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Vascular Dimensions oftheCerebral Arteries Follow thePrinciple ofMinimumWork

Vascular Dimensions oftheCerebral Arteries Follow thePrinciple ofMinimumWork,Sandro Rossitti

Vascular Dimensions oftheCerebral Arteries Follow thePrinciple ofMinimumWork  
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Background andPurpose: Theprinciple ofminimumworkisa parametric optimization modelforthe growthandadaptation ofarterial trees. Itestablishes a balance between energy dissipation dueto frictional resistance oflaminar flow(shear stress) andtheminimumvolumeofthevascular system, implying thattheradius ofthevessel isadjusted tothecuberootofthevolumetric flow. Thepurpose of thisstudy istoverify whether theinternal carotid artery systemobeystheprinciple ofminimumwork. Methods: Measurements oftheradius ofparentandbranch segmentsoftheinternal carotid, anterior, andmiddlecerebral arteries were performed on analogangiographs chosenatrandomfroma set classified as normal. Thebranchangles were measured fromlateral projections inbifurcations ofthe anterior cerebral artery. Therelation ofthecalibers ofparentandbranchvessels was analyzed. Results: The area ratioofthebifurcations (N=174)was 1.2±0.4(mean+±SD). The equation (r0)n=(rl)n+(r2) ' was solved forn,resulting inn=2.9+0.7 (mean-+-SD, N=157).Optimumproportions between theradii ofparent(ro) andbranch(r1andr2)vessels intheinternal carotid artery system were verified innormalcarotid angiographs up tofourbranchgenerations, according tothetheoretical equation rj3=r13+r23 (r=0.989, N=174).Noclear correlation was foundbetween themeasured branch angles, therelative branchcross-sectional area,andthetheoretical optimumangles. Conclusions: Thisstudy demonstrates thattheprocessofbranching oftheinternal carotid artery system obeystheprinciple ofminimumwork,as thediameter exponentapproximates 3.Theprinciple of minimumworkestablishes strict functional relations between volumetric flow, flowvelocity, andvessel radius. Thismodel was extended toparametric optimization ofbranch angles, whichhasproved irrelevant intermsoffunctional optimization. Ourresults corroborate this finding. Shearstress-induced endothe- lial mediation seems tobetheregulating mechanism forthemaintenance ofthis optimumvessel design. Themagnitude ofwallshear stress isthesame ateverypoint ina vascular network obeying theprinciple ofminimumwork,because theflowrateinfluences theshearstress proportionally tothethird power of thevessel radius. Thisobservation hasimplications forunderstanding theremodeling ofthecerebral vascular network inthepresenceofarteriovenous malformations andforthepathogenesis ofsaccular aneurysms.(Stroke 1993;24:371-377)
Published in 2010.
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