A Theoretical Framework for Quantifying Tumour Resistance to Standardized Treatments: A Novel Rudimentary Scalar Mathematical Model with Implications for Breast Cancer Prognosis and Treatment.

Background: In the complex landscape of cancer treatment challenges, personalized therapeutic strategies have gained significant importance. This study focuses on addressing the limitations of cytotoxic drugs by introducing a novel graphical and scalar model that establishes a connection between tumour biology, treatment modalities, and survival outcomes in breast cancer. The central hypothesis posits that the unique biological characteristics of an individual tumour plays a crucial role in determining the response to therapy and overall survival. Results: The model evaluates past treatments and outcomes, utilizing basic mathematical expressions to link tumour biology, treatment strategies and individualized survival projections. A key element of the model is the patient-specific constant, Kc, which serves as an indicator of an individual's distinct response to treatment. The abstract highlights that a high Kc implies a greater likelihood of benefit from the administered chemotherapy, while a low Kc suggests the opposite. The findings underscore a crucial revelation: the growth dynamics of a tumour, regardless of cell quantity, holds comparable significance in determining outcomes. This is exemplified by associating different tumour scenarios with specific stage classifications and tumour proliferation index [Ki67] scores. In essence, the model reveals a pivotal insight: the growth dynamics of a tumour, whether comprising 50% of 2 billion cells or 1% of 100 billion cells, wield comparable significance in determining the ultimate outcome. This distinction is illustrated by associating the former with stage a stage I tumour featuring a [Ki67] score of 4 and latter with a stage IV tumour exhibiting a [Ki67] of 1. The sensitivity, specificity, AUC of ROC curve are 93.65, 87.5 and 0.82 respectively suggesting the model is fit for purpose. Conclusion: The model reveals that 50% of 2 billion tumour cells and 1% of 100 billion tumour cells in proliferation phase have comparable impacts on outcomes, contingent upon their respective stage and [Ki67] scores. The model emphasizes the critical threshold above or below which the scale tips against or towards better survival.