1Interstitial flow,pathologicalstatesandstemcelldelivery in the brainRaghu Raghav anTherataxis, LLC, JHU Eastern Complex, Suite B305, 1101 E. 33rd St., Baltimore MD 21218,USAAbstract.A prolonged period of enhanced microvascular permeability resulting in vasogenic edema isa characteristic of several pathological states in the brain. We offer a model for interstitial fluidflow in both normal and pathological brain, and highlight specific predictions that arise fromknown features of brain physiology and biomechanics. Alteration of brain parenchyma outsidethe principal site of the pathology is predicted to have a very strong effect on interstitial flow,and upon on how far and with what strength of concentration chemo-attractants releasedat the site of the pathology may travel. This arises as a consequence of expansion of theinterstitial space and increase in oncotic pressure due to spread of plasma content in theparenchyma surrounding a site of pathology. Incorporating these effects of perilesional edema,and concomitant increase of hydraulic conductivity, has previously been neglected in models ofparenchymal transport of biologically active molecules. We present n umerical results from ourmodel for a range of flow and movement parameters of chemoattractants of different lifetimescorrelated with varied states of the int erstitial pathology. Two robust conclusions in ourmodel are that: (i) the shorter lived chemoattractants have significantly greater concentrationgradients that migh t serv e to attract stem cells than long—lived ones, and (ii) the alterationsof the perilesional interstitium envisaged here make a very significant difference to the spreadISF in pathological states 1 INTRODUCTIONof the chemoattractan ts.1. IntroductionStudies of in terstitia l fluid (ISF) and flow, separate from (though connected to) treatments ofthe cerebrospina l fluid(CSF)anditsflow [1], [2] – named the third circulatio n [3] – have beencoming into their ow n in recent decades. Endog enou s interstitial fluid production constitutesa noticeable proportion of the circulating CSF [4]. Drainage path ways of the ISF in theperivascular spaces are significa nt sites of accumulation of plaqu e in Alzh eimer’s disease [5], [6],[7]. Indeed these spaces and the brain pulsatility tha t is manifest at the arterial interface withparenchyma are increasingly being seen as vital in the flow of the interstitial fluid itself (see [8]and prior references therein). W hile the white matter tracts have long been know n as preferredpathways of migration for primary brain cancer cells, more recently the possible role of the ISFflow in assisting this m igration has been poin ted ou t [9], [10]. The tum or interstitium itself(in terstitiu m in this paper is abbreviated INTS instead of IS to avoid confusion with the v e rbis), and the effect of the flo w s with in it in assisting or hampering drug deliv ery to tumors, ha vebeen the subject of intense study within the group of Rakesh Jain and his colleagues [11], [12],[13], [14], [15], as w ell as others [16]. The role of the ISF in the transport of mor phogen s hasbeen described [17], and the effect of morphogen gradien ts upon tissue formation and growthregulation has been exte nsively explored [18], [19], [20], [21]. Further, neural stem cellsdeposited in the brain move to sites of injury or pathology such as brain cancer [22], strok e ofeither kind [23], [24], presumably due to the c hemoattractants for stem cells released b y thepathology [25]. (P ar ticularly in stroke these observations pertain to stem cells injected intothe blood stream , but we here concern ourselv es only with volume transmission, or in terstitia ltransport, of the cells.) The movement of endog eno us neural stem cells in the adult is knownto relate to CSF flo w [26]. This movem ent, as well as the migration of brain cancer stem cells[27], is presumably related also to ISF flow. Indeed, IS F flow is of such importance in brainfunction that it deserv es being called the Fourth Circulation.2ISF in pathological states 1 INTRODUCTIONThe purpose of this note is to point out an aspect of in terstitial flow and its consequencesin certain pathological states. The treatm ent is based upon our mathematical m odel of thephysio logy, and is therefore in need of test and validaton. The sections are as follo w s. In theintroduction itself, w e explain the simp lified model for the in teraction of fluid flow with tissuemechanics that we shall be emplo ying. We conclude the in troduction with a list of symbols, orglossary, alon g with typical values used for the quantities. Then the second section is dev otedto the model itself and its predictions for fluid flo w in the peritumoral INTS (more generally,the INT S surrounding a cen tr al path ology), the transport of c hemoattracta nts in the presenceof a pathology, and finally the resulting c hemoattractan t concentration gradient that is assumedto be the driv e r for stem cell chemotaxis. Our description of in terstitium is complem entary toJain’s work in related areas that focuses on the tum o r INT S itself, which we assume simply asa source of pressure, oncotic (serum ) proteins, a nd of chem oattractants. We do not treat theINTS within the tumor. Based on our description of pathology-induced ISF flow, we suggestthat the chemoattractant-associated m igratio n of stem cells that has been noted in the case ofparticular pathological states involving compr om ised blood-brain barriers (BBB ) or hemorr hagesin the brain can be exp lained only when the alterations in the INTS ar e accounted for. On lythen, w e claim, can one understand how ch emo attractants m ove a sufficien t distance to developconcentration gradients sensed by neural stem cells in, for instance, the contralateral hemisphereof hum an-sized brains. In the next and concluding section, w e suggest experiments to test ourh y potheses, and the potentia l applications and significance of our model, if correct. Througho ut,w e neglect endogenous interstitial flow that pertains ev en in the ab sence of a pa tholog y in ahealth y brain. An appendix is devo ted to our model for endogenous flo w, and why its neglectin the main body of the paper is justified. We then go beyond the steady flo w model to examinethe rectified effe cts of pulsa tility, where there is an attributable , nonlinear rectification effect ofthe oscillatory heartbeat. Finally, we examine whether our model can support the
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