Heather Harrington Group

MPI-CBG > Research > Research Groups > Current Groups > Heather Harrington > Publications

* joint first author # joint corresponding author

2024
Bernadette J Stolz✳︎, Jagdeep Dhesi✳︎, Joshua A Bull, Heather Harrington, Helen M Byrne, Iris H R Yoon
Relational Persistent Homology for Multispecies Data with Application to the Tumor Microenvironment.
Bull Math Biol, 86(11) 128-128 (2024)
Open Access DOI
Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods in TDA such as persistent homology (PH) are typically focused on the analysis of data consisting of a single entity (e.g., cells or molecular species). However, state-of-the-art data collection techniques now generate exquisitely detailed multispecies data, prompting a need for methods that can examine and quantify the relations among them. Such heterogeneous data types arise in many contexts, ranging from biomedical imaging, geospatial analysis, to species ecology. Here, we propose two methods for encoding spatial relations among different data types that are based on Dowker complexes and Witness complexes. We apply the methods to synthetic multispecies data of a tumor microenvironment and analyze topological features that capture relations between different cell types, e.g., blood vessels, macrophages, tumor cells, and necrotic cells. We demonstrate that relational topological features can extract biological insight, including the dominant immune cell phenotype (an important predictor of patient prognosis) and the parameter regimes of a data-generating model. The methods provide a quantitative perspective on the relational analysis of multispecies spatial data, overcome the limits of traditional PH, and are readily computable.


Thomas Chaplin, Heather Harrington, Ulrike Tillmann
Grounded Persistent Path Homology: A Stable, Topological Descriptor for Weighted Digraphs.
Found. Comput. Math., Art. No. doi: 10.1007/s10208-024-09679-2 (2024)
Open Access
Weighted digraphs are used to model a variety of natural systems and can exhibit interesting structure across a range of scales. In order to understand and compare these systems, we require stable, interpretable, multiscale descriptors. To this end, we propose grounded persistent path homology (GrPPH)-a new, functorial, topological descriptor that describes the structure of an edge-weighted digraph via a persistence barcode. We show there is a choice of circuit basis for the graph which yields geometrically interpretable representatives for the features in the barcode. Moreover, we show the barcode is stable, in bottleneck distance, to both numerical and structural perturbations.


Richard Culliford✳︎, Samuel E D Lawrence✳︎, Charlie Mills, Zayd Tippu, Daniel Chubb, Alex J Cornish, Lisa Browning, Ben Kinnersley, Robert Bentham, Amit Sud, Husayn Pallikonda, Husayn null, Anna Frangou, Andreas J Gruber, Kevin Litchfield, David C Wedge, James Larkin, Samra Turajlic, Richard S Houlston
Whole genome sequencing refines stratification and therapy of patients with clear cell renal cell carcinoma.
Nat Commun, 15(1) Art. No. 5935 (2024)
Open Access DOI
Clear cell renal cell carcinoma (ccRCC) is the most common form of kidney cancer, but a comprehensive description of its genomic landscape is lacking. We report the whole genome sequencing of 778 ccRCC patients enrolled in the 100,000 Genomes Project, providing for a detailed description of the somatic mutational landscape of ccRCC. We identify candidate driver genes, which as well as emphasising the major role of epigenetic regulation in ccRCC highlight additional biological pathways extending opportunities for therapeutic interventions. Genomic characterisation identified patients with divergent clinical outcome; higher number of structural copy number alterations associated with poorer prognosis, whereas VHL mutations were independently associated with a better prognosis. The observations that higher T-cell infiltration is associated with better overall survival and that genetically predicted immune evasion is not common supports the rationale for immunotherapy. These findings should inform personalised surveillance and treatment strategies for ccRCC patients.


Hadrien Oliveri, Derek E. Moulton, Heather Harrington, Alain Goriely
Active shape control by plants in dynamic environments.
Phys Rev E, 110(1-1) Art. No. 014405 (2024)
Open Access DOI
Plants are a paradigm for active shape control in response to stimuli. For instance, it is well known that a tilted plant will eventually straighten vertically, demonstrating the influence of both an external stimulus, gravity, and an internal stimulus, proprioception. These effects can be modulated when a potted plant is additionally rotated along the plant's axis, as in a rotating clinostat, leading to intricate shapes. We use a previously derived rod model to study the response of a growing plant and the joint effects of both stimuli at all rotation speeds. In the absence of rotation, we identify a universal planar shape towards which all shoots eventually converge. With rotation, we demonstrate the existence of a stable family of three-dimensional dynamic equilibria where the plant axis is fixed in space. Further, the effect of axial growth is to induce steady behaviors, such as solitary waves. Overall, this study offers insight into the complex out-of-equilibrium dynamics of a plant in three dimensions and further establishes that internal stimuli in active materials are key for robust shape control.


Katherine Benjamin✳︎, Aneesha Bhandari✳︎, Jessica D Kepple, Rui Qi, Zhouchun Shang, Yanan Xing, Yanru An, Nannan Zhang, Yong Hou, Tanya L Crockford, Oliver McCallion, Fadi Issa, Joanna Hester, Ulrike Tillmann, Heather Harrington#, Katherine R Bull#
Multiscale topology classifies cells in subcellular spatial transcriptomics.
Nature, 630(8018) 943-949 (2024)
Open Access DOI
Spatial transcriptomics measures in situ gene expression at millions of locations within a tissue1, hitherto with some trade-off between transcriptome depth, spatial resolution and sample size2. Although integration of image-based segmentation has enabled impactful work in this context, it is limited by imaging quality and tissue heterogeneity. By contrast, recent array-based technologies offer the ability to measure the entire transcriptome at subcellular resolution across large samples3-6. Presently, there exist no approaches for cell type identification that directly leverage this information to annotate individual cells. Here we propose a multiscale approach to automatically classify cell types at this subcellular level, using both transcriptomic information and spatial context. We showcase this on both targeted and whole-transcriptome spatial platforms, improving cell classification and morphology for human kidney tissue and pinpointing individual sparsely distributed renal mouse immune cells without reliance on image data. By integrating these predictions into a topological pipeline based on multiparameter persistent homology7-9, we identify cell spatial relationships characteristic of a mouse model of lupus nephritis, which we validate experimentally by immunofluorescence. The proposed framework readily generalizes to new platforms, providing a comprehensive pipeline bridging different levels of biological organization from genes through to tissues.


2023
David Beers, Despoina Goniotaki, Diane P Hanger, Alain Goriely, Heather Harrington
Barcodes distinguishing morphology of neuronal tauopathy.
Phys Rev Research, 5(4) Art. No. 043006 (2023)
Open Access DOI
The geometry of neurons is known to be important for their functions. Hence, neurons are often classified by their morphology. Two recent methods, persistent homology and the topological morphology descriptor, assign a morphology descriptor called a barcode to a neuron equipped with a given function, such as the Euclidean distance from the root of the neuron. These barcodes can be converted intomatrices called persistence images, which can then be averaged across groups. We show that when the defining function is the path length from the root, both the topological morphology descriptor and persistent homology are equivalent. We further show that persistence images arising from the path length procedure provide an interpretable summary of neuronal morphology. We introduce topological morphology functions, a class of functions similar to the Sholl functions, that can be recovered from the associated topological morphology descriptor. To demonstrate this topological approach, we compare healthy cortical and hippocampal mouse neurons to those affected by progressive tauopathy. We find a significant difference in the morphology of healthy neurons and those with a tauopathy at a postsymptomatic age. We use persistence images to conclude that the diseased group tends to have neurons with shorter branches as well as fewer branches far from the soma.


Luis David García Puente, Elizabeth Gross, Heather A Harrington, Matthew Johnston, Nicolette Meshkat, Mercedes Pérez Millán, Anne Shiu
Absolute concentration robustness: Algebra and geometry
arXiv preprint arXiv:2401.00078
DOI

Heather Harrington, Hal Schenck, Mike Stillman
Kuramoto Oscillators: algebraic and topological aspects
arXiv preprint arXiv:2312.16069 
DOI

W Reise, X Fernández, M Dominguez, HA Harrington, M Beguerisse-Díaz
Topological fingerprints for audio identification
arXiv preprint arXiv preprint arXiv:2309.03516
DOI

Robert A. McDonald, Rosanna Neuhausler, Martin Robinson, Laurel G. Larsen, Heather A. Harrington, Maria Bruna
Zigzag persistence for coral reef resilience using a stochastic spatial model.
Journal of the Royal Society Interface 20 (205), 20230280
DOI

Jingjie Yang, Heidi Fang, Jagdeep Dhesi, Iris H.R. Yoon, Joshua A. Bull, Helen M. Byrne, Heather A. Harrington, Gillian Grindstaff
Topological classification of tumour-immune interactions and dynamics
arXiv preprint arXiv:2308.05294

Katherine Benjamin, Lamisah Mukta, Gabriel Moryoussef, Christopher Uren, Heather A. Harrington, Ulrike Tillmann and Agnese Barbensi
Homology of homologous knotted proteins
Journal of the Royal Society Interface 20 (201), 20220727
DOI

Z Gao, D Ghosh, HA Harrington, JG Restrepo, D Taylor
Dynamics on networks with higher-order interactions
Chaos: An Interdisciplinary Journal of Nonlinear Science 33 (4)
DOI

Carroll, Thomas M.Ahern, David et al.
Tumor monocyte content predicts immunochemotherapy outcomes in esophageal adenocarcinoma
Cancer Cell, Volume 41, Issue 7, 1222 - 1241.e7
DOI​​​​​​​

R Dong, C Goodbrake, HA Harrington, G Pogudin
Differential elimination for dynamical models via projections with applications to structural identifiability
SIAM Journal on Applied Algebra and Geometry 7 (1), 194-235

Hosuk Ryou, Korsuk Sirinukunwattana, Alan Aberdeen, Gillian Grindstaff, Bernadette J. Stolz, Helen Byrne, Heather A. Harrington, Nikolaos Sousos, Anna L. Godfrey, Claire N. Harrison, Bethan Psaila, Adam J. Mead, Gabrielle Rees, Gareth D. H. Turner, Jens Rittscher & Daniel Royston
Continuous Indexing of Fibrosis (CIF): Improving the assessment and classification of MPN patients
Leukemia 37 (2), 348-358
DOI

Uzu Lim, Rodrigo Leal Cervantes, Gillian Coughlan, Renaud Lambiotte, Hugo J. Spiers, Michael Hornberger, Heather A. Harrington
Geometry of navigation identifies genetic-risk and clinical Alzheimer's disease
medRxiv, 2023.10. 01.23296035
DOI

C Bick, E Gross, HA Harrington, MT Schaub
What are higher-order networks?
SIAM Review 65 (3), 686-731

2022

Lewis Marsh, Felix Y. Zhou, Xiao Qin, Xin Lu, Helen M. Byrne, Heather A. Harrington
Detecting Temporal shape changes with the Euler Characteristic Transform
arXiv preprint arXiv:2212.10883
DOI

Annalise Katz-Summercorn, Iliana Peneva, Anna Frangou, Sriganesh Jammula, Maria O'Donovan, Monika Tripathi, Shalini Malhotra, Massimiliano di Pietro, Ginny Devonshire, Aisling Redmond, David Wedge, Rebecca Fitzgerald
OGC P04 Spatial sampling of Barrett's oesophagus reveals that tumour heterogeneity is not a useful predictor of progression to cancer
British Journal of Surgery, Volume 109, Issue Supplement_9, December 2022, znac404.167
DOI

Wilfred Offord, Michael Coughlan, Ian J. Hewitt, Heather A. Harrington, Gillian Grindstaff
Topological Data Analysis Detects Percolation Thresholds in Arctic Melt-Pond Evolution
arXiv preprint arXiv:2212.07961
 

Katherine Benjamin, Aneesha Bhandari, Zhouchun Shang, Yanan Xing, Yanru An, Nannan Zhang, Yong Hou, Ulrike Tillmann, Katherine R. Bull, Heather A. Harrington
Multiscale topology classifies and quantifies cell types in subcellular spatial transcriptomics
arXiv preprint arXiv:2212.06505
 

Heather A. Harrington, Mike Stillman, Alan Veliz-Cuba
Algebraic network reconstruction of discrete dynamical systems
arXiv preprint arXiv:2212.02601
 

Lewis Marsh, Emilie Dufresne, Helen M. Byrne, Heather A. Harrington
Algebra, geometry and topology of ERK kinetics
Bulletin of Mathematical Biology 84 (12), 137
 

David Beers, Heather A. Harrington, Alain Goriely
Stability of topological descriptors for neuronal morphology
arXiv preprint arXiv:2211.09058
 

Thomas Chaplin, Heather A. Harrington, Ulrike Tillmann
Grounded persistent path homology: a stable, topological descriptor for weighted digraphs
arXiv preprint arXiv:2210.11274
 

A Barbensi, HR Yoon, CD Madsen, DO Ajayi, MPH Stumpf, HA Harrington
Hypergraphs for multiscale cycles in structured data
arXiv preprint arXiv:2210.07545

CP Kotanidis, C Xie, D Alexander, JCL Rodrigues, K Burnham, A Mentzer, ...
Constructing custom-made radiotranscriptomic signatures of vascular inflammation from routine CT angiograms: a prospective outcomes validation study in COVID-19
The Lancet Digital Health 4 (10), e705-e716

RA McDonald, R Neuhausler, M Robinson, LG Larsen, HA Harrington, ...
Topological descriptors for coral reef resilience using a stochastic spatial model
arXiv preprint arXiv:2209.08974

C Goodbrake, D Beers, TB Thompson, HA Harrington, A Goriely
Brain Chains as Topological Signatures for Alzheimer's Disease
arXiv preprint arXiv:2208.12748

RS Hoekzema, L Marsh, O Sumray, TM Carroll, X Lu, HM Byrne, ...
Multiscale methods for signal selection in single-cell data
Entropy 24 (8), 1116

BJ Stolz, J Kaeppler, B Markelc, F Braun, F Lipsmeier, RJ Muschel, ...
Multiscale topology characterizes dynamic tumor vascular networks
Science Advances 8 (23), eabm2456

EL Brown, TL Lefebvre, PW Sweeney, BJ Stolz, J Gröhl, L Hacker, ...
Quantification of vascular networks in photoacoustic mesoscopy
Photoacoustics 26, 100357

T Thorne, PDW Kirk, HA Harrington
Topological approximate Bayesian computation for parameter inference of an angiogenesis model
Bioinformatics 38 (9), 2529-2535

A Seigal, HA Harrington, V Nanda
Principal components along quiver representations
Foundations of Computational Mathematics, 1-37

D Beers, D Goniotaki, DP Hanger, A Goriely, HA Harrington
Barcodes distinguish morphology of neuronal tauopathy
arXiv preprint arXiv:2204.03348

DJ Ahern, Z Ai, M Ainsworth, C Allan, A Allcock, B Angus, MA Ansari, ...
A blood atlas of COVID-19 defines hallmarks of disease severity and specificity
Cell 185 (5), 916-938. e58

Katz-Summercorn, A.C., Jammula, S., Frangou, A. et al.
Multi-omic cross-sectional cohort study of pre-malignant Barrett’s esophagus reveals early structural variation and retrotransposon activity.
Nat Commun 13, 1407 (2022).
DOI

2021

O Vipond, JA Bull, PS Macklin, U Tillmann, CW Pugh, HM Byrne, ...
Multiparameter persistent homology landscapes identify immune cell spatial patterns in tumors
Proceedings of the National Academy of Sciences 118 (41), e2102166118

JT Nardini, BJ Stolz, KB Flores, HA Harrington, HM Byrne
Topological data analysis distinguishes parameter regimes in the Anderson-Chaplain model of angiogenesis
PLOS Computational Biology 17 (6), e1009094

BJ Stolz, T Emerson, S Nahkuri, MA Porter, HA Harrington
Topological data analysis of task-based fMRI data from experiments on schizophrenia
Journal of Physics: Complexity 2 (3), 035006

E Dufresne, HA Harrington, JD Hauenstein, PG Kevrekidis, P Tripoli
On some configurations of oppositely charged trapped vortices in the plane
Advances in Applied Mathematics 124, 102099

COvid-19 Multi-omics Blood ATlas (COMBAT) Consortium (203 authors, HAH member of integrative data analysis team).
A blood atlas of COVID-19 defines hallmarks of disease severity and specificity
Cell 2022 185:916-938. medRXiv.

R Dong, C Goodbrake, HA Harrington, G Pogudin
Computing input-output projections of dynamical models with applications to structural identifiability.
CoRR

2020

BJ Stolz, J Tanner, HA Harrington, V Nanda
Geometric anomaly detection in data
Proceedings of the national academy of sciences 117 (33), 19664-19669

E Gross, H Harrington, N Meshkat, A Shiu
Joining and decomposing reaction networks
Journal of mathematical biology 80, 1683-1731

MF Adamer, HA Harrington, EA Gaffney, TE Woolley
Coloured noise from stochastic inflows in reaction–diffusion systems
Bulletin of Mathematical Biology 82, 1-28

E Yeung, S McFann, L Marsh, E Dufresne, S Filippi, HA Harrington, ...
Inference of multisite phosphorylation rate constants and their modulation by pathogenic mutations
Current Biology 30 (5), 877-882. e6

A Barbensi, D Celoria, HA Harrington, A Stasiak, D Buck
Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology
Science advances 6 (9), eaay1458

HA Harrington, D Mehta, HM Byrne, JD Hauenstein
Decomposing the parameter space of biological networks via a numerical discriminant approach
Maple in Mathematics Education and Research: Third Maple Conference, MC 2019 …

2019

Dufresne E, Edwards PB, Harrington HA, Hauenstein JD
Sampling real algebraic varieties for topological data analysis
2019 18th IEEE International Conference On Machine Learning And Applications (ICMLA) 2020 1531-1536. arXiv:1802.07716.

Byrne HM, Harrington HA,Muschel R, Reinert G, Stolz BJ, Tillmann U
Topology characterises spatial networks of tumour vasculature
Mathematics Today, 2019 55(5):206-210. arXiv:1907.08711.

E Gross, H Harrington, N Meshkat, A Shiu
Linear compartmental models: input-output equations and operations that preserve identifiability
SIAM Journal on Applied Mathematics 79 (4), 1423-1447

HA Harrington, N Otter, H Schenck, U Tillmann
Stratifying multiparameter persistent homology
SIAM Journal on Applied Algebra and Geometry 3 (3), 439-471

2018

A Barbensi, D Buck, HA Harrington, M Lackenby
Double branched covers of knotoids
arXiv preprint arXiv:1811.09121

L Speidel, HA Harrington, SJ Chapman, MA Porter
Topological data analysis of continuum percolation with disks
Physical Review E 98 (1), 012318

2017

MF Adamer, TE Woolley, HA Harrington
Graph-facilitated resonant mode counting in stochastic interaction networks
Journal of the Royal Society Interface 14 (137), 20170447

N Otter, MA Porter, U Tillmann, P Grindrod, HA Harrington
A roadmap for the computation of persistent homology
EPJ Data Science 6, 1-38

Smith RCG, Stumpf PS, Ridden SJ, Sim A, Filippi S, Harrington HA, MacArthur BD
Nanog fluctuations in embryonic stem cells highlight the problem of measurement in cell biology
Biophysical journal 112 (12), 2641-2652
DOI

BJ Stolz, HA Harrington, MA Porter
Persistent homology of time-dependent functional networks constructed from coupled time series
Chaos: An Interdisciplinary Journal of Nonlinear Science 27 (4)
DOI

Drellich E, Gainer-Dewar A, Harrington HA, He Q, Heitsch C, Poznanovic S.
Geometric combinatorics and computational molecular biology: Branching polytopes for RNA sequences
Accepted (to appear AMS Contemporary Mathematics Volume). arXiv:1509.04090. 

Kay SK, Harrington HA, Shepherd S, Brennan K, Dale T, Osborne JM, Gavaghan DJ, Byrne HM
The role of the Hes1 crosstalk hub in Notch-Wnt interactions of the intestinal crypt
PLoS computational biology 13 (2), e1005400
DOI

2016

R Van Gorder, H Harrington
Reduction of dimension for nonlinear dynamical systems
Nonlinear Dynamics 88 (1)

E Gross, B Davis, KL Ho, DJ Bates, HA Harrington
Numerical algebraic geometry for model selection and its application to the life sciences
Journal of The Royal Society Interface 13 (123), 20160256
DOI

BJ Stolz, HA Harrington, MA Porter
The topological" shape" of Brexit
arXiv preprint arXiv:1610.00752

E Dufresne, HA Harrington, DV Raman
The geometry of sloppiness
arXiv preprint arXiv:1608.05679

D Levy, HA Harrington, RA Van Gorder
Role of seasonality on predator–prey–subsidy population dynamics
Journal of theoretical biology 396, 163-181

HA Harrington, KL Ho, N Meshkat
Differential algebra for model comparison
arXiv preprint arXiv:1603.09730

A Seigal, M Beguerisse-Diaz, B Schoeberl, M Niepel, HA Harrington
Tensors and algebra give interpretable groups for crosstalk mechanisms in breast cancer
arXiv preprint arXiv:1612.08116 1

E Gross, HA Harrington, Z Rosen, B Sturmfels
Algebraic systems biology: a case study for the Wnt pathway
Bulletin of mathematical biology 78, 21-51
DOI

AL MacLean, HA Harrington, MPH Stumpf, HM Byrne
Mathematical and statistical techniques for systems medicine: the Wnt signaling pathway as a case study
Systems Medicine, 405-439

2015

*Taylor D, *Klimm F, Harrington HA, Kramar M, Mischaikow K, Porter MA, Mucha PJ.
Topological data analysis of contagion maps for examining spreading processes on networks
Nature communications 6 (1), 7723 

AL MacLean, Z Rosen, HM Byrne, HA Harrington
Parameter-free methods distinguish Wnt pathway models and guide design of experiments
Proceedings of the National Academy of Sciences 112 (9), 2652-2657

Jonanovic G, Sheng X, Ale A, Feliu E, Harrington HA, Kirk P, Wiuf C, Buck M, Stumpf MPH.
Phosphorelay of non-orthodox two component systems functions through a bi-molecular mechanism in vivo: the case of ArcB
Molecular BioSystems 11 (5), 1348-1359

2014

AL MacLean, HA Harrington, MPH Stumpf, MDH Hansen
Epithelial-mesenchymal transition in metastatic cancer cell populations affects tumor dormancy in a simple mathematical model
Biomedicines 2 (4), 384-402

Michailovici I, Harrington H, Azogui HH, Yahalom-Ronen Y, Plotnikov A, Ching S, Stumpf MPH, Klein OD, Seger R, Tzahor E.
Nuclear to cytoplasmic shuttling of ERK promotes differentiation of muscle stem/progenitor cells
Development 141 (13), 2611-2620

2013

HA Harrington, E Feliu, C Wiuf, MPH Stumpf
Cellular compartments cause multistability and allow cells to process more information
Biophysical journal 104 (8), 1824-1831

HA Harrington, MB Díaz, MP Rombach, LM Keating, MA Porter
Teach network science to teenagers
arXiv preprint arXiv:1302.6567

Chaidos A, Barnes C, Cowan G, May P, Melo V, Hatjiharissi E, Papaioannou M, Harrington H, Doolittle H, Terpos E, Abdalla S, Yarranton H, Naresh K, Foroni L, Reid A, Rahemtulla A, Stumpf M, Roberts I, Karadimitris A.
Clinical drug resistance linked to interconvertible phenotypic and functional states of tumor-propagating cells in multiple myeloma
Blood, The Journal of the American Society of Hematology 121 (2), 318-328

2012

*Harrington HA, *Ho K, Thorne T, Stumpf MPH.
A parameter-free model selection criterion based on steady-state coplanarity
Proc Nat Acad Sci. 2012 Sept;109(39):15746-15751.arXiv:1109.3670.
DOI

Harrington HA, Komorowski M, Beguerisse-Díaz M, Ratto GM, Stumpf MPH.
Mathematical modeling reveals the functional implications of the different nuclear shuttling rates of Erk1 and Erk2
Physical biology 9 (3), 036001

2011

RJ Tanaka, M Ono, HA Harrington
Skin barrier homeostasis in atopic dermatitis: feedback regulation of kallikrein activity
PLoS One 6 (5), e19895

2010

KL Ho, HA Harrington
Bistability in apoptosis by receptor clustering
PLoS computational biology 6 (10), e1000956

2009

Boyle J, Harrington HA, Piper E, Elderfield K, Stark J, Landis RC, Haskard DO.
Coronary intraplaque hemorrhage evokes a novel atheroprotective macrophage phenotype
The American journal of pathology 174 (3), 1097-1108

2008

HA Harrington, KL Ho, S Ghosh, KC Tung
Construction and analysis of a modular model of caspase activation in apoptosis
Theoretical Biology and Medical Modelling 5, 1-15

2007

HA Harrington, M Maier, L Naidoo, N Whitaker, PG Kevrekidis
A hybrid model for tumor-induced angiogenesis in the cornea in the presence of inhibitors
Mathematical and Computer Modelling 46 (3-4), 513-524