Research Article Mathematical Based Calculation of Drug Penetration Depth in Solid Tumors Hamidreza Namazi, 1 Vladimir V. Kulish, 1 Albert Wong, 2 and Sina Nazeri 3 1 School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798 2 Department of Radiotherapy, Oncology and Palliative Care, Sarawak General Hospital, 93586 Kuching, Sarawak, Malaysia 3 Faculty of Cognitive Sciences and Human Development, Universiti Malaysia Sarawak, 94300 Kota Samarahan, Sarawak, Malaysia Correspondence should be addressed to Hamidreza Namazi; hnamazi@ntu.edu.sg Received 27 March 2016; Accepted 17 May 2016 Academic Editor: Osmar Nascimento Silva Copyright © 2016 Hamidreza Namazi et al. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Cancer is a class of diseases characterized by out-of-control cells’ growth which afect cells and make them damaged. Many treatment options for cancer exist. Chemotherapy as an important treatment option is the use of drugs to treat cancer. he anticancer drug travels to the tumor and then difuses in it through capillaries. he difusion of drugs in the solid tumor is limited by penetration depth which is diferent in case of diferent drugs and cancers. he computation of this depth is important as it helps physicians to investigate about treatment of infected tissue. Although many eforts have been made on studying and measuring drug penetration depth, less works have been done on computing this length from a mathematical point of view. In this paper, irst we propose phase lagging model for difusion of drug in the tumor. hen, using this model on one side and considering the classic difusion on the other side, we compute the drug penetration depth in the solid tumor. his computed value of drug penetration depth is corroborated by comparison with the values measured by experiments. 1. Introduction Chemotherapy is an important option for cancer treatment which uses chemical substances (anticancer drug) to ight cancer. Considering application of drug through blood stream, drug travels to the cancer tumor and difuses in it through capillaries as is shown in Figure 1. Drug concentration in the tumor is dependent on drug production (supply, release, and activation), transport (dif- fusion and advection), and elimination (decay, deactivation, and cellular intake) [1]. hese processes involve various bio- chemical, mechanical, and biophysical factors which make the process complex. Mathematical modeling provides a mean to better understand this complexity. Also mathemat- ical modeling allows scientists to link the laboratory exper- iments with clinical applications by providing the means to extrapolate the in vivo results from mouse models to humans. here are valuable attempts in modeling of steps which afect drug concentrations, which have been reported in the literature. We can call the mathematical/computational models addressing drug vascular supply [2–6], drug release and activation [7–13], drug difusive transport [14–24], drug advective transport [5, 25–27], and drug decay, deactivation, and cellular uptake [28–31]. In chemotherapy, it is also important that drug reaches the entire tumor, otherwise its efectiveness will be com- promised [32]. So, in chemotherapy, a minimum efective concentration is required in all parts of the tumor for the efective treatment. One of the factors that come to account in discussion about drug concentration is drug penetration depth in the tumor. Penetration depth can be deined as the depth from a capillary at which the minimum concentration (required for cancer treatment) is achieved. hus, studying and measuring the drug penetration depth in solid tumor are important issues in chemotherapy. Beside numerous experimental studies which have been done on measuring the drug penetration depth in solid tumors [33–37], limited works on mathematical modeling Hindawi Publishing Corporation BioMed Research International Volume 2016, Article ID 8437247, 8 pages http://dx.doi.org/10.1155/2016/8437247