Quantifying the difference between cellular distributions  

Jan 23, 2023 at 02:20 pm by Staff



By Dr. Amanda Randles, Ph.D., Professor of Biomedical Sciences — Duke University 


 Year after year, incredible strides are made in the area of cancer research. With regard to virtual models capturing a circulating tumor cell’s trajectory as it moves through a plethora of surrounding red blood cells, advances are being made that are opening up new roads to tracking individual cancer cells and other movements of particles that aid in areas of physics and biomedical research. 


Need to account for cellular interactions 

Vascular studies have evolved over time. It was Sir William Harvey who discovered blood circulation in 1628. Since that initial discovery, technology and further extensive studies have allowed us to use precise numbers to describe how blood flows through the body. Accuracy has remained a pain point, however. Getting an accurate picture of the blood flow down to the level of individual cells interacting with each other as they transit through the circulatory system has historically posed scientific challenges. The number of cells itself presents a grand challenge as knowing the specific location and orientation of every red blood cell is not feasible. Instead, it is critical to survey sufficient potential orientations to assess likely interactions and subsequent effects, but the question remained of how many is enough.

Our team took a specific interest in this problem and set out to see if we could provide a means to quantify the difference between potential distributions of blood cells and identify how many groupings need to be sampled. The question of quantifying the difference between configurations is endemic to granular materials at large. These materials consist of individual solid particles packed together. The organization of these particles strongly influences the behavior of the material. In the case of the transit of a cancer cell in circulation, the orientation and location of red blood cells that it interacts with will significantly alter its trajectory and influence where it may adhere and potentially initiate a secondary tumor site. As there are twenty-five trillion red blood cells in the body, a cancer cell moving even a short distance can interact with several million cells. Understanding its path through the body requires taking into account any red blood cells it could interact with along the way.

Virtual models of cellular interactions in realistic or image-derived geometries are gaining traction as a means to assess the effect of different cellular properties on its transit. For example, in recent years computational models have been able to simultaneously simulate the interaction of hundreds of millions of individual red blood cells. These digital platforms provide a quantitative and controlled method to assess how certain cells will move through vascular anatomies or microfluidic devices of interest. However, while it is a remarkable computational advance to enable simulations of this scale, they bring out a key problem. One simulation of one potential distribution of cell locations and orientations is not enough. Given how much the specific location of red blood cells may influence the trajectory of for instance a circulating tumor cell, it is critical that we assess the effect of the full ensemble of potential cell locations in order to make any scientific conclusions.

When we know the path of a tumor cell, we can better predict where it will arrive at a blood vessel wall where it will likely latch on and create a secondary tumor site. This could lead to a significant breakthrough in cancer research and provide insight into the underlying mechanisms driving metastasis. 


Simulations lead to breakthroughs 

Quantifying the structure of red blood cell distributions or the path of tumor cells is a complex question. In the case of the circulating tumor cell, we realized through our research that we needed to sample a wide range of potential configurations of the surrounding cells in order to account for the cell's possible behaviors. What we didn't know yet was how many configurations we would need. Our research aimed to create a method of identifying random cell distributions and quantifying cell configurations. These different patterns could be described and measured by using computer simulations.

Modeling and simulation can further the advancement of biomedical research, and innovations in computational modeling have allowed researchers to test hypotheses with more speed and accuracy. This is especially true in cases where there is a multitude of patterns to study and test. 

In our work, we took the first steps to establish a heuristic for identifying not only how many instances should be studied but determining which ones.  Our study began with a computer simulation of an extensive system with densely packed red blood cells. We then introduced a three-dimensional circulating tumor cell to the simulated system. Through computational modeling, we created thousands of configurations — refilling our simulated vascular system at different points and studying the results. We then applied the radial distribution function, which is the formula researchers use to calculate randomness within a dense distribution. This formula confirmed the random nature of the placement and spacing of the red blood cells within the simulation. 

A significant part of our experiment came with the application of the Jaccard Index. This statistic gauges how sample sets are similar and different. A range between 0% and 100% is used, with the higher number showing a higher similarity between the two sets. We applied the Jaccard Index to determine whether the groupings of red blood cells were distinct. We also used it to determine how many spatial similarities occurred between cell configurations. By taking this first necessary step of identifying the metrics to use, we have provided a means for determining how many samples are needed and ensuring they are different “enough.”

Our research marks a large step in the right direction for predicting cellular behavior. Going forward, if we know the origin point of a tumor cell, we can now make accurate predictions about where it may travel. 

Simulations and computational modeling have allowed us to make great strides in cellular research. We can now accurately simulate the movement of cells through the bloodstream — and the usefulness of the technology does not stop there. In other situations, particles, atoms, and cells can all be more accurately studied using this advanced technology. With this robust technology and advanced computation and research, we can soon see the real-world application and the advancement of predictive biology. 

​​Amanda E. Randles, Ph.D., is the Alfred Winborne Mordecai and Victoria Stover Mordecai Assistant Professor of Biomedical Sciences at Duke University. Randles has made significant contributions to the fields of high performance computing and vascular modeling. Randles is the recipient of the NSF CAREER award, the ACM Grace Murray Hopper Award,  IEEE-CS Technical Consortium on High Performance Computing (TCHPC)  Award, the NIH Director’s Early Independence Award, the LLNL Lawrence  Fellowship. Randles was also named to the World Economic Forum Young Scientist List and the MIT Technology Review World’s Top 35 Innovators under the Age of 35 list. She holds 120 U.S. patents and has published 71 peer reviewed articles.


Sections: Clinical