On systems and control approaches to therapeutic gain

Abstract

Background: Mathematical models of cancer relevant processes are being developed at an increasing rate. Conceptual frameworks are needed to support new treatment designs based on such models.

Methods: A modern control perspective is used to formulate two therapeutic gain strategies.

Results: Two conceptually distinct therapeutic gain strategies are provided. The first is direct in that its goal is to kill cancer cells more so than normal cells, the second is indirect in that its goal is to achieve implicit therapeutic gains by transferring states of cancer cells of non-curable cases to a target state defined by the cancer cells of curable cases. The direct strategy requires models that connect anti-cancer agents to an endpoint that is modulated by the cause of the cancer and that correlates with cell death. It is an abstraction of a strategy for treating mismatch repair (MMR) deficient cancers with iodinated uridine (IUdR); IU-DNA correlates with radiation induced cell killing and MMR modulates the relationship between IUdR and IU-DNA because loss of MMR decreases the removal of IU from the DNA. The second strategy is indirect. It assumes that non-curable patient outcomes will improve if the states of their malignant cells are first transferred toward a state that is similar to that of a curable patient. This strategy is difficult to employ because it requires a model that relates drugs to determinants of differences in patient survival times. It is an abstraction of a strategy for treating BCR-ABL pro-B cell childhood leukemia patients using curable cases as the guides.

Conclusion: Cancer therapeutic gain problem formulations define the purpose, and thus the scope, of cancer process modeling. Their abstractions facilitate considerations of alternative treatment strategies and support syntheses of learning experiences across different cancers.

Figure 1

Treatment design via two interacting cycles, one in which models are developed iteratively through predictions followed by experimental validations, and a second in which control systems are developed iteratively through comparisons of new design performances in controller-model combined simulations. As these cycles evolve, the current best control law will be the current best proposal for a state feedback based clinical trial. The trials will be individualized via polymorphism-based model parameter perturbations and differences in initial states.

Figure 2

IUdR treatment of MMR defective cancers.

Figure 3

Model-based approaches to therapeutic gain. The direct approach (A) requires a model which includes the anti-cancer agents, the cause of the cancer, and an endpoint which correlates with the probability of cell death. The indirect approach (B) requires that the cancer be separable into poor and good prognosis groups and that the model includes the anti-cancer input agents and a critical determinant of treatment failure.

Figure 4

Folate model [3] DNPS vs. DNTS flux predictions based on the gene expression data of Yeoh et al [36] (see Methods and [18]). Shown are TEL-AML1 patients who had either a hematological relapse (HR) (green T), a continuous complete remission (CCR) (blue t), or other outcome (gray t), and BCR-ABL patients who had either a HR (red b), CCR (green B), or a censored, missing, or other outcome (jointly, gray b).

Figure 5

MAS5 U95av2 probeset summaries for ABL expression [36]. Symbols are as in Fig. 4. P values were obtained using the Rank Sum Test for differences between leukemias.