Tumor Growth Kinetic Modeling

This is an excerpt from our white paper, “Tumor Growth Kinetic Modeling.” To access the full white paper, click here.

UNDERSTANDING TUMOR GROWTH KINETICS

Estimating the changes in tumor burden that an individual or cohort of patients experience during treatment can provide important insights into the effectiveness of therapy. At the most fundamental level, the tumor burden present at any point in time will reflect the interplay between tumor growth and death. When tumor death (tumor decay) exceeds tumor growth, then the tumor burden will decline over time. In contrast, when tumor growth exceeds tumor decay, then the tumor burden will increase. The determination of tumor burden is typically estimated on radiologic studies by assessing the size (or volume) of selected tumors at baseline and on follow-up imaging studies, usually on CT or MRI. Alternatively, measuring the concentration of blood or tissue tumor markers (e.g., CA19-9 or PSA) as a surrogate of tumor burden can be used. Regardless of the method used to measure tumor burden, tumor growth kinetics (TGK) can provide an estimate of the rate of tumor burden change, leading to a better understanding of anti-tumor activity. Several mathematical models have been suggested to measure the rate of tumor burden change over time. At Imaging Endpoints, we use an exponential tumor growth kinetic model to calculate the rate of change, based upon the theory that solid tumors demonstrate exponential changes in volume. Using this principle as our foundation, the rate of change in tumor burden can be described by the following equation—which accounts for a large majority of observed longitudinal changes in tumor volume:

Where:

• t represents the time on treatment days.
• f(t) represents the patient’s total tumor burden relative to their starting tumor burden at time t.
• d is a constant representing tumor decay.
• g is a constant representing tumor growth.

In most situations, the data from measured tumor burden can be fitted into Equation 1 which reflects the balance between tumor growth and decay.

However, when a treatment results in the complete cessation of tumor growth (g = 0), then Equation 1 is reduced to:

with d being an exponential measurement of tumor decay.

In contrast, when a treatment has no impact on tumor death (d=0), then Equation 1 can be simplified to:

with g being an exponential measurement of tumor growth.

When determining g and d, a best-fit approach of the data is performed through a curve-fitting exercise whereby constants g and d are optimized to account for the observed change in tumor burden. Using this approach, a high percentage of tumor burden changes can be explained either by pure growth, pure decay, or mixed growth-decay.