Modeling of radiation therapy and radiosensitizing agents in tumor xenografts
Poster (konferens), 2018

III-36 Tim Cardilin Modeling of radiation therapy and radiosensitizing agents in tumor xenografts

Tim Cardilin (1,2), Joachim Almquist (1), Mats Jirstrand (1), Astrid Zimmermann (3), Floriane Lignet (4), Samer El Bawab (4), and Johan Gabrielsson (5)

(1) Fraunhofer-Chalmers Centre, Gothenburg, Sweden, (2) Department of Mathematical Sciences, Chalmers University of Technology and Gothenburg University, Gothenburg, Sweden, (3) Merck, Translational Innovation Platform Oncology, Darmstadt, Germany, (4) Merck, Global Early Development - Quantitative Pharmacology, Darmstadt, Germany, (5) Division of Pharmacology and Toxicology, Department of Biomedical Sciences and Veterinary Public Health, Swedish University of Agricultural Sciences, Uppsala, Sweden

Objectives: To conceptually and mathematically describe the treatment effects of radiation and radiosensitizing agents on tumor volume in xenografts with respect to short- and long-term effects.

Methods: Data were generated in FaDu xenograft mouse models, where animals were treated with radiation given either as monotherapy (2 Gy per dose) or together with an early-discovery radiosensitizing agent (25 or 100 mg/kg per dose) that interferes with the repair of the DNA damage induced by irradiation. Animals received treatment following a clinically-relevant administration schedule with doses five days a week for six weeks. Tumor diameters were measured by caliper twice a week for up to 140 days. A pharmacodynamic tumor model was adapted from a previously-published model [1,2]. The improved model captures both short- and long-term treatment effects including tumor eradication and tumor regrowth. Short-term radiation effects are described by allowing lethally irradiated cells up to one more cell division before apoptosis. Long-term radiation effects are described by an irreversible decrease in tumor growth rate. The radiosensitizing agent was assumed to stimulate both processes. The model also includes a natural death rate of cancer cells. The model was calibrated to the xenograft data using a mixed-effects approach based on the FOCE method that was implemented in Mathematica [3]. Between-subject variability was accounted for in initial tumor volume, as well as in the short- and long-term radiation effects.

Results: Data across all treatment groups were well-described by the model. All model parameters were estimated with acceptable precision and biologically reasonable values. Vehicle growth was approximately exponential during the observed time period with an estimated tumor doubling time of approximately 5 days. Tumor growth following radiation therapy resulted in significant tumor regression followed by either tumor eradication (2 animals) or slow regrowth (7 animals). The short- and long-term effects incorporated into the tumor model were able to account for both of these scenarios. A simple analysis shows that if the tumor growth rate is decreased below the natural death rate, the tumor will be eradicated. Otherwise, the tumor will regrow but at a slower rate compared to pre-treatment. The model predicts that each fraction of radiation (2 Gy) results in lethal damage in 15 % of viable cells, and that a total dose above 120 Gy will eradicate the tumor. Tumor growth following combination therapy with a lower dose (25 mg/kg) resulted in more cases of tumor eradication (6 animals) and fewer cases of regrowth (3 animals), whereas combination therapy with the higher dose (100 mg/kg) resulted in tumor eradication in all 9 animals. When radiation therapy was complemented by radiosensitizing treatment (100 mg/kg per dose), each fraction of 2 Gy was estimated to kill 25 % of viable cells, and the total radiation dose required for tumor eradication was decreased by a factor four to 30 Gy.

Conclusions: A tumor model has been developed to describe the treatment effects of radiation therapy, as well as combination therapies involving radiation, in tumor xenografts. The model distinguishes between short- and long-term effects of radiation treatment and can describe different tumor dynamics, including tumor eradication and tumor regrowth at different rates. The novel tumor model can be used to predict treatment outcomes for a broad range of treatments including radiation therapy and combination therapies with different radiosensitizing agents.

[1] Cardilin T, Almquist J, Jirstrand M, Zimmermann A, El Bawab S, Gabrielsson J. Model-based evaluation of radiation and radiosensitizing agents in oncology. CPT: Pharmacometrics & Syst. Pharmacol. (2017).
[2] Cardilin T, Zimmermann A, Jirstrand M, Almquist J, El Bawab S, Gabrielsson J. Extending the Tumor Static Concentration Curve to average doses – a combination therapy example using radiation therapy. PAGE 25 (2016) Abstr 5975 [].
[3] Almquist J, Leander J, Jirstrand M. Using sensitivity equations for computing gradients of the FOCE and FOCEI approximations to the population likelihood. J Pharmacokinet Pharmacodyn (2015) 42: 191-209.

Combination Therapy


PKPD modeling

Radiation Therapy


Tim Cardilin

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Joachim Almquist


Mats Jirstrand

Stiftelsen Fraunhofer-Chalmers Centrum för Industrimatematik

Astrid Zimmermann

Merck KGaA

Floriane Lignet

Merck KGaA

Samer El Bawab

Merck KGaA

Johan Gabrielsson

Sveriges lantbruksuniversitet (SLU)

Proceedings of the 27th Annual meeting of the Population Approach Group in Europe, PAGE2018
Montreux, Switzerland,


Farmaceutisk vetenskap

Radiologi och bildbehandling

Cancer och onkologi


Livsvetenskaper och teknik