy in 20 fractions over 10 consecutive days. Cell kinetics and tumour regrowth parameters were monitored during and after treatment by measuring tumour volume and analysing cellular DNA content and proliferation parameters with flow cytometry. Repopulation occurred rapidly, beginning during irradiation and largely attributable to an increased growth fraction and decreased potential doubling time, apparently triggered by increased cell loss. Cell cycle time, in contrast, remained relatively constant throughout. Extrapolation of these results to humans suggests that treatment times should be minimised whenever possible, since regrowth rates exceeded those predicted from pretreatment Tpot measurements.

Repopulation characteristics and cell kinetic parameters resulting from multi-fraction irradiation of xenograft tumors in SCID mice

PURPOSE

Cell kinetics and repopulation rates during multifraction irradiation have previously been measured in SiHa human cervical carcinoma cells grown as spheroids. The current study applied similar techniques to SiHa tumor xenografts with the ultimate goal of assessing the clinical prognostic value of in situ cell kinetics.

METHODS AND MATERIALS

SiHa (human squamous cell cervical tumor) cells were inoculated subcutaneously in the flank or back of SCID mice. When tumors reached a size of 200-300 mg, they received 25 Gy in 10 fractions over 5 days. Tumor regrowth and cell kinetics parameters were followed during treatment, and for 10 days after completion by measuring tumor volume and analyzing cellular BrdUrd and IdUrd incorporation with flow cytometry.

RESULTS

Tumor volume was of limited use in assessing response to irradiation. The fraction of proliferating cells increased early during irradiation as did the labeling index; potential doubling time (Tpot) decreased during treatment and returned to the pre-irradiation value after treatment. Cell cycle time remained relatively constant throughout the experiments.

CONCLUSION

These results confirm the feasibility of evaluating cell cycle kinetics and repopulation parameters in a murine tumor model undergoing a fractionated course of irradiation. Repopulation of clonogenic tumor cells occurred more rapidly than predicted by pretreatment measurements, primarily due to an increased growth fraction and consequent decrease in Tpot.

The effect of heterogeneity in tumor cell kinetics on radiation dose-response. An exploratory investigation of a plateau effect

PURPOSE

To investigate the effect of heterogeneity in tumor cell kinetics on radiation dose-response curves for a population of patients.

MATERIALS AND METHODS

A series of exploratory calculations have been performed using an improved geometric-stochastic model of tumor cure.

RESULTS

Radiation therapy dose-response curves may plateau, or nearly so, at tumor control levels well below 100%, if a proportion of tumors would grow sufficiently fast to counterbalance the effect of fractionated radiotherapy. If the model assumptions of doubling time heterogeneity are correct, the difference between a short and protracted radiation regimen would be not only in the position and steepness of the radiation dose-response curve, but also in the level of the predicted plateau.

CONCLUSIONS

For a given rate of dose accumulation, the one-sided flattening in dose-response curves at high doses is predicted from the modeling, and determined by the proportion of most radioresistant and rapidly growing tumors. This shows that empirical models of tumor control probability which assume a symmetric sigmoid relationship from 0 to 100% have apparent limitations, seemingly not well acknowledged in the literature.

The lifetime of hypoxic human tumor cells

PURPOSE

For hypoxic and anoxic cells in solid tumors to be a therapeutic problem, they must live long enough to be therapeutically relevant, or else be rapidly recruited into the proliferating compartment during therapy. We have, therefore, estimated lifetime and recruitment rate of hypoxic human tumor cells in multicell spheroids in vitro, or in xenografted tumors in SCID mice.

MATERIALS AND METHODS

Cell turnover was followed by flow cytometry techniques, using antibodies directed at incorporated halogenated pyrimidines. The disappearance of labeled cells was quantified, and verified to be cell loss rather than label dilution. Repopulation was studied in SiHa tumor xenografts during twice-daily 2.5-Gy radiation exposures.

RESULTS

The longevity of hypoxic human tumor cells in spheroids or xenografts exceeded that of rodent cell lines, and cell turnover was slower in xenografts than under static growth as spheroids. Human tumor cells remained viable in the hypoxic regions of xenografts for 4-10 days, compared to 3-5 days in spheroids, and 1-3 days for most rodent cells in spheroids. Repopulation was observed within the first few radiation treatments for the SiHa xenografts and, with accumulated doses of more than 10 Gy, virtually all recovered cells had progressed through at least one S-phase.

CONCLUSION

Our results suggest an important difference in the ability of human vs. rodent tumor cells to withstand hypoxia, and raise questions concerning the increased longevity seen in vivo relative to the steady-state spheroid system.