PID controllers and cancer care

It's a very interesting time for progress in cancer care. Solid tumor patients can now expect to have their tumors sequenced and compared to normal cells in order to determine which targeted therapies are appropriate for their tumors. However, our ability to predict future behavior of an individual cancer is still quite crude.

A quick primer on the state of the world: Tumorigenesis is usually seen as a direct sequelae of naturally occuring mutagenic conditions in diploid cells that confer a direct evolutionary advantage to the cancer cell relative to its normal neighbors and also promotes growth and replication that displaces or disrupts the ordinary cells, either by resource hogging or by direct physical disruption. It used to be believed that such changes happen in an initial cancer cell (two-hit hypothesis) after which the tumor would grow and develop without undergoing genetic drift, meaning the genotype of the tumor would not undergo clinically meaningful change.

It's now known, of course, that tumors do genetically drift, often in a way that is clinically significant. For instance, EGFR mutant non-small cell lung cancer tumors will, upon treatment with first line EGFR inhibitors like erlotinib, acquire resistance to such treatments, usually with T790M mutations [1]. Researchers have developed new therapies against this latter mutation, but it is clear that cancers continue to drift even beyond this.

Of course, clinicians have an array of different options for attacking tumors in a non-targeted way - for instance, going after the resource co-opting with drugs like bevacizumab, general cytotoxic chemotherapy regimens, and more recently using immune modulating therapies. However, most oncologists recognize that the future of cancer care will be in targeted mechanisms, given that each case, even with similar histology to other tumors, will display unique genetic characteristics that both make its response difficult to assess and the ideal treatment highly nuanced. (Though arguably, immune therapies fall into this category as well.)

Thus drifting cancers don't just represent a unique quirk of these patients, but represent a shift from the static pathology-then-treatment paradigm that more or less accurately describes most other disorders. (Note, I'm speaking a bit loosely, but the point stands...for instance, I would argue that the arterial narrowing one sees in atherosclerosis patients is not a distinct change in pathology but rather an ordinary progression of disease that must be combatted. Thus it is not that the disease is changing that makes cancer different, but that the change is one of kind rather than degree). Indeed, for patients with metastatic disease who eventually relapse, genotyping of the relapsing cells often finds such remarkable changes that there are often arguments about whether "it's the same cancer", as all cancers are usually logged in national registries by their genotypes and mets are usually logged differently.

Given this dynamic nature of tumor proliferation in response to treatment it may be interesting to pursue variant treatment regimens that adjust depending on the state of the cancer. The state of the cancer thus represents the dependent variable in a standard control system [2]:

PID equation

where P, I, and D correspond to proportional, integral, and derivative controlling mechanisms respectively.

The left side of the equation is simply the progression of the cancer. We do not currently have a robust mechanism to measure this at a time interval satisfactory for a real control system, but improvements in detection via circulating tumor DNA [3], and machine learning of real-time images to monitor progression [4] both constitute tangible ways to do this.

Proportional response to tumor progression is, of course, the status quo. Specifically, surgical and non-targeted chemotherapy regimens are often initially scaled in proportion to the size and penetration of the tumor. Targeted therapy is sometimes scaled, but therapeutic dose to fully saturate exposed tumor cells does not vary much.

As with all proportional only control systems, the tendency is for either the therapy to be too little (undershoot) or too much (overshoot). For undershooting, the cancer remains or is not meaningfully reduced; we will discuss the standard solution to this shortly. In the case of overshooting, one version of this is when the therapy side effects and overall morbidity exceed the therapeutic value of the drug (for instance, aggressively treating benign prostate tumors that the patient is more likely to die with, rather than die from). More salient to this essay though, overshooting could also be characterized as a tumor that was attacked via too few mechanisms, and not completely, thus encouraging the overall tumor to genetically drift into resistance to the existing therapy. This type of overshoot is particularly vexing because the targeted therapies initially used will no longer be effective against the tumor. Note, the assertion in this latter case is that there are doses of known targeted therapeutics that will promote adverse selection of tumor cells, and thus the ideal dosage of even targeted therapies is below the maximum tolerable dose. This assertion is not currently widely accepted in the medical community, where the conduction of Phase 1 studies is not conducive to measuring ideal dosage with this in mind.

The standard solution to undershooting is, of course, the integral response, which steps up the dosage / regimen of potential treatments until significant movement in progression is seen. The integral response will prevent the patient from being on chemotherapy for too long, and indeed, the integral response is the one place where physicians seem to be correct in their push to "turn up the heat" if they aren't seeing adequate responsiveness on post-therapeutic imaging. Note also that the main criticism of the integral response - that it continues aggressive correction even after progression appears to be hitting diminishing returns, is also a pretty accepted standard that oncologists regularly push for. You are not going to stop taking chemo until the physician is quite sure nothing else is to be gained, which is usually long after the gains cease.

Last is derivative controlling, which in actual systems is used as a dampening function to prevent precession around the ideal state. It's hard to know what this looks like in cancer care - the closest solution appears to be immune modulating therapy, which indeed scales its response according to both the proportional issue (how much cancer there is) but also by the derivative (whether the cancer is going down efficiently enough to not promote a more aggressive immune response). Certainly we see the precession problem, though physicians usually describe it as "heterogeneity in the primary tumor" - the tumor mutates faster than new treatments can be developed and targeted against it, and the patient dies.

My overall purpose in explaining all of this is to show that oncologists already are using control systems-like logic in dictating therapy regimens against a dynamic, ever-adjusting disease. However, because our current perspective is that cancer is a relatively static disease (as if mutation happens at a single moment, rather than as an ongoing process that is measurable), we are exhibiting gross neglect in not monitoring the state of the system at a higher time interval and not incorporating our understanding of too-aggressive treatment morbidity. Certainly we are far away from the ideal solution, where one would wear a constant monitor of cancer disease state and would adjust cytotoxic, targeted, and immune therapy drugs via a true control system (as we currently do for type 1 diabetics, for instance), but that doesn't mean we should relegate ourselves to the existing crude mechanisms of measurement and response.

Specifically, we should be measuring tumor heterogeneity and propensity for future mutation, as well as plotting tumor-treatment response curves, and taking such measurements into account when deciding how to attack a given cancer. Static-like tumors that are unlikely to exhibit meaningful drift are good candidates for the existing scheme of proportional and integral aggressive regimens, while dynamic tumors should be treated with less targeted therapy than one might expect, in order to retain therapeutic value for the existing regimen, while focusing more on preventing driftability of tumor (possibly through therapies targeting excision repair) and non-targeted chemotherapy. Once tumor is significantly ablated, that would be the time for targeted therapy or immunotherapies to achieve final remission.


[1] Lipinski et al. "Cancer Evolution and the Limits of Predictability in Precision Cancer Medicine" PMC

[2] "PID Controller", Wikipedia

[3] Beije et al. "Somatic mutation detection using various targeted detection assays in paired samples of circulating tumor DNA..." Wiley

[4] Kourou et al. "Machine learning applications in cancer prognosis and prediction" Science Direct