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Systems biology analysis of vasodynamics in mouse cerebral arterioles during resting state and functional hyperemia.

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Paper

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The authors' code

MATLAB · 363 lines · 9.2 KB · no license

  1. function CubicSplineNetworkNew(G,Q, KStimInd)
  3. A = G.adjacency;
  4. D = normalize(G.Edges.D,'range',[1 8]);
  5. % D=D/10;
  7. % D(G.Edges.Type == 1) = 6;
  8. % % D(G.Edges.Type == 3) = 1;
  9. % % D(G.Edges.Type == 2) = 2;
  10. % D(G.Edges.Type == 3) = 4;
  11. % % D(G.Edges.Type == 4) = 1;
  12. % % D(G.Edges.Type == 5) = 5;
  13. REdges = D;
  15. npts = length(A);
  16. nodenames = cell(1,npts);
  18. npts2 = length(G.Edges.D);
  19. edgenames = cell(1,npts2);
  21. for ii = 1:npts
  22. nodenames{ii} = num2str(ii);
  23. end
  25. for ii = 1:npts2
  26. edgenames{ii} = num2str(ii);
  27. end
  28. xsl_0=25;
  29. % xsl_1=1000;
  30. % x_max=sqrt((xsl_1-xsl_0)^2);
  31. % y_min=sqrt((xsl_1-xsl_0)^2);
  33. AttributeList = ...
  34. {'EndNodes' 'Weight' 'REdges', 'Q'};
  35. edgenod = G.Edges{:,1};
  36. nseg = numedges(G);
  37. EdgeTable = table([edgenod(:,1) edgenod(:,2)],ones(nseg,1),REdges, Q,...
  38. 'VariableNames',AttributeList);
  40. X = G.Nodes.X; Y = G.Nodes.Y; Z = G.Nodes.Z;
  41. NodeTable = table(X,Y,Z,nodenames', 'VariableNames',{'X' 'Y' 'Z' 'nodenames'});
  42. g = graph(EdgeTable,NodeTable);
  43. xyz = [g.Nodes.X, g.Nodes.Y, g.Nodes.Z];
  46. %% remove edges of the nodes with degree higher than 2
  47. % find all nodes with degrees higher than 2
  48. Bif_nodeIDs = find(g.degree>2);
  49. g_modified = g;
  50. for ii = 1:numel(Bif_nodeIDs)
  51. g_modified = g_modified.rmedge(g_modified.outedges(Bif_nodeIDs(ii)));
  52. end
  54. %%
  55. [bins,binsizes] = g_modified.conncomp('outputform','cell');
  56. strands = bins;
  58. %%
  60. remove_indx = [];
  61. badstrands = [];
  63. for ii = 1:numel(strands)
  64. strand = strands{ii};
  65. if isequal(numel(strand), 1)
  66. continue
  67. end
  69. End_nodes = strand((ismember(g_modified.degree(strand),[0,1])));
  70. full_strand = strand;
  71. if ~isempty(End_nodes)
  72. for jj = 1:numel(End_nodes)
  73. Add_Neighbor = intersect(g.neighbors(End_nodes(jj)), Bif_nodeIDs);
  74. full_strand = [Add_Neighbor', full_strand];
  75. end
  76. end
  77. full_strand = unique(full_strand,'stable');
  78. strands{ii} = full_strand;
  80. % check if the order is okay
  81. check = 1;
  82. istrand = strands{ii};
  83. for i = 1:numel(istrand) - 1
  84. nod1 = istrand(i);
  85. nod2 = istrand(i + 1);
  86. iedge = findedge(g, nod1, nod2);
  87. if isequal(iedge, 0)
  88. check = 0;
  89. break
  90. end
  91. end
  93. if check
  94. continue
  95. end
  97. sg = subgraph(g,full_strand);
  99. % find degree ones of the strand
  100. NodeDegrees = sg.degree(1:numel(full_strand));
  101. Deg1Nodes = find(NodeDegrees == 1);
  102. if isempty(Deg1Nodes)
  103. % loop is happening
  104. % remove one egde
  105. nodeIDs = sg.Edges{1,1};
  106. node1 = nodeIDs(1);
  107. node2 = nodeIDs(2);
  108. sg1 = sg;
  109. sg1 = rmedge(sg1,node1,node2);
  110. full_strand = full_strand(shortestpath(sg1,node1,node2));
  111. strands{ii} = full_strand;
  112. continue
  113. end
  114. startNode = Deg1Nodes(1);
  115. new_strand = [startNode];
  116. sg_modified = sg;
  118. while length(new_strand)<length(full_strand)
  119. % find neighbors of start node
  120. neighbor_nodes = sg_modified.neighbors(startNode);
  121. new_strand = [new_strand, neighbor_nodes];
  122. sg_modified = sg_modified.rmedge(sg_modified.outedges(startNode));
  123. startNode = new_strand(end);
  124. end
  125. new_strand = unique(new_strand,'stable');
  126. strands{ii} = full_strand(new_strand);
  128. end
  130. %%
  131. ind = find(binsizes == 1);
  132. count = numel(strands);
  133. for i = 1:numel(ind)
  134. istrand = strands{ind(i)};
  135. if isstring(istrand)
  136. strand = str2double(istrand);
  137. else
  138. strand = istrand;
  139. end
  140. Add_Neighbor = g.neighbors(strand);
  141. for j = 1:numel(Add_Neighbor)
  142. count = count + 1;
  143. strands{count} = [strand, Add_Neighbor(j)];
  144. end
  145. end
  147. %% plot with cubic spline
  149. disp('plotting.......')
  150. tic
  151. CubicSplineFig = figure;
  152. CubicSplineFig.WindowState = 'maximized';
  153. % set(gca, 'ZDir','reverse')
  154. set(gcf, 'visible','off');
  155. hold all
  157. n = 30; % number of faces for tubes
  158. inner_points = 3; % number of points in the axial direction for each segment
  160. errcount = 0;
  161. errs = [];
  162. count = 1;
  164. for s = 1:length(strands)
  166. strand = strands{s};
  167. if numel(strand) == 1
  168. continue
  169. end
  171. XYZ = xyz(strand,:)';
  172. cs = cscvn(XYZ);
  173. for ii = 1:length(cs.breaks) - 1
  174. nod1 = strand(ii);
  175. nod2 = strand(ii + 1);
  176. iedge = findedge(g, nod1, nod2);
  177. if length(iedge) == 2
  178. iedge=iedge(1);
  179. end
  181. if iedge == 0
  182. errcount = errcount + 1;
  183. errs = [errs, s];
  184. continue
  185. else
  186. rval = g.Edges.REdges(iedge);
  187. strandQ = g.Edges.Q(iedge);
  188. end
  189. xtest = linspace(cs.breaks(ii),cs.breaks(ii+1),inner_points);
  190. ytest = linspace(cs.breaks(ii),cs.breaks(ii+1),inner_points);
  191. ztest = linspace(cs.breaks(ii),cs.breaks(ii+1),inner_points);
  193. ctestx = 0;
  194. ctesty = 0;
  195. ctestz = 0;
  197. for jj = 1:cs.order
  198. ctestx = ctestx + cs.coefs((ii-1)*3+1,jj)*(xtest - cs.breaks(ii)).^(cs.order - jj);
  199. ctesty = ctesty + cs.coefs((ii-1)*3+2,jj)*(ytest - cs.breaks(ii)).^(cs.order - jj);
  200. ctestz = ctestz + cs.coefs((ii-1)*3+3,jj)*(ztest - cs.breaks(ii)).^(cs.order - jj);
  201. end
  203. [X,Y,Z] = tubeplot([ctestx;ctesty;ctestz],rval,n,0);
  204. h = surface(X,Y,Z,'edgecolor','none');
  205. all_hs(count) = h;
  206. allEdgeIDs(count) = iedge;
  207. count = count + 1;
  210. end
  211. end
  213. fig = figure(CubicSplineFig);
  214. fig.Color = 'w';
  216. % shading interp
  217. view(44,6)
  218. brighten(1)
  221. map = jet;
  222. colormap(map)
  223. % caxis([0 5])
  224. caxis([min(g.Edges.Q) max(g.Edges.Q)])
  226. ax = gca;
  227. ax.Color = 'k';
  228. ax.LineWidth = 1;
  229. ax.FontSize = 16;
  230. ax.FontName = 'arial';
  231. ax.FontWeight = 'bold';
  232. ax.XTick = [];
  233. ax.YTick = [];
  234. ax.ZTick = [];
  235. axis image;
  236. axis equal
  237. toc
  239. %% assign color for edges
  240. for i = 1:numel(all_hs)
  241. h = all_hs(i);
  242. iedge = allEdgeIDs(i);
  243. strandQ = g.Edges.Q(iedge);
  244. h.CData = strandQ*ones(size(h.ZData));
  245. end
  247. %% add spheres at stimulated nodes
  248. stimNodes = KStimInd;
  249. for i = 1:length(stimNodes)
  250. nodeID = stimNodes(i);
  251. rs = 3*mean(g.Edges.REdges); % radius for the sphere representing the cells
  253. [Xs,Ys,Zs] = sphere(10);
  255. Xs = rs*Xs + g.Nodes.X(nodeID);
  256. Ys = rs*Ys + g.Nodes.Y(nodeID);
  257. Zs = rs*Zs + g.Nodes.Z(nodeID);
  259. h = surf(Xs,Ys,Zs,'linestyle','none');
  260. h.FaceColor = 'w';
  261. end
  263. %% add text( Edge number) at Edges
  264. % % for i = 1:length(G.Edges.D)
  265. % % nodeID1 = G.Edges.EndNodes(i,1);
  266. % % nodeID2 = G.Edges.EndNodes(i,2);
  267. % %
  268. % % Xs = ((G.Nodes.X(nodeID1)+G.Nodes.X(nodeID2))/2);
  269. % % Ys = ((G.Nodes.Y(nodeID1)+G.Nodes.Y(nodeID2))/2);
  270. % % Zs = (G.Nodes.Z(nodeID1)+G.Nodes.Z(nodeID2))/2;
  271. % %
  272. % % text(Xs,Ys,Zs,edgenames{i},'Color','w','FontSize',3,'FontWeight','bold');
  273. % % end
  274. % view(2)
  275. colorbar
  276. end
  278. function [x,y,z]=tubeplot(curve,r,n,ct)
  279. % Usage: [x,y,z]=tubeplot(curve,r,n,ct)
  280. %
  281. % Tubeplot constructs a tube, or warped cylinder, along
  282. % any 3D curve, much like the build in cylinder function.
  283. % If no output are requested, the tube is plotted.
  284. % Otherwise, you can plot by using surf(x,y,z);
  285. %
  286. % Example of use:
  287. % t=linspace(0,2*pi,50);
  288. % tubeplot([cos(t);sin(t);0.2*(t-pi).^2],0.1);
  289. % daspect([1,1,1]); camlight;
  290. %
  291. % Arguments:
  292. % curve: [3,N] vector of curve data
  293. % r the radius of the tube
  294. % n number of points to use on circumference. Defaults to 8
  295. % ct threshold for collapsing points. Defaults to r/2
  296. %
  297. % The algorithms fails if you have bends beyond 90 degrees.
  298. % Janus H. Wesenberg, july 2004
  300. if nargin<3 || isempty(n), n=8;
  301. if nargin<2, error('Give at least curve and radius');
  302. end;
  303. end;
  304. if size(curve,1)~=3
  305. error('Malformed curve: should be [3,N]');
  306. end;
  307. if nargin<4 || isempty(ct)
  308. ct=0.5*r;
  309. end
  312. %Collapse points within 0.5 r of each other
  313. npoints=1;
  314. for k=2:(size(curve,2)-1)
  315. if norm(curve(:,k)-curve(:,npoints))>ct;
  316. npoints=npoints+1;
  317. curve(:,npoints)=curve(:,k);
  318. end
  319. end
  320. %Always include endpoint
  321. if norm(curve(:,end)-curve(:,npoints))>0
  322. npoints=npoints+1;
  323. curve(:,npoints)=curve(:,end);
  324. end
  326. %deltavecs: average for internal points.
  327. % first strecth for endpoitns.
  328. dv=curve(:,[2:end,end])-curve(:,[1,1:end-1]);
  330. %make nvec not parallel to dv(:,1)
  331. nvec=zeros(3,1);
  332. [buf,idx]=min(abs(dv(:,1))); nvec(idx)=1;
  334. xyz=repmat([0],[3,n+1,npoints+2]);
  336. %precalculate cos and sing factors:
  337. cfact=repmat(cos(linspace(0,2*pi,n+1)),[3,1]);
  338. sfact=repmat(sin(linspace(0,2*pi,n+1)),[3,1]);
  340. %Main loop: propagate the normal (nvec) along the tube
  341. for k=1:npoints
  342. convec=cross(nvec,dv(:,k));
  343. convec=convec./norm(convec);
  344. nvec=cross(dv(:,k),convec);
  345. nvec=nvec./norm(nvec);
  346. %update xyz:
  347. xyz(:,:,k+1)=repmat(curve(:,k),[1,n+1])+...
  348. cfact.*repmat(r*nvec,[1,n+1])...
  349. +sfact.*repmat(r*convec,[1,n+1]);
  350. end;
  352. %finally, cap the ends:
  353. xyz(:,:,1)=repmat(curve(:,1),[1,n+1]);
  354. xyz(:,:,end)=repmat(curve(:,end),[1,n+1]);
  356. %,extract results:
  357. x=squeeze(xyz(1,:,:));
  358. y=squeeze(xyz(2,:,:));
  359. z=squeeze(xyz(3,:,:));
  361. %... and plot:
  362. if nargout<3, surf(x,y,z); end;
  363. end

CubicSplineNetworkNew.m at commit 6c46349, no license · at the source

Overview

Authors: Hadi Esfandi1,2, Mahshad Javidan1,2, Eric R. McGregor2, Rozalyn M. Anderson2,3, Ramin Pashaie1
ORCID iDs: Ramin Pashaie
  1. Department of Electrical Engineering and Computer Science, Florida Atlantic University, Boca Raton, Florida, United States of America
  2. Department of Medicine, University of Wisconsin-Madison, Madison, Wisconsin, United States of America
  3. Geriatric Research, Education, and Clinical Center, William S. Middleton Memorial Veterans Hospital, Madison, Wisconsin, United States of America
Institutions: Florida Atlantic University (United States); University of Wisconsin–Madison (United States)
Journal: PLoS computational biology, volume 22, issue 4, article e1013113
Dates: received 5 May 2025; accepted 4 April 2026; published online 27 April 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1371/journal.pcbi.1013113 · PMID 42044149 · PMCID PMC13138759 · OpenAlex W4410253551
Open access: gold, a free copy (OpenAlex)
Preprint: doi:10.1101/2025.05.06.652356
Status: code verified
Categories: computational modeling (no new data) (modality), mouse (organism), stroke (population)
Methods: Connectivity
MeSH: Cerebrovascular Circulation*, Hyperemia*, Models, Cardiovascular*, Systems Biology*, Animals, Arterioles, Astrocytes, Computer Simulation, Mice, Vasoconstriction, Vasodilation (* major topic)
Journal subjects: Biology and Life Sciences, Physiology, Electrophysiology, Membrane Potential, Medicine and Health Sciences, Vascular Medicine, Vasodilation, Hematology, Hemodynamics, Cell Biology, Cellular Types, Animal Cells, Glial Cells, Macroglial Cells, Astrocytes, Hyperpolarization, Anatomy, Body Fluids, Blood, Blood Flow, Cardiovascular Anatomy, Blood Vessels, Arterioles, Biophysics, Ion Channels, Potassium Channels, Physical Sciences, Physics, Neurophysiology, Neuroscience, Biochemistry, Proteins
Topic: Neurological Disease Mechanisms and Treatments (Neurology, Neuroscience), according to OpenAlex
Funding: NIH (R01AG067330); NSF (2154267, 1830145); Army Research Office (US) (W911NF1810323)
Citations: not cited yet (Europe PMC); 182 references in the paper

Abstract

Cerebral hemodynamics is tightly regulated by arteriolar vasodynamics. In this study, a systems biology approach was employed to investigate how the interplay between passive, myogenic, neurogenic, and astrocytic responses shapes arteriolar vasodynamics in small rodents. A model of neurovascular coupling is proposed in which neurons inhibit and dampen the myogenic response to promote vasodilation during activation, and facilitate the myogenic response to promote rapid vasoconstriction immediately post-activation. In this model, inhibition of the myogenic response is mediated by the hyperpolarization of smooth muscle and endothelial cells. Dampening and facilitation of the response are mediated by neuronal production of nitric oxide and release of neuropeptide Y, respectively. We also introduce a model for gliovascular coupling, in which astrocytes periodically inhibit the myogenic response upon detecting an increase in myogenic activity through interactions between their endfeet and arterioles. Our simulations suggest that in the resting state, delays in myogenic autoregulation can intrinsically generate low-frequency (∼0.1 Hz) oscillations in vessel diameter (vasomotion), in the absence of extrinsic neurogenic or systemic rhythmic inputs. In the active state, these oscillations are disrupted by the neurogenic and astrocytic responses. The biophysical model of arteriolar vasodynamics presented in this study lays the foundation for quantitative analysis of cerebral hemodynamics for cerebrovascular health diagnostics and hemodynamic neuroimaging.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above.

hesfandi/Mouse-cerebral-Arteriolar-vasodynamics_Model

License: none: the authors keep all their rights
State: the link answers, verified on 30 September 2026
Evidence: files inventoried
Commit: 6c46349b42dccbb6628c6e9a5aadbda60db8de47, 17 February 2026
Languages: MATLAB (41)
Size: 50 files, 41 scripts
Software Heritage: not archived
Found in: “Data Availability”
Holds: README
Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 30 September 2026: the link answers
  • 30 September 2026: the link answers
42 files
At the source: github.com/hesfandi/Mouse-cerebral-Arteriolar-vasodynamics_Model

The paper's code and data availability statement is in the Data section.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 41 scripts, each with its path and the digest of its content;
  • no match between paragraphs and code yet;
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Data Availability

All data supporting the findings of this study are publicly available. The two-photon microscopy imaging data of arteriolar vasodynamics and electrophysiological signals used in this study were obtained from previously published sources cited in the manuscript. All simulation scripts developed for this work are available at: https://github.com/hesfandi/Mouse-cerebral-Arteriolar-vasodynamics_Model.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 5 authors, 11 MeSH terms, 3 funders, 179 references.

Cite

This paper

Esfandi, H., Javidan, M., McGregor, E. R., Anderson, R. M., & Pashaie, R. (2026). Systems biology analysis of vasodynamics in mouse cerebral arterioles during resting state and functional hyperemia. PLoS computational biology, 22(4), e1013113. https://doi.org/10.1371/journal.pcbi.1013113

BibTeX

@article{esfandi2026systems,
author = {Esfandi, Hadi and Javidan, Mahshad and McGregor, Eric R. and Anderson, Rozalyn M. and Pashaie, Ramin},
title = {{Systems biology analysis of vasodynamics in mouse cerebral arterioles during resting state and functional hyperemia}},
journal = {PLoS computational biology},
year = {2026},
month = apr,
volume = {22},
number = {4},
pages = {e1013113},
publisher = {PLOS},
issn = {1553-734X},
doi = {10.1371/journal.pcbi.1013113},
url = {https://doi.org/10.1371/journal.pcbi.1013113},
pmid = {42044149},
pmcid = {PMC13138759}
}

RIS

TY - JOUR
AU - Esfandi, Hadi
AU - Javidan, Mahshad
AU - McGregor, Eric R.
AU - Anderson, Rozalyn M.
AU - Pashaie, Ramin
TI - Systems biology analysis of vasodynamics in mouse cerebral arterioles during resting state and functional hyperemia
T2 - PLoS computational biology
J2 - PLoS Comput Biol
PY - 2026
DA - 2026/04/27
VL - 22
IS - 4
SP - e1013113
SN - 1553-734X
PB - PLOS
DO - 10.1371/journal.pcbi.1013113
UR - https://doi.org/10.1371/journal.pcbi.1013113
LA - en
ER -

CSL-JSON

{
"id": "10.1371/journal.pcbi.1013113",
"type": "article-journal",
"title": "Systems biology analysis of vasodynamics in mouse cerebral arterioles during resting state and functional hyperemia",
"container-title": "PLoS computational biology",
"author": [
{
"family": "Esfandi",
"given": "Hadi"
},
{
"family": "Javidan",
"given": "Mahshad"
},
{
"family": "McGregor",
"given": "Eric R."
},
{
"family": "Anderson",
"given": "Rozalyn M."
},
{
"family": "Pashaie",
"given": "Ramin"
}
],
"container-title-short": "PLoS Comput Biol",
"volume": "22",
"issue": "4",
"page": "e1013113",
"DOI": "10.1371/journal.pcbi.1013113",
"PMID": "42044149",
"PMCID": "PMC13138759",
"ISSN": "1553-734X",
"publisher": "PLOS",
"URL": "https://doi.org/10.1371/journal.pcbi.1013113",
"language": "en",
"issued": {
"date-parts": [
[
2026,
4,
27
]
]
}
}

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