A computational study of circulating large tumor cells traversing microvessels

Circulating tumor cells (CTCs) are known to be a harbinger of cancer metastasis. The CTCs are known to circulate as individual cells or as a group of interconnected cells called CTC clusters. Since both single CTCs and CTC clusters have been detected in venous blood samples of cancer patients, they needed to traverse at least one capillary bed when crossing from arterial to venous circulation. The diameter of a typical capillary is about 7 µm, whereas the size of an individual CTC or CTC clusters can be greater than 20 µm and thus size exclusion is believed to be an important factor in the capillary arrest of CTCs – a key early event in metastasis. To examine the biophysical conditions needed for capillary arrest, we have developed a custom-built viscoelastic solid–fluid 3D computational model that enables us to calculate, under physiological conditions, the maximal CTC diameter that will pass through the capillary. We show that large CTCs and CTC clusters can successfully cross capillaries if their stiffness is relatively small. Specifically, under physiological conditions, a 13 µm diameter CTC passes through a 7 µm capillary only if its stiffness is less than 500 Pa and conversely, for a stiffness of 10 Pa the maximal passing diameter can be as high as 140 µm, such as for a cluster of CTCs. By exploring the parameter space, a relationship between the capillary blood pressure gradient and the CTC mechanical properties (size and stiffness) was determined. The presented computational platform and the resulting pressure–size–stiffness relationship can be employed as a tool to help study the biomechanical conditions needed for capillary arrest of CTCs and CTC clusters, provide predictive capabilities in disease progression based on biophysical CTC parameters, and aid in the rational design of size-based CTC isolation technologies where CTCs can experience large deformations due to high pressure gradients.