How Mathematical Modeling Could Contribute to the Quantification of Metastatic Tumor Burden Under Therapy: Insights in Immunotherapeutic Treatment of Non-Small Cell Lung Cancer

Abstract

Background: Cancer is one of the leading death causes globally with about 8.2 million deaths per year and an increase in numbers in recent years. About 90% of cancer deaths do not occur due to primary tumors but due to metastases, of which most are not clinically identifiable because of their relatively small size at primary diagnosis and limited technical possibilities. However, therapeutic decisions are formed depending on the existence of metastases and their properties. Therefore non-identified metastases might have huge influence in the treatment outcome. The quantification of clinically visible and invisible metastases is important for the choice of an optimal treatment of the individual patient as it could clarify the burden of non identifiable tumors as well as the future behavior of the cancerous disease. Results: The mathematical model presented in this study gives insights in how this could be achieved, taking into account different treatment possibilities and therefore being able to compare therapy schedules for individual patients with different clinical parameters. The framework was tested on three patients with non-small cell lung cancer, one of the deadliest types of cancer worldwide, and clinical history including platinum-based chemotherapy and PD-L1-targeted immunotherapy. Results yield promising insights into the framework to establish methods to quantify effects of different therapy methods and prognostic features for individual patients already at stage of primary diagnosis.

Mechanistic modeling of brain metastases in NSCLC provides computational markers for personalized prediction of outcome

“…The doubling time 𝜏 𝑃 (𝑠) of a primary tumor of size 𝑆 𝑃 (𝑇 𝑑 ) at time of diagnosis 0 ≤ 𝑇 𝑑 ≤ 𝑇 𝑆 , i.e. the time a tumor of size 𝑠 needs to grow to a size of 2𝑠, is implicitly given by 51 𝜏 𝑃 (𝑠) = − 1 𝛽 𝑃 ln ( 𝛽 𝑃 ln(2𝑆 𝑃 ) − 𝛼 𝑃 𝛽 𝑃 ln(𝑆 𝑃 ) − 𝛼 𝑃 )…”

“…T S , i.e. the time a tumor of size s needs to grow to a size of 2 s , is implicitly given by 51 and from exp ( α P / β P ) = 10 12 we determined the parameters α P and β P from the primary tumor histology and the primary tumor size at diagnosis. Since on the other hand exp ( α / β ) = 10 12 for the metastases’ dynamics, the parameter β was determined from the value of parameter α , which in turn was a fitted parameter (cf.…”

“…The latter is often successfully described using the Gompertz model [47][48][49] . For metastatic spread, we have developed models based on pioneering work by Iwata et al 45,46,50,51 . Our team further developed these mathematical constructs to be applicable in the clinic, for example on breast 52 or kidney 53 cancer.…”