Integrated Systems and Technologies : Mathematical Oncology Pharmacokinetic Modeling of Tumor Bioluminescence Implicates Efflux , and Not Influx , as the Bigger Hurdle in Cancer Drug Therapy

In vivo bioluminescence imaging is a powerful tool for assessing tumor burden and quantifying therapeutic response in xenograft models. However, this technique exhibits significant variability as a consequence of differences in substrate administration, as well as the tumor size, type, and location. Here, we present a novel pharmacokinetic (PK) approach that utilizes bioluminescence image data. The sample data are taken from mice implanted with a melanoma tumor cell line that was transfected to express the firefly (Photinus pyralis) luciferase gene. At 5, 7, and 10 days postimplant, intraperitoneal injections of D-luciferin were given to monitor the uptake into the tumor, and the tumor volume was measured using ultrasound. A multicompartment PK model was used to simultaneously fit all experiments for each mouse. We observed that the rates of luciferin transport in and out of the tumor exhibited a clear dependence on the tumor volume. Also, the rate of tumor influx increased faster than did the efflux, resulting in a shortening of the time to peak-luciferin concentration as the tumor grows. The time of the peak concentration correlated poorly with the tumor volume, but the peak bioluminescence signal and the area under the curve both exhibited a dependence on the tumor surface area. These results agree with Starling's hypothesis relating the higher interstitial fluid pressure in the tumor with flux across the boundary, and suggest that drug transport may depend more strongly on the surface area of the tumor than its volume. These observations provide a quantitative physical rationale for molecular targeting of therapeutics that enhance trapping and overcome the accelerated efflux kinetics.