# Evaluation of performance of distributed delay model for chemotherapy-induced myelosuppression

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## Abstract

The distributed delay model has been introduced that replaces the transit compartments in the classic model of chemotherapy-induced myelosuppression with a convolution integral. The maturation of granulocyte precursors in the bone marrow is described by the gamma probability density function with the shape parameter (*ν*). If *ν* is a positive integer, the distributed delay model coincides with the classic model with *ν* transit compartments. The purpose of this work was to evaluate performance of the distributed delay model with particular focus on model deterministic identifiability in the presence of the shape parameter. The classic model served as a reference for comparison. Previously published white blood cell (WBC) count data in rats receiving bolus doses of 5-fluorouracil were fitted by both models. The negative two log-likelihood objective function (-2LL) and running times were used as major markers of performance. Local sensitivity analysis was done to evaluate the impact of *ν* on the pharmacodynamics response WBC. The *ν* estimate was 1.46 with 16.1% CV% compared to *ν* = 3 for the classic model. The difference of 6.78 in − 2LL between classic model and the distributed delay model implied that the latter performed significantly better than former according to the log-likelihood ratio test (P = 0.009), although the overall performance was modestly better. The running times were 1 s and 66.2 min, respectively. The long running time of the distributed delay model was attributed to computationally intensive evaluation of the convolution integral. The sensitivity analysis revealed that *ν* strongly influences the WBC response by controlling cell proliferation and elimination of WBCs from the circulation. In conclusion, the distributed delay model was deterministically identifiable from typical cytotoxic data. Its performance was modestly better than the classic model with significantly longer running time.

### Keywords

Transit compartments Convolution integral Integro-differential equations Distributed delay Leukopenia### References

- 1.Friberg LE, Freijs A, Sandstrom M, Karlsson MO (2000) Semiphysiological model for the time course of leukocytes after varying schedules of 5-fluorouracil in rats. J Pharmacol Exp Ther 295:734–740PubMedGoogle Scholar
- 2.Friberg LE, Henningsson A, Maas H, Nguyen L, Karlsson MO (2002) Model of chemotherapy-induced myelosuppression with parameter consistency across drugs. J Clin Oncol 20:4713–4721CrossRefPubMedGoogle Scholar
- 3.Sun YN, Jusko WJ (1998) Transit compartments versus gamma distribution function to model signal transduction processes in pharmacodynamics. J Pharm Sci 87:732–737CrossRefPubMedGoogle Scholar
- 4.Savic RM, Jonker DM, Kerbusch T, Karlsson MO (2007) Implementation of a transit compartment model for describing drug absorption in pharmacokinetic studies. J Pharmacokinet Pharmacodyn 34:711–726CrossRefPubMedGoogle Scholar
- 5.De Suza DC, Craig M, Cassidy T, Li J, Nekka F, Belair J, Humphries AR (2017) Transit and lifespan in neutrophil production: implication for drug intervension. J Pharmacokinet Pharmacodyn. https://doi.org/10.1007/s10928-017-9560-y Google Scholar
- 6.Freise KJ, Widness JA, Schmidt RL, Veng-Pedersen P (2008) Modeling time variant distributions of cellular lifespans: increases in circulating reticulocyte lifespans following double phlebotomies in sheep. J Pharmacokinet Pharmacodyn 35:285–323CrossRefPubMedPubMedCentralGoogle Scholar
- 7.Dunlavey M, Hu S (2017) Use of distributed delay in PML. Page 26 (2017) Abstr 6080. www.page-meeting.org/?abstract=6080
- 8.Siripuram VK, Wright DFB, Barclay ML, Duffull SB (2017) Deterministic identifiability of population pharmacokinetic and pharmacokinetic-pharmacodynamic models. J Pharmacokinet Pharmacodyn 44(5):415–423CrossRefPubMedGoogle Scholar
- 9.Davis PJ (1972) Gamma function and related function. In: Abramowitz M, Stegun IA (eds) Handbook of mathematical functions. Dover Publications, New YorkGoogle Scholar
- 10.Zelen M, Severeo NC (1972) Probability functions. In: Abramowitz M, Stegun IA (eds) Handbook of mathematical functions. Dover Publications, New YorkGoogle Scholar
- 11.Bonate PL (2011) Pharmacokinetic-pharmacodynamic modeling and simulation. Springer, New YorkCrossRefGoogle Scholar
- 12.Smith H (2010) An introduction to delay differential equations with application to the life sciences. Springer, New YorkGoogle Scholar
- 13.Hale JK, Lunel SMV (1998) Introduction to functional differential equations. Springer, New YorkGoogle Scholar