Math, magnets, and medicine: enabling personalized oncology

Towards personalized medicine

While the past decade has seen the development of a myriad of targeted therapeutics, immunotherapies, and radiotherapy technologies, coordinated optimized delivery of novel and existing therapeutic regimens personalized to individual patients remains an aspiration. Current, standard-of-care treatment regimens are guided by the result of large clinical trials that evaluate the efficacy of interventions in cohorts of highly selected patient populations. Undoubtedly, clinical trial data have limited ability to predict an individual patient’s response. As exhaustive investigations of all possible combinations of therapeutic regimens across all possible patient cohorts is impossible to pursue using current clinical trial approaches, alternative strategies to identify suitable regimens that optimize outcomes for the individual are essential. Personalized therapeutic regimens may be generated using an in silico surrogate of the patient’s tumor, or digital twin, enabling systematic evaluations of all practical regimens [1]. To achieve this goal, we need both a practical theory of the biophysical processes detailing tumor response to therapy and a means to inform the biophysical theory with the characteristics of an individual patient’s tumor. The recent convergence of biophysical modeling and medical imaging technologies has resulted in personalized forecasting methods capable of predicting response to therapy that we postulate may yet deliver systematic, personalized evaluations of therapeutic regimens.

Math

To personalize therapeutic regimens, the approach needs to be grounded in a biophysical theory describing the mechanisms of cancer progression and interaction with therapies. Without theory, we are left with trial and error. High-consequence decisions, like those made in oncology, must be based on clear descriptions of biophysical processes and not simply “black box” data analytics to provide a robust rationale for treatment efficacy so that as further data becomes available, it can be integrated in order to iterate on our optimization of personalized therapeutic plans. To accurately forecast therapeutic response on a personalized basis, we require a mathematical theory connecting the unique biology of a patient’s tumor with the biophysical mechanisms of specific treatments. Mathematical oncology is an emerging field that investigates these fundamental biophysical mechanisms within a mathematical framework [2]. The Hallmarks of Cancer [3] provide a starting point for identifying the fundamental components to develop a reliable theory for tumor forecasting. However, we must also consider whether the ultimate clinical quantities of interest can be both calculated via simulations and measured at the spatial-temporal scale required to accurately initialize and constrain the model. While cancer is inherently a multi-scale and complex disease, a complete theory from the intracellular level to tissue level may not be needed to reliably forecast response in terms of the target clinical quantities of interest. Therefore, we must also determine what are the key components that, if absent, would fundamentally weaken forecasting accuracy. For instance, within the setting of predicting the response of breast cancer to neoadjuvant therapy, we have methodically evolved our forecasting framework from a reduced model of tumor cell proliferation and death [4] to more comprehensive models detailing cell mobility [5], influence of tissue mechanics [5], drug delivery [6], and receptor status [7]. The model evolution has been driven by the integration of further biophysical mechanisms constrained by additional patient measurements to address the inadequacies of previous models. Without the requisite patient data, biophysical theories of tumor growth and treatment response are useful but have limited utility for studying and optimizing therapeutic regimens. Therefore, theory must be united with data; but without patient-specific data, we are left with population-based metrics and, therefore, a population-based forecast.

Magnets

Anatomical imaging modalities are primarily used clinically for screening, diagnosis and staging, guiding cancer treatments, monitoring for recurrence, and evaluating treatment efficacy. Thus, these imaging data are essential to guide the current decision-making in oncological patient care. However, tumor size and location are fundamentally insufficient to effectively inform therapeutic decisions on how a particular treatment regimen will interact with a patient’s unique tumor biology. Cancer is a spatially and temporally evolving disease, which leads to local physiological variations in cellularity, vascularity, and oxygenation that ultimately influence response to systemic and localized therapies [8,9]. Therefore, to guide future decision-making in oncology, we need biologically-sensitive imaging techniques that can capture both tumor geometry and its dynamic physiology [10]. Magnetic resonance imaging (MRI) technologies such as diffusion-weighted (DW-) MRI and dynamic contrast-enhanced (DCE-) MRI can provide time-resolved snapshots of the 3D state of a patient’s tumor biology, which is otherwise overlooked using standard anatomical imaging techniques [10]. In particular, DW-MRI and DCE-MRI respectively report tumor cellularity and vasculature function, but they are also directly correlated with tumor response to therapy [10]. Additionally, the combination of positron emission tomography with appropriate radiotracers can map receptor status, hypoxia, and glucose metabolism in the patient’s tumor [11]. Therefore, these biologically-sensitive imaging techniques are excellent candidates to integrate with biophysical theory to personalize forecasts of therapeutic response via computer simulations of mathematical models. We and others have been investigating these image-driven computational forecasting frameworks [2,12]. Imaging enables repeated observations and measurements of a patient’s tumor non-invasively, which are fundamental to initializing and calibrating patient-specific biophysical model parameters of tumor growth and treatment response. Image-driven mathematical modeling has shown encouraging results for predicting therapeutic outcome across various disease and treatments [12]. With this convergence of imaging, mathematical, and computational sciences, we are now well positioned to not only begin validating forecasts of response to standard-of-care regimens, but also to begin strategizing how to mathematically identify possible alternative, personalized regimens that might increase treatment efficacy for each individual patient [13].

Medicine

If successful, what will oncological care look like in a decade from now? Let us consider a case where a woman notices an unusual lump during a routine breast self-exam. Her primary care physician recommends a diagnostic mammogram and/or ultrasound, where this evaluation indicates a high probability of malignancy in the affected breast. This is followed by MR-guided targeted biopsies of the different imaging unique subregions of this lump for definitive diagnosis and tumor subtyping and imaging-based mapping of the tumor characteristics, which facilitates an initial selection of potential treatment approaches. These patient-specific data along with the acquisition of imaging data can be united with the biophysical theory to define a digital twin for the patient’s tumor [1]. This biophysical model features a group of model parameters describing tumor cell proliferation, death, and invasion that are fundamentally linked to the patient’s unique tumor physiology. The combination of biologically-sensitive imaging data and other relevant clinical information allows estimating these parameter values on a patient-specific basis. Additionally, a second group of model parameters accounts for the potential treatments that the patient may receive—for example, the dosage, timing, and efficacy of neoadjuvant or radiation therapy. Using the tumor’s digital twin parameterized with patient-specific data and further accounting for a range of possible treatment plans, we can forecast not only the response to the standard-of-care therapy, but also any clinically-relevant candidate treatment. By leveraging high-performance computing, we can simultaneously simulate multiple hypothetical regimens for this in silico tumor, and hence identify the most effective therapy for the individual patient. More specifically, this approach may be able to identify patients with more aggressive tumors (and aggressive early-onset cancers) that may benefit from personalized therapeutic regimens. Recent modeling studies into forecasting response to chemotherapy and radiotherapy regimens are providing the foundations towards the ultimate goal of personalized therapeutic regimens [2,13,14].

In the setting of neoadjuvant therapy for breast cancer, there are various standard combinations of targeted and chemotherapy agents, for which the order and timing of their delivery may impact overall regimen efficacy. A personalized in silico tumor surrogate could be used to investigate the optimal dosage and ordering of these agents for individual patients to maximize the synergistic effects of the combined regimen. A recent study [13] investigated how image-based biophysical modeling could potentially be used to identify patient-specific therapeutic regimens by accounting for each patient’s tumor physiology to quantify the intratumoral distribution and retention of drugs.

The delivery of radiotherapy is already heavily guided by anatomical medical imaging and computer-optimized dose treatment maps. With the advent of highly conformal radiotherapy and image-guided systems, radiotherapy treatment plans are already being adapted daily to account for shift in tumor location and size, thereby ensuring that the prescribed radiation plan is actually delivered to the tumor. An in silico surrogate [14,15] could evolve these adapted plans beyond responding to just changes in tumor geometry, by further individualizing the radiation dose and schedule according to patient-specific forecasts of response and toxicity.

The mechanism-based modeling approaches discussed here rely primarily on tissue-scale tumor measurements; however, there is an abundance of other factors ranging from patient lifestyle, history, molecular pathologies, genetics, and environment that also influence outcomes. Currently, many of these factors are implicitly captured through the personalization of model parameters (e.g., proliferation rates, sensitivity to treatment). However, to explicitly incorporate a broader range of factors we need to also develop the mathematical theory relating the biophysical processes at, for example, the genetic or molecular level to patient outcomes. These are promising areas for further investigation.

Summary

The past decade has witnessed incredible advances in our collective knowledge of cancer and therapeutic options, yet for many cancers, patient outcomes have not experienced parallel improvements. Progress towards truly personalized therapeutic regimens has been fundamentally limited by the impossibility to evaluate all candidate regimens through the current clinical trial paradigm. The development of a practical theory of cancer united with precise patient-specific data, such as those acquired via biologically-sensitive imaging techniques, may fundamentally shift how the efficacy of therapeutic regimens are evaluated for individual patients. The burden of cancer, along with recent scientific and technological advances in imaging science, provide both the incentive and the capacity for developing computational tumor prediction methods to enable personalized therapeutic regimens in the 21^st century.