Compound Droplet Modelling of Circulating Tumor Cell Microfiltration

The Circulating Tumor Cell (CTC) is the cancer cell that has shed into the circulation system (i.e. cancer cell in the bloodstream). These CTCs are potential indicators for early cancer detection, which is critical for the whole process in cancer treatment. Among all new techniques, early detection of cancer from a single blood drop sample using the mechanical method by CTC microfiltration is promising for its simplicity, low cost, and ease of use. In the microfiltration of circulating tumor cells, the problem of a single CTC passing through a microfilter at a constant flow rate is a basic model for further device design and optimization. In our present paper, we developed a compound droplet model for the CTC passing through a microfilter. Numerically, we used the Volume of Fraction (VOF), three phase flow method. In this model, we take the blood, CTC cytoplasm and CTC nucleus as three individual fluids/phases. To build a more realistic model, the CTC cytoplasm and nucleus are taken as two fluids with their own surface tension coefficients and viscosities; the viscosity of the cytoplasm is considered as twice that of the bloodstream; the stiffness of the nucleus is set as four times that of the cytoplasm. Through the pressure signature and CTC deformation, the interaction between the compound droplet CTC, bloodstream, as well as the channel wall are studied numerically. As demonstrated in the previous Newtonian single droplet model, this critical passing pressure can be predicted by Young-Laplace equation. However, for the compound droplet model, no equation description is available. Through our study, the critical passing pressure, as well as the dynamic process of CTC passing pressure signature, is provided together with corresponding CTC deformation in each key stage. The pressure signature and deformation difference between the simple droplet model and compound droplet model are also compared. Additionally, the biological parameter, like the radius of cancer nucleus, is also an important parameter in the early cancer detection device design. In the following part of our study, we introduced a clinical parameter called N/C ratio, or nucleus/ cytoplasm ratio, which is a key parameter to discriminate between the healthy cell and tumor cell. By bringing this parameter into our study, the interaction among the nucleus, cytoplasm, bloodstream, as well as the wall of microfilter are studied for soft, medium and hard CTCs. In the end, the drawback of our method is also provided with advice for improvement.