# Predicting Patient Response Dynamics: How Many Measurements are Sufficient?

## Mentor Information

Heiko Enderling (Department on Oncologic Science)

## Description

Tumor growth dynamics can be described by many mathematical models, such as the logistic growth model. This model is governed by the interaction between the tumor growth rate and carrying capacity. Accurately determining optimal values for these parameters may enable us to make predictions individual patient responses. This study investigated the number of measurements (three versus four) necessary to accurately predict the carrying capacity of 18 untreated breast cancer patients. Three measurements corresponded to breast cancer screenings (mammograms) at day 0, 7, and 30, and the additional fourth measurement would occur at day 60. The location of these points along the curve may determine the confidence at which the carrying capacity is predicted. For some patients, three measurements may be sufficient to determine the carrying capacity. By assessing how close the tumor volume at the third measurement is to the inflection point of the logistic growth curve, we may be able to predict whether a fourth measurement is needed to know the carrying capacity. The distance between the inflection point and the volume measurement at a certain time may be dependent upon the growth rate of the cancer. By determining each patient’s growth rate from their initial dynamics, we may be able to recommend optimal personalized screening dates for breast cancer patients to best predict their later carrying capacity.

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Predicting Patient Response Dynamics: How Many Measurements are Sufficient?

Tumor growth dynamics can be described by many mathematical models, such as the logistic growth model. This model is governed by the interaction between the tumor growth rate and carrying capacity. Accurately determining optimal values for these parameters may enable us to make predictions individual patient responses. This study investigated the number of measurements (three versus four) necessary to accurately predict the carrying capacity of 18 untreated breast cancer patients. Three measurements corresponded to breast cancer screenings (mammograms) at day 0, 7, and 30, and the additional fourth measurement would occur at day 60. The location of these points along the curve may determine the confidence at which the carrying capacity is predicted. For some patients, three measurements may be sufficient to determine the carrying capacity. By assessing how close the tumor volume at the third measurement is to the inflection point of the logistic growth curve, we may be able to predict whether a fourth measurement is needed to know the carrying capacity. The distance between the inflection point and the volume measurement at a certain time may be dependent upon the growth rate of the cancer. By determining each patient’s growth rate from their initial dynamics, we may be able to recommend optimal personalized screening dates for breast cancer patients to best predict their later carrying capacity.