Quantitative mathematical modeling of clinical brain metastasis dynamics in non-small cell lung cancer

Abstract

Brain metastases (BMs) are associated with poor prognosis in non-small cell lung cancer (NSCLC), but are only visible when large enough. Therapeutic decisions such as whole brain radiation therapy would benefit from patient-specific predictions of radiologically undetectable BMs. Here, we propose a mathematical modeling approach and use it to analyze clinical data of BM from NSCLC. Primary tumor growth was best described by a gompertzian model for the pre-diagnosis history, followed by a tumor growth inhibition model during treatment. Growth parameters were estimated only from the size at diagnosis and histology, but predicted plausible individual estimates of the tumor age (2.1–5.3 years). Multiple metastatic models were further assessed from fitting either literature data of BM probability (n = 183 patients) or longitudinal measurements of visible BMs in two patients. Among the tested models, the one featuring dormancy was best able to describe the data. It predicted latency phases of 4.4–5.7 months and onset of BMs 14–19 months before diagnosis. This quantitative model paves the way for a computational tool of potential help during therapeutic management.

Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors

“…Indeed, an older tumor has a greater probability of having already spread than a younger one. Altogether, the present findings could contribute to the development of personalized computational models of metastasis [24,64,65].…”

Metastasis Initiation Precedes Detection of Primary Cancer—Analysis of Metastasis Growth in vivo in a Colorectal Cancer Test Case

“…Formerly published works (Benzekry et al, 2014 ; Bilous et al, 2019 ; Vaghi et al, 2020 ) suggest that the Gompertzian model describes best the metastatic growth, and that considering Gompertzian growth instead of exponential may change extrapolation results, as the curves differ greatly at early times. However, in our case, the Gompertzian models for metastases #1–3 degenerate into exponent, which means that our data is given in an early period of time in the metastatic process when metastasis sizes had not reached their capacity.…”

“…Since such clinical data of untreated metastasis growth is not common, robust conclusions on the metastatic growth pattern are difficult to achieve. An example of a way to deal with this challenge is a population model approach, which was used lately by Benzekry et al to analyze clinical data from brain metastases in NSCLC (Bilous et al, 2019 ). Their model, comprising of metastasis dissemination and size distribution as a function of primary tumor size, suggests the Gompertzian growth law as most suitable to the data.…”

Population Modeling of Tumor Growth Curves, the Reduced Gompertz Model and Prediction of the Age of a Tumor

“…Nevertheless, the encouraging results obtained here could allow to give approximate estimates. Such predictions could be informative in clinical practice to determine the extent of invisible metastatics at the time of diagnosis, by refining published methods [5].…”