Paul Macklin's Math Cancer Lab Website

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Recent news

Friday, Feb 20th, 2015
Banner and Logo Contest : MultiCellDS Project: As the MultiCellDS (multicellular data standards) project continues to ramp up, we could use some artistic skill.Right now, we don't have a banner (aside from a ... [read more]

Thursday, Dec 11th, 2014
2015 Speaking Schedule: Here is my current speaking schedule for 2015. Please join me if you can! Feb. 13, 2015: Seminar at the Institute for Scientific Computing Research, ... [read more]

Research Projects

Our research focuses upon developing cutting-edge computational technologies for use in patient-specific cancer simulators. Our ultimate goal is to create quantitative platforms that integrate patient data from multiple sources (proteomics, histopathology, radiology), to help guide surgical and therapeutic planning.

Core Technologies

Agent-based cell model screenshot

PhysiCell: Physics-based cell model

This core technology, in development since 2007, models individual cells as agents. Each agent has a lattice-free position (center of mass), a velocity that is determined by the balance of biomechanical forces, and a phenotype that depends upon the cell's internal genomic/proteomic state and its sampling of the local microenvironment. Cell cycle progression and apoptotic and necrotic cell death are modeled as stochastic processes that vary with the microenvironment. Detailed, state-dependent "submodels" regulate the cell's fluid and biomass content. We are the first to model the critical process of nuclear cell calcification, and have the most detailed model of cell necrosis.

This agent model is the foundation of our cutting-edge patient calibration techniques, which can be uniquely constrained to patient immuno­his­to­chem­is­try and other his­to­path­o­log­ic (e.g., mor­pho­met­ric) mea­sure­ments. PhysiCell is capable of simulating 105 to 106 cells on desktop processors in complex 3-D tissue structures. Click here to read more.

Recent reference: Macklin et al. (2012)
Recent multimedia: DCIS simulations

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BioFVM: A biological transport solver

This code simulates the diffusive transport of multiple substrates (e.g., oxygen, glucose, growth factors, drugs) as they are secreted/released/absorbed by biological elements in 3-D tissues. We use this code to simulate the microenvironment and its interactions with cells. BioFVM is capable of simulating diffusive transport of 5-10 substrates on 1-10 million voxel meshes (generally 5-100 mm3) on desktop processors. Click here to read more.

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Continuum tissue-scale model screenshot Hybrid & Multiscale Model Screenshot

Tissue-scale model

Our continuum tissue-scale model simulates the tumor-host interface as a moving boundary problem, using advanced level set techniques that can automatically handle changes in the tumor shape (e.g., splitting into fragments, developing invasive fingers that can merge or split, etc.). Substrate transport is coupled using nonlinear reaction-diffusion equations. We have successfully tied this simulation to models of angiogenesis and blood flow.

The simulator is capable of modeling tumor growth in complex, heterogeneous 2-D tissues at large spatial scales (approximately 1 cm) on a single CPU. This model was originally developed from 2001 to 2007, and has been superceded (for the time being) by agent-based modeling.

Recent references: Macklin and Lowengrub (2007), Frieboes et al. (2007), Macklin and Lowengrub (2008), Macklin et al. (2009)
Recent multimedia: Coupled tumor-angiogenesis simulation
intracranial tumor simulations

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Patient-Calibrated Cancer Modeling Programs

Solid-type DCIS with comedonecrosis

Modeling breast cancer

Basic Background

Breast cancer is the second-leading cause of death in American women. Ductal carcinoma in situ (DCIS)—a type of breast cancer whose growth is restricted to the duct lumen by the basement membrane—is a significant precursor to invasive ductal carcinoma (IDC). Breast-conserving surgery is generally very successful in treating DCIS, but re-resection is required in 40-50% of patients due to inadequate surgical margins. This highlights difficulties in accurately estimating the DCIS volume and shape based upon the pattern of microcalcifications observed in mammography, and current deficiencies in integrating patient his­to­path­ol­ogy mea­sure­ments with radiology to improve surgical planning.

The progression from DCIS to IDC is currently poorly understood. The impact of inadequate surgical margins on microinvasion has not been thoroughly investigated. There is no clear consensus on how to tailor optimal adjuvant therapies (e.g., chemotherapy, hormonal therapy, radiotherapy) to minimize the risk of microinvasion following unsuccessful surgery. The process of breast cancer metastasis (e.g., to the bone and brain) is not fully characterized, and definitive treatments to minimize or eliminate such metastases have not yet emerged. All these could be better investigated with quantitative, patient-calibrated computational models.

Multidisciplinary Team

We have assembled a broad multidisciplinary team in the US and the UK to investigate breast cancer. Paul Macklin leads the mathematical modeling, as well as the overall integration of the multidisciplinary effort. In the United Kingdom at the University of Dundee Medical School/Ninewells Hospital and NHS Tayside, Colin Purdie and Lee Jordan obtain and process histopathology on clinical samples, Andrew Evans leads our ra­di­ol­ogy/mam­mo­gra­phy analysis, and Alastair Thompson contributes clinical and surgical expertise.

In the United States, we are beginning new collaborations with the Center for Applied Molecular Medicine at USC to conduct in vitro experiments to further pin down cell cycle, apoptosis, necrosis, motility, and adhesion parameters in breast cell lines. We are also beginning collaborations with Hermann Frieboes at the University of Louisville to conduct microinvasion and chemotherapy assays to calibrate and validate next-generation models of invasive breast cancer.

Early DCIS Results and Model Validation

Early work on DCIS has been very successful. In Macklin et al. (2012), we developed patient-specific calibration protocols using Ki-67 and cleaved Caspase-3 immunohistochemistry and various mor­phometric measurements in H&E histopathology. Agent-based simulations captured the correct DCIS microstructure: an outer viable rim with the greatest proliferation along the basement membrane, surrounding a necrotic core, with a mechanical "tear" along the perinecrotic rim. Furthermore, the simulated necrotic core is stratified, with swelling necrotic cells along the perinecrotic boundary, increasing cytoplasmic volume loss and pyknosis (nuclear degradation) towards the center, and cell calcification in the very center. These are all observed in patient histopathology.

Furthermore, the Macklin et al. (2012) work predicted that necrotic cell lysis acts as a major biomechanical stress relief that redirects a significant fraction of proliferative cell flux towards the duct center rather than along the duct. As a result, the tumor advances along the duct at a linear (rather than exponential) rate. This is consistent with clinical mammographic estimates. Furthermore, the model predicts that the tumor grows at 7 to 13 mm per year, in quantitative agreement with numerous clinical estimates. Significantly, the model predicted a linear relationship between the calcification size (as measured by mammography) and the (post-surgical) pathology size, with excellent quantitative agreement to 87 independent clinical cases spanning two orders of magnitude in size. Hence, the model is capable of using patient-specific microscopic measurements to make clinically-useful macroscopic predictions.

An early, static upscaling based upon this calibration was successful in predicting patient DCIS volumes in 14 of 17 test cases. See Edgerton et al. (2011) and Macklin et al. (2010).

Ongoing Work

Description coming soon!

Further Information

Recent reference: Macklin et al. (2012)
Recent multimedia: DCIS simulations

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Mathematical model of oxygen distribution near a colon cancer metastasis in the liver

Modeling colon cancer metastases in bioengineered liver tissues

Basic Background

This is being rewritten.

Goals and methods



(Image source: Leeming et al. (2008).)

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