Paul Macklin's Math Cancer Lab Website

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 350,000 cells in 3-4 mm3 domains in very reasonable times (< 48 hours) on high-end desktop and mid-end server machines. Numerous publications are in preparation. For now, here are a few early tests.

3-D Agent-based simulation of a necrotic tumor spheroid (80k agents)

Caption: An early 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 in a 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 in a 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)