2370 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 56, NO. 10, OCTOBER 2009 Diffusion–Drift Modeling of a Growing Breast Cancerous Cell Ahmed M. Hassan ∗ , Student Member, IEEE, and Magda El-Shenawee, Senior Member, IEEE Abstract—This paper presents a 2-D model to calculate the elec- tric current densities and the biopotential differences generated due to a breast cancerous cell during the hyperpolarization of the G1/synthesis (G1/S) transition. The proposed model is based on semiconductor diffusion–drift analysis, and aims to understand the biophysics associated with growing breast cancerous cells. The effect of the duration of the G1/S transition, and the diffusivity and the mobility of the cancerous cell boundary is investigated. The results show that shorter G1/S transition durations, and higher diffusivity and mobility at the cell boundary provide higher mag- nitude of the electric signals. Index Terms—Bioelectric phenomena, biological cells, bio- physics, cancer, MCF-7 cells. I. INTRODUCTION T HE COMPLEXITY of breast cancer detection has fueled extensive research in finding new detection modalities ca- pable of discovering and treating breast tumors at early stages. Passive detection of breast cancer takes advantage of electro- magnetic signals naturally produced by growing tumors, which has recently received increasing attention [1]–[7]. There are two main modalities for the passive electromagnetic detection of breast cancer: 1) biomagnetic [1]–[3] and 2) biopotential [4]–[7] detection. In passive biomagnetic detection of breast cancer, the magnetic field produced due to growing breast tumors was recorded using highly sensitive magnetometers termed super conducting quantum interference devices (SQUIDs) [1]–[3]. In passive biopotential diagnosis of breast cancer, two electrodes are employed: one electrode is placed on top of the breast le- sions, and the second on a different part of the patient. Sensing natural electromagnetic signals could indicate to tumor activ- ity, in the sense that, the more malignant the tumor grows, the higher the produced electromagnetic signals [1]–[7]. Passive biomagnetic and biopotential techniques are noninvasive with no exposure to any type of radiation. The concept of biopotential and biomagnetic detection from adult brains as well as fetal brains where the signals are much weaker is well established [8], [9]. In this paper, we are trying to understand the biomagnetic and biopotential signals of a single breast cancerous cell. Understanding the biophysics of a single Manuscript received February 10, 2009; revised April 26, 2009. First pub- lished June 12, 2009; current version published September 16, 2009. This work was supported in part by the Doctoral Academy Fellowship at the University of Arkansas and in part by the National Science Foundation (NSF) under Award ECS-0524042. Asterisk indicates corresponding author. ∗ A. M. Hassan is with the Department of Electrical Engineering, University of Arkansas, Fayetteville, AR 72701 USA (e-mail: amhassan@uark.edu). M. El-Shenawee is with the Department of Electrical Engineering, University of Arkansas, Fayetteville, AR 72701 USA (e-mail: magda@uark.edu). Digital Object Identifier 10.1109/TBME.2009.2024539 breast cancerous cell is vital for answering these questions. A biophysics-based model and computer simulations will be employed here to obtain the spatial and the temporal electric current densities, and the associated biopotentials produced by a single breast cancerous cell. These electric current densities can be integrated to calculate the biomagnetic fields produced by a cancerous lesion [10, eq. (4)]. Cancerous cells modulate their membrane potential during cell division [11]–[17]. A common pattern for a dividing can- cerous cell is to decrease (depolarize) its membrane potential at the beginning of the G1 state followed by an increase in the membrane potential (hyperpolarization) in the G1/synthesis (G1/S) state transition [13], [14]. A standard breast cancer cell line, MCF-7, was found to hyperpolarize its membrane potential during the G1/S state transition by increasing the permeability of its membrane to potassium ions [15]–[17]. The numerical results of this paper are validated with these experimental data. In addition, the proposed paper aims to explain the macroscopic electric signals measured on or outside the breast based on these G1/S cellular activities. The motivations for developing such a model are to provide a tool to understand the experimental measurements and prove that the growing tumor cells are indeed generating electric sig- nals. The proposed model will be able to answer the question whether weak electromagnetic signals can propagate from the tissue near the tumor to the sensor positions outside the breast. The spatial and temporal distribution of the simulated electro- magnetic signals can help in providing information regarding the optimum distribution of sensors around the breast, as sug- gested by Cuzick et al. in [7], but it is not in the scope of this paper. In this paper, the electric current densities and biopotential variations associated with a growing breast tumor cell are cal- culated. In most models for cellular activity, the cell is assumed to exist in an infinite homogeneous medium with constant prop- erties such as constant ion concentrations [18]. However, the proposed model avoids such simplification by placing the cell in a semifinite dynamic environment with realistic anatomical features such as a blood vessel and a tissue boundary. This allows the calculation of the spatial as well as the temporal variations in the electric signals. Even though only a single cell is considered here, the analysis is challenging due to the fact that both the 2-D spatial as well as the temporal variations of the charged ion distributions need to be calculated. This means that the ion concentrations at each pixel and at each time step needs to be calculated, which can lead to extensive computational requirements. In addition, four nonlinear coupled differential equations are solved to describe 0018-9294/$26.00 © 2009 IEEE Authorized licensed use limited to: University of Arkansas. Downloaded on November 25, 2009 at 18:09 from IEEE Xplore. Restrictions apply.