Paul Macklin's Math Cancer Lab Website

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

Agent-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 adhesive and other biomechanical forces, and a phenotypic state that depends upon the cell's internal genomic/proteomic state and its sampling of the local microenvironment. The phenotypic state transitions (based upon exponentially-distributed random variables) can be directly related to nonhomogeneous Poisson processes. Detailed, state-dependent "submodels" regulate the cell's volume, which is decomposed into nuclear and cytoplasmic solid and fluid components. 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.

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

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Continuum tissue-scale model screenshot

Continuum 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 topological changes in the tumor morphology (e.g., splitting into fragments, developing invasive fingers that can merge or split, etc.). Substrate transport is coupled using nonlinear reaction-diffusion equations.

The simulator is capable of modeling tumor growth in complex, heterogeneous tissues at large spatial scales (approximately 1 cm) on a single CPU. This model was originally developed from 2001 to 2007; updates are now being incorporated to improve efficiency, parallelize, and facilitate coupling to the agent-based cell model.

Recent reference: Macklin and Lowengrub (2008)
Recent multimedia: intracranial tumor simulations

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Hybrid & Multiscale Model Screenshot

Hybrid & Multiscale Modeling

Historically, multiscalarity has been built into models in multiple ways. Cell-scale models can easily incorporate molecular-scale models by including signaling models (e.g., boolean networks, systems of ordinary differential equations, compartmental models, etc.). Tissue-scale models have been made multiscale by (1) incorporating multiscale constitutive relations derived from cell-scale simulations or other biological considerations (e.g., as in Frieboes et al. (2007)), (2) by coupling discrete models of one phenomenon (e.g., angiogenesis) with continuum models of another (e.g., tumor growth) -- see Macklin et al. (2009), and (3) by coupling simultaneous discrete and continuum representations of the same phenomenon (e.g., continuum models of tumor bulk growth and discrete models of metastatic cells -- see the discussions in Lowengrub et al. (2010)). See our recent review in Deisboeck et al. (2011).

In current work, we are developing direct links between the agent-based (cell-scale) model and molecular-scale signaling, improved constitutive relations for continuum models based upon patient-calibrated cell-scale models, and dynamic switching between discrete and continuum models of tumor growth that effectively link our agent and continuum codes. This should enable efficient, large-scale simulations of tumor growth, angiogenesis, and metastasis in realistic geometries.

Recent reference: Macklin et al. (2009)
Recent multimedia: Coupled tumor-angiogenesis simulation

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Patient-Calibrated Cancer Modeling Programs

Solid-type DCIS with comedonecrosis

Breast Cancer Modeling Program

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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Immunostain for a prostate cancer bone metastasis

Prostate Cancer Modeling Program

We are beginning an ambitious prostate cancer program similar to the breast cancer program that is already well underway. Description coming soon!

Interested postdoctoral candidates may contact Paul Macklin. (Image source: Leeming et al. (2008).)

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