The motility of cells crawling on a substratum has its origin in a thin cell organ called lamella. We present a 2-dimensional continuum model for the lamella dynamics of a slowly migrating cell, such as a human keratinocyte. The central components of the model are the dynamics of a viscous cytoskeleton capable to produce contractile and swelling stresses, and the formation of adhesive bonds in the plasma cell membrane between the lamella cytoskeleton and adhesion sites at the substratum. We will demonstrate that a simple mechanistic model, neglecting the complicated signaling pathways and regulation processes of a living cell, is able to capture the most prominent aspects of the lamella dynamics, such as quasi-periodic protrusions and retractions of the moving tip, retrograde flow of the cytoskeleton and the related accumulation of focal adhesion complexes in the leading edge of a migrating cell. The developed modeling framework consists of a nonlinearly coupled system of hyperbolic, parabolic and ordinary differential equations for the various molecular concentrations, two elliptic equations for cytoskeleton velocity and hydrodynamic pressure in a highly viscous two-phase flow, with appropriate boundary conditions including equalities and inequalities at the moving boundary. In order to analyse this hybrid continuum model by numerical simulations for different biophysical scenarios, we use suitable finite element and finite volume schemes on a fixed triangulation in combination with an adaptive level set method describing the free boundary dynamics.

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We study the steady-state dynamics of sedimenting non-Brownian particles in confined geometries with full hydrodynamic interactions at small but finite Reynolds numbers. We employ extensive computer simulations using a method where a continuum liquid phase is coupled through Stokesian friction to a discrete particle phase. In particular, we consider a sedimentation box which is otherwise periodic except that it is confined by two parallel walls parallel to gravity with a spacing L x . By systematically varying L x we explore the change in dynamics from a quasi-two-dimensional (2D) case to a three-dimensional case. We find that in such confined geometries there is a depletion of particle number density at the walls for small volume fractions, while for large volume fractions there is an excess number of particles at the walls. For the average sedimentation velocity, we find that the Richardson-Zaki law is well obeyed but the decrease of the velocity for dilute systems is slower for smaller values of L x . We study the anisotropy of the velocity fluctuations and find that in the direction of gravity there is excellent agreement with the predicted scaling with respect to L x . We also find that the behavior of the corresponding diffusion coefficients as a function of L x is qualitatively different in the direction parallel to gravity and perpendicular to it. In the quasi-2D limit where particles block each other, the velocity fluctuations behave differently from the other confined systems.

Knowledge‐based planning (KBP) can be used to estimate dose–volume histograms (DVHs) of organs at risk (OAR) using models. The task of model creation, however, can result in estimates with differing accuracy; particularly when outlier plans are not properly addressed. This work used RapidPlan™ to create models for the prostate and head and neck intended for large‐scale distribution. Potential outlier plans were identified by means of regression analysis scatter plots, Cook's distance, coefficient of determination, and the chi‐squared test. Outlier plans were identified as falling into three categories: geometric, dosimetric, and over‐fitting outliers. The models were validated by comparing DVHs estimated by the model with those from a separate and independent set of clinical plans. The estimated DVHs were also used as optimization objectives during inverse planning. The analysis tools lead us to identify as many as 7 geometric, 8 dosimetric, and 20 over‐fitting outliers in the raw models. Geometric and over‐fitting outliers were removed while the dosimetric outliers were replaced after re‐planning. Model validation was done by comparing the DVHs at 50%, 85%, and 99% of the maximum dose for each OAR (denoted as V50, V85, and V99) and agreed within −2% to 4% for the three metrics for the final prostate model. In terms of the head and neck model, the estimated DVHs agreed from −2.0% to 5.1% at V50, 0.1% to 7.1% at V85, and 0.1% to 7.6% at V99. The process used to create these models improved the accuracy for the pharyngeal constrictor DVH estimation where one plan was originally over‐estimated by more than twice. In conclusion, our results demonstrate that KBP models should be carefully created since their accuracy could be negatively affected by outlier plans. Outlier plans can be addressed by removing them from the model and re‐planning.

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