Single-cell studies of phenotypic heterogeneity reveal more information about pathogenic processes than conventional bulk-cell analysis methods. By enabling high-resolution structural and functional imaging, a single-cell three-dimensional (3D) imaging system can be used to study basic biological processes and to diagnose diseases such as cancer at an early stage. One mechanism that such systems apply to accomplish 3D imaging is rotation of a single cell about a fixed axis. However, many cell rotation mechanisms require intricate and tedious microfabrication, or fail to provide a suitable environment for living cells. To address these and related challenges, we applied numerical simulation methods to design new microfluidic chambers capable of generating fluidic microvortices to rotate suspended cells. We then compared several microfluidic chip designs experimentally in terms of: (1) their ability to rotate biological cells in a stable and precise manner; and (2) their suitability, from a geometric standpoint, for microscopic cell imaging. We selected a design that incorporates a trapezoidal side chamber connected to a main flow channel because it provided well-controlled circulation and met imaging requirements. Micro particle-image velocimetry (micro-PIV) was used to provide a detailed characterization of flows in the new design. Simulated and experimental results demonstrate that a trapezoidal side chamber represents a viable option for accomplishing controlled single cell rotation. Further, agreement between experimental and simulated results confirms that numerical simulation is an effective method for chamber design.

Predicting the timing of a castrate resistant prostate cancer is critical to lowering medical costs and improving the quality of life of advanced prostate cancer patients. We formulate, compare and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen (PSA). We accomplish these tasks by employing clinical data of locally advanced prostate cancer patients undergoing androgen deprivation therapy (ADT). While these models are simplifications of a previously published model, they fit data with similar accuracy and improve forecasting results. Both models describe the progression of androgen resistance. Although Model 1 is simpler than the more realistic Model 2, it can fit clinical data to a greater precision. However, we found that Model 2 can forecast future PSA levels more accurately. These findings suggest that including more realistic mechanisms of androgen dynamics in a two population model may help androgen resistance timing prediction.

Background:
Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor.

Results:
We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise.

Conclusions:
The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling.