Numerical and experimental investigation of effects of deformability of circulating tumor cells in physical occlusion

Abstract

The hematogenous spread of metastasis, an indispensable pathway in metastasis progression, occurs when primary tumor cells enter the bloodstream and circulate throughout the body. Understanding the genetic, biochemical, and biomechanical factors contributing to this spread could significantly advance the early diagnosis and treatment of metastasis. Among these factors, the hemodynamic forces in the blood play a crucial role in spreading metastasis to distant organs, as the blood flow is the primary means of transporting the circulating tumor cells (CTC) in the bloodstream. The survival, intravascular arrest, and extravasation of CTCs are significantly influenced by shear stresses from their interactions with blood plasma, blood cells, and endothelial cells forming the inner layer of blood vessels. However, our understanding of these interactions is still limited due to the complex nature of the phenomena. Advanced numerical methods, capable of accounting for the high deformability of CTCs and fluid dynamics in microcapillaries, offer a promising approach to deciphering CTCs' responses to the hemodynamic forces in their microenvironment. Physics-based cellular-scale numerical methods capable of simulating a large number of highly deformable objects immersed in a fluidic domain came into being as advanced methods to help researchers unravel the CTC's role in metastasis. The discrete nature of these numerical methods comes with the price of defining several unknown parameters for the cell model, which directly impact the deformation behavior of the cell interacting with the force sources that exist in CTC’s microenvironment. Therefore, in the first step of this study, a systematic approach has been developed to identify the unknown parameters of the numerical cell model accurately. In this step, the power of the developed identification method has been credited by using the experimental data reported in the literature for various experiments such as stretch experiments of Red Blood Cells (RBCs) and lung cancer cell deformability measurement with constricted microchannels. However, the experimental data in the literature are insufficient to be applied in identifying the cancer cell parameters, mainly because not only the measured time is too high, making the identification step almost impossible to perform, but the reported data also lack various inputs for cancer cell deformability measurement, hindering the acquiring of stable cell models. Therefore, in the second step, experiments of cells passing the constricted microfluidic devices were performed, and the deformability of highly invasive breast cancer cell lines were measured. By creating the numerical domains of the constricted channels and identifying the cell parameters, cell models of various sizes ranging from 13-18 µm that their motion and deformation behavior have been validated according to the experimental data were acquired. As presented in detail in this study, the developed models can replicate the gradual squeezing and shape change of cancer cells into the constricted microchannels as well as the drop of the flow rate during the cell entrance into the constrictions. Targeting CTC mechanical entrapment in the microcapillaries, in the third step, a predictive numerical tool that can predict the CTC's occlusion fate in an arbitrary microvascular system has been developed. The obstacle in this step is that tracking the CTC’s fate within a large fluidic domain is still beyond the capabilities of the cellular scale in-silico models. Therefore, devising a method that divides an arbitrary microvascular system into smaller domains amenable for the in-silico method to calculate the CTC’s fate is the key to overcome the mentioned obstacle. Therefore, substantial numerical investigations were performed on smaller models to determine the relationship between cell fate and mechanical factors in the blood, such as plasma flow rate, cell deformability, capillary geometry, and cell size. The outputs of the numerical investigations have been stored and used later to predict the cell fate and the site of cell entrapment in the arbitrary microvascular system. Afterward, an algorithm for tracking the CTC in the microvasculature and pinpointing its occluded location has been developed. This algorithm takes the initial cell position and size, communicates with the stored data at every microcapillary branch that contains the CTC, and predicts the CTC trajectory from the previously provided information of the microvascular system's anatomic structure and fluid flow.