Multimedia
Below, you can find animations of simulations I have performed over the past several years. For each movie, please click on the direct YouTube link and the corresponding papers for further details.
3-D Agent-based model
In very recent work, my lab has performed numerous optimizations to extend the agent-based model to 3D. Thus far, we have tested simulations of up to 5,000,000 cells in 10 mm3 domains in very reasonable times (< 48 hours) on high-end desktop and mid-end server machines. We are preparing a method article on this simulator (see PhysiCell) for late 2015 submission and release as open source. For now, here are a few early tests.
3-D Agent-based simulation of a tumor spheroid (80k agents) (2012)
Caption: An early (2012) test of our new 3-D agent-based cell model, growing from
10 to 80,000 agents in about 25 days (24-threaded simulation required about 5 hours).
Rendered in 3D using POVRAY (with a cutaway when the tumor gets big enough).
Further description: Click here
for further description on YouTube.
References: in preparation
Ductal Carcinoma in Situ (DCIS)
In recent work, I have developed a lattice-free, agent-based cell model, which I have applied primarily to DCIS--a type of cancer where growth is constrained within the breast duct lumen by a basement membrane. Each cell agent has a well-defined nucleus, lattice-free location governed by the balance of adhesive and other biomechanical forces, and a stochastic phenotypic state network regulated by exponentially-distributed random variables (arising from nonhomogeneous Poisson processes).
Virtual H&E histopathology test
Caption: This is an early test of improved intracellular water
transport, solid synthesis, and calcification, along with our first virtual
hematoxylin and eosin (H&E) pathology (and virtual transmitted light microscopy) visualization.
Further description: Click here
for further description on YouTube.
References: in preparation
Solid-type DCIS simulation (with comedo necrosis)
Caption: Solid-type DCIS simulation (with comedo necrosis) in a 1.5 mm length of breast
duct. Parameters have been calibrated to patient immunohistochemical and histopathologic data.
Further description: Click here
for further description on YouTube.
References:
Macklin et al. (2012)
Older version: here
DCIS simulation with unstable perinecrotic boundary
Caption: Solid-type DCIS simulation (with comedo necrosis) in a 1 mm length of breast
duct. Parameters have been calibrated to patient immunohistochemical and histopathologic data.
In this simulation, the proliferating (green) cells uptake oxygen at 100 times the rate of
non-proliferating cells, leading to an unstable perinecrotic boundary.
Further description: Click here
for further description on YouTube.
References:
Macklin et al. (2012)
Level-Set/Ghost Fluid Method Tumor Modeling
In these simulations, the level set method is used to represent the tumor-microenvironment interface as a sharp boundary, which evolves under Darcy's law. Proliferation scales with local substrate availability, which, in turn, is nonlinearly affected by the tumor morphology. The tissue biomechanics are related to the ECM density via the Darcy coefficient. Linear and nonlinear elliptic-type reaction-diffusion equations are solved using the ghost fluid method, with a nonlinear adaptive Gauss-Seidel-type iterative (NAGSI) solver.
Tumor growth in a large, heterogeneous microenvironment
Caption:
Here, we model an intracranial tumor in a 1 cm × 1 cm square of brain tissue, including white matter, grey
matter, cerebrospinal fluid, and cranium. Functional relationships forge multiscale
links between the ECM density, tumor biomechanical properties, and the overall morphology.
Further description: Click here
for further description on YouTube.
References:
Frieboes et al. (2007),
Macklin & Lowengrub (2008),
Tumor growth coupled to angiogenesis
Caption: The sharp interface tumor growth model of Macklin & Lowengrub is
coupled with the DATIA angiogenesis model of McDougall, Chaplain and Anderson to study
the nonlinear dynamics between tumor growth, ECM degradation, and heterogeneous distributions
of hypoxia. Notice the advanced coupling between vesssel flow (see the hematocrit distribution),
biomechanical pressure (which can cut off flow), oxygen release by the vessels, and
tumor proliferation (red regions in the top left plot).
Further description: Click here
for further description on YouTube.
References:
Macklin et al. (2009)
Tumor growth: hypoxic microenvironment
Caption:
Oxygen diffuses
towards the tumor from the outer edge of the domain, leading to large gradients and differential
cell proliferation (in red regions) and necrosis (in black regions). The tumor breaks into
fragments that invade the tissue. The apparent outward motion of each fragment is not due to
motility, but rather the combination of cell birth on the outer edge and cell death on the
inner edge of each fragment, leading to net outward motion.
Further description: Click here
for further description on YouTube.
References:
Macklin & Lowengrub (2007)
Macklin & Lowengrub (2006)
Macklin & Lowengrub (2005)
Tumor growth: normoxic, mechanically-stiff microenvironment
Caption:
Here, the nearby tissue is largely normoxic but biomechanically unrepsonsive to pressure gradients,
leading to an unstable, invasive fingering morphology. Note the emergence of a characteristic
thickness of the viable (red) region.
Further description: Click here
for further description on YouTube.
References:
Macklin & Lowengrub (2007)
Macklin & Lowengrub (2006)
Macklin & Lowengrub (2005)
Tumor growth in a normoxic, mechanically-compliant tissue
Caption:
Increasing the biomechanical compliance of the tissue eliminates the fingering instability. The white
regions in the center are analogous to the buildup of necrotic debris and fluid in the tumor core.
Further description: Click here
for further description on YouTube.
References:
Macklin & Lowengrub (2007)
Macklin & Lowengrub (2006)
Macklin & Lowengrub (2005)
