Guidance cues and pattern prediction in the developing retinal vasculature: a combined experimental and theoretical modelling approach

Lead Research Organisation: University of Dundee
Department Name: Mathematics

Abstract

Summary The aim of this project is to use the latest mathematical modelling (MM) techniques coupled with state-of-the-art 3-D imaging to discover how the final patterning of the mouse retinal vasculature plexus (RVP) is regulated in both normally developing mice and mice with severe vascular defects (VEGF-transgenics); similar to those observed to cause a lifetime of blindness in human babies . As the retina grows, its metabolic needs are supported by a 3-D network of blood vessels that form a characteristic pattern of capillary networks linking the arterioles and veins in its different layers. The final structure of the RVP is determined by molecular pathways in the tissue, on which the endothelial cells (the main cell forming the blood vessels) and pericytes (cells which give structural/functional stability to the vessels) migrate. The direction of migration of these cells is dependent on the concentration gradients of both soluble and matrix-associated factors which chemically (chemotaxis) attract the cells towards the rim of the optic cup. Using confocal and 2-photon microscopy (allowing the collection and assimilation of 3-D images of cells, pathways and chemotactic agents) we will examine the retina from different developmental stages of normal and neonatal mice with vascular malformations to discover which molecular pathways and chemotactic agents are critical in determining the patterning and final maturation of the RVP. The images are generated by labelling cells with specific dyes (for instance endothelium with an isolectin called BSI-B4; perictes, with a probe against smooth muscle actin and pathways/chemotactic agents with specific antibodies) exciting the tissue with a laser and capturing the light from the fluorescing dyes with a confocal microscope. As all the images collected in these studies are essentially snapshots of what happens at one particular time during the growth of the RVP, it is essential to be able to overlay these results and discover how the cells respond to the underlying expression patterns of the pathways and chemotactic agents being produced over time (temporally). This is where the powerful tool of MM can lead to new discoveries about how the combination of events (at the tissue, cell and molecular level) are regulated. The first proposed MM will initially rely on data generated from studies performed in normal and VEGF-transgenic neonatal mice. After collecting, digitising and quantitating a series of parameters (i.e. vessel lengths, branch-points, fractal dimension [how often a basic pattern is repeated at different scales], cell-type, location and concentration of molecules) this information is used to inform the MM, so that a virtual model of the RVP can be generated. This MM is then verified and improved, by testing its ability to predict the RVP patterning at later stages during development. Gaps in the biological data (in both the pathways and the chemotactic gradients) can be anticipated by the MM that will then be used to inform biological experiments by proposing new studies which will further elucidate the cellular and molecular mechanisms underlying the development of the 3-D structure of the RVP. This is a unique collaboration between biologists and mathematicians, in which both disciplines are instructive in discovering how a complex 3-D tissue, the RVP, grows and contributes to the final structure of the eye in both normal animals and animals with a serious ocular pathology. The final portion of the project will employ the MM to predict which therapeutic approaches to treat the VEGF-transgenic mice, will prevent progression of ocular pathology. This research will benefit basic biological understanding of how blood vessels grow in 3-D (which determines the growth of all organs), how the eye grows normally and more specifically in ocular conditions characterised by inapprpriate blood vessel formation (all major diseases that cause blindness in neonates and adults).

Technical Summary

The retinal vascular plexus (RVP) is a complex 3-D structure which supports the metabolic demands of a rapidly developing and differentiating retina during neonatal life in mammals. The architecture is tightly regulated by coupling of angiogenic sprout growth along an underlying structural matrix, in response to chemotactic cues which are spatio-temporally resticted during the matruation of the RVP. Since the direct visualization of tissue, cellular, matrix and chemotactic cues in a temporal fashion is currently unattainable, we will combine the latest confocal/2-photon microscopic imaging techniques in 3-D (along with parameterization of these images) with mathematical modelling (MM) in order to generate a temporally-resolved 3-D architecture of the RVP, which recapitulates experimental observations. This should result in a realistic, temporally-defined 3-D vascular growth pattern, which grows along the pathways and responds to chemotactic gradients as defined from the in vivo studies. Initially the MM will entirely rely on data generated from in vivo studies, with verification and improvement of the model being performed. Later iterations of the MM, will be used to inform biological studies (such as focussing on specific chemotactic cues, time-points or indicators of cellular behaviour), thus integrating the biological and MM approaches. This is a unique collaboration between biologists and mathematicians, in which both disciplines are instructive in discovering how a complex 3-D tissue, the RVP, grows and contributes to the final structure of the eye in both normal animals and animals with a serious ocular pathology. Finally, the MM will be used to predict how agents can modify RVP growth in both normal and VEGF-transgenic mice, with one aim being to prevent progression of ocular pathology. This research will benefit basic biological understanding of how blood vessels grow in 3-D (which determines the growth of all organs) and more specifically in the eye.

Publications

10 25 50
 
Description We have discovered that the blood vessel networks (i.e. angiogenesis) which develop during retinal development are controlled by several important factors in the blood flow which prevent the formation of shunt formation. Also very important in order to distribute oxygen throughout the developing network is the concept of "phase separation" which means that when the blood encounters a bifurcation in a vessel, the red blood cells do not split evenly between each branch, but a higher proportion of blood cells goes down one of the vessels.
Exploitation Route Our mathematical model of angiogenesis is state-of-the-art and is capable of making quantitative predictions. Others may use this approach in predicting blood vessel growth in various systems e.g. wound healing, retinal development, tumour-induced angiogenesis.
Sectors Digital/Communication/Information Technologies (including Software),Education,Healthcare,Pharmaceuticals and Medical Biotechnology

URL http://www.smb.org/prizes/segel/citations/2014_best_paper.shtml
 
Description We are currently working with a team at Harvard University, led by Bruce Rosen, Professor in Radiology, Harvard Medical School Director, Athinoula A. Martinos Center for Biomedical Imaging and including also Dr. Thomas S. Deisboeck, Founder and Managing Director of ThinkMotu LLC, an innovation strategy firm in healthcare and life sciences. Our angiogenesis model is being used to predict drug delivery to solid tumours in the brains of mice (gliomas) and to try to optimise drug scheduling to glioma patients.
First Year Of Impact 2015
Sector Healthcare
Impact Types Societal

 
Description European Research Council, Advanced Investigator Award
Amount € 1,690,000 (EUR)
Funding ID 227619 
Organisation European Research Council (ERC) 
Sector Public
Country European Union (EU)
Start 09/2009 
End 08/2014
 
Title Computational model of developing retinal vasculature 
Description A two-dimensional hybrid PDE-discrete model was developed that tracks the migration of individual astrocytes and endothelial tip cells towards the outer retinal boundary of the developing retinal plexus in mice embryos. Blood perfusion is included throughout plexus development and the emergent retinal architectures adapt and remodel in response to various biological factors. 
Type Of Material Model of mechanisms or symptoms - mammalian in vivo 
Provided To Others? No  
Impact The resulting in silico retinal vascular plexus (RVP) structures were compared with whole-mounted retinal vasculatures at various stages of development, and the agreement was found to be excellent. Having successfully bench-marked the model against wild-type data, the effect of transgenic over-expression of various genes was predicted, based on the ocular-specific expression of VEGF-A during murine development. These results can be used to help inform future experimental investigations of signalling pathways in ocular conditions characterised by aberrant angiogenesis. 
 
Title Retinal vasculature 
Description Individual-based model of blood vessel formation during retinal development in mice embryos. Dynamic, adaptive vasculatures. 
Type Of Material Computer model/algorithm 
Provided To Others? No  
Impact Improved predictive ability of the model for vascular diseases in the eye. 
 
Description Mathematical modelling of lymphangiogenesis 
Organisation University of California, Irvine
Country United States 
Sector Academic/University 
PI Contribution Developed a novel hybrid mathematical model of lymphangiogenesis with applications to chemotherapy treatment of solid tumours.
Collaborator Contribution Developed a novel hybrid mathematical model of lymphangiogenesis with applications to chemotherapy treatment of solid tumours.
Impact Wu, M., Frieboes, H.B., McDougall, S.R., Chaplain, M.A.J., Cristini, V., Lowengrub, J. (2013) "The effect of interstitial pressure on tumor growth: Coupling with the blood and lymphatic vascular systems" J. Theor. Biol. 320, 131-151. Wu, M., Frieboes, H.B., Chaplain, M.A.J., McDougall, S.R., Cristini, V., Lowengrub, J.S. (2014) "The effect of interstitial pressure on therapeutic agent transport: Coupling with the tumor blood and lymphatic vascular systems" J. Theor. Biol. 355, 194-207.
Start Year 2010
 
Title Individual-based model of retinal vasculature development 
Description Computational model of blood vessel formation in the developing retina. 
Type Of Technology New/Improved Technique/Technology 
Year Produced 2014 
Impact Improved prediction of the developing retinal vasculature. 
 
Description research talk given to school pupils 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? Yes
Geographic Reach National
Primary Audience Schools
Results and Impact General talk given to schoolchildren as part of the "Meet the Mathematicians" programme in the British Applied Mathematics Colloquium 2011 at Birmingham University.

Talk sparked questions and discussion afterwards and was covered by the media.
Year(s) Of Engagement Activity 2011
URL https://www.youtube.com/watch?v=Ir578ZCZfAA&list=PLA0F0FD1B1350F54D