(182o) Optimization in Cancer Therapeutics: Model Integration for Tumor Dynamics and Myelosuppression to Predict Chemotherapy Dosing Profiles

Optimization in Cancer Therapeutics: Model
Integration for Tumor Dynamics and Myelosuppression to Predict Chemotherapy
Dosing Profiles

Ian
C. Dunn¹, and Kirti M. Yenkie^1,*

¹Department of Chemical Engineering, Henry M. Rowan College of
Engineering,

Rowan University, NJ - 08028, USA

(Tel: 856-256-5375; e-mail: yenkie@rowan.edu)

Abstract

In
2016, cancer was reported to be the second most common cause of death in the
United States and according to 2017 projections, there will be around 1.7
million new cancer diagnoses and 700 thousand cancer deaths [1]. Fig. 1 shows the
estimate by National Cancer Institute’s (NCI) Surveillance, Epidemiology, and
End Results (SEER) program, and by the Centers for Disease Control and
Prevention’s (CDC) National Program of Cancer Registries (NPCR) on the incidence
of new cancer cases for 2018 in the United States.

Fig. 1.
Estimated new cancer cases for 2018 in the United States, categorized by gender
and cancer incidence sites [2].

By
analyzing these reported numbers, it can be inferred that the occurrence of a
lumped cancerous mass, as observed in prostrate, breast, colon, bladder,
kidney, etc., is quite high and deserves attention. In such cancers, the tumors
grow much faster as compared to normal cells and spread to other parts of the
body. However, tumor growth can be controlled as well as the undesired cells
can be killed using Chemotherapy, the most established and widely used
anti-cancer treatment [3]. However, the medicines
and drugs involved also affect the healthy cells which decrease patient
immunity and lead to multiple side-effects.

One of the major side-effects of chemotherapeutic
drugs is myelosuppression [4],
[5], a condition when the bone marrow activity is decreased, resulting in fewer
red blood cells, white blood cells, and platelets. The WBCs, also known as
leukocytes, are responsible for protecting the body against infectious disease
and foreign invaders. The immunity of a person depends on their blood count,
which should be maintained within a certain threshold, thus rendering them as a
dose-limiting factor during treatment. Additionally, it is not impractical to
measure a patient’s WBC concentration during the course of treatment. Effective
chemotherapy treatment must simultaneously balance treatment efficacy and
toxicity to the patient; herein lies an optimization problem that may be
addressed with optimal control theory [6],
[7].

In phase-I, a simplified model to simulate
tumor growth dynamics and white blood cell concentrations during chemotherapy
was developed.  Parameter estimation was conducted using tumor growth data from
literature [8].
This model was evaluated via the methods of maximum-principle and discretized
non-linear programming (NLP) to obtain an optimal drug-concentration profile
that minimized the tumor volume while keeping the white blood cell
concentration above a certain threshold [9].

Fig. 2. Combined model
showing two compartments C1 (blood plasma) and C2 (tumor) [adpated from 8]. Leukocytes are present in C1 and their structured model is
shown below with five compartments: proliferative cells (Prol), three transit
compartments (T1, T2, and T3), and circulating blood cells (Circ) [adpated from 10].

In phase II of this work, this tumor
dynamics model was expanded to include pharmacokinetic compartment models to simulate
the concentration of the anticancer agent in different parts of the body.
Additionally, a more complex model of myelosuppression (leukocyte dynamics in
the blood plasma (C1) compartment) with demonstrated accuracy [10]
was integrated with the existing model to quantitate hematological toxicities
induced by the anticancer agent (see Fig. 2). This combined model was evaluated
via maximum principle and discretized NLP methods to gain insights into optimal
dosage regimens for several anticancer agents (e.g. CPT-11 for the treatment of
colon cancer).

This model consists of drug-specific and
patient-specific parameters. A drug-specific parameter accounts for the
efficacy of the drug. A patient-specific parameter accounts for how quickly the
drug is eliminated from the body. In theory, the modeling and optimization
strategy developed in this work will not only be robust enough to be applied to
multiple types of chemotherapies but also capable of being personalized for the
individual patient. This work will contribute to the design of reliable,
personalized tools to optimize chemotherapy treatment and improve patient
outcomes.

Keywords: Model formulation, Myelosuppression, Chemotherapy,
Pharmacokinetics, Personalized Medicine, Optimal control

References:

[1]     A. B. Ryerson et al., Cancer,
vol. 122, no. 9, pp. 1312–1337, May 2016.

[2]     R.
L. Siegel, K. D. Miller, and A. Jemal, CA: A Cancer Journal for Clinicians,
vol. 66, no. 1, pp. 7–30, Jan. 2016.

[3]     M.
Engelhart, D. Lebiedz, and S. Sager, Mathematical Biosciences, vol. 229,
no. 1, pp. 123–134, Jan. 2011.

[4]     S.
Nanda, H. Moore, and S. Lenhart, Mathematical Biosciences, vol. 210, no.
1, pp. 143–156, Nov. 2007.

[5]     A.
L. Quartino, L. E. Friberg, and M. O. Karlsson, Invest New Drugs, vol.
30, no. 2, pp. 833–845, Apr. 2012.

[6]     F.
S. Lobato, V. S. Machado, and V. Steffen, Computer Methods and Programs in Biomedicine,
vol. 131, pp. 51–61, Jul. 2016.

[7]     K.
M. Yenkie and U. Diwekar, Journal of theoretical biology, vol. 355, pp.
219–228, 2014.

[8]     M.
M. Hadjiandreou and G. D. Mitsis, IEEE Transactions on Biomedical
Engineering, vol. 61, no. 2, pp. 415–425, Feb. 2014.

[9]     K.
M. Yenkie and U. M. Diwekar, Computers & Chemical Engineering, vol.
71, pp. 708–714, 2014.

[10]   L. E.
Friberg, A. Henningsson, H. Maas, L. Nguyen, and M. O. Karlsson, J. Clin.
Oncol., vol. 20, no. 24, pp. 4713–4721, Dec. 2002.