1 Interstitial flow pathological states and stem cell delivery in the brain Raghu Raghavan Therataxis LLC JHU Eastern Complex Suite B305 1101 E 33rd St Baltimore MD 21218 USA Abstract A prolonged period of enhanced microvascular permeability resulting in vasogenic edema is a characteristic of several pathological states in the brain We o er a model for interstitial fluid flow in both normal and pathological brain and highlight specific predictions that arise from known features of brain physiology and biomechanics Alteration of brain parenchyma outside the principal site of the pathology is predicted to have a very strong e ect on interstitial flow and upon on how far and with what strength of concentration chemo attractants released at the site of the pathology may travel This arises as a consequence of expansion of the interstitial space and increase in oncotic pressure due to spread of plasma content in the parenchyma surrounding a site of pathology Incorporating these e ects of perilesional edema and concomitant increase of hydraulic conductivity has previously been neglected in models of parenchymal transport of biologically active molecules We present numerical results from our model for a range of flow and movement parameters of chemoattractants of di erent lifetimes correlated with varied states of the interstitial pathology Two robust conclusions in our model are that i the shorter lived chemoattractants have significantly greater concentration gradients that might serve to attract stem cells than long lived ones and ii the alterations of the perilesional interstitium envisaged here make a very significant di erence to the spread ISF in pathological states 1 INTRODUCTION of the chemoattractants 1 Introduction Studies of interstitial fluid ISF and flow separate from though connected to treatments of the cerebrospinal fluid CSF and its flow 1 2 named the third circulation 3 have been coming into their own in recent decades Endogenous interstitial fluid production constitutes a noticeable proportion of the circulating CSF 4 Drainage pathways of the ISF in the perivascular spaces are significant sites of accumulation of plaque in Alzheimer s disease 5 6 7 Indeed these spaces and the brain pulsatility that is manifest at the arterial interface with parenchyma are increasingly being seen as vital in the flow of the interstitial fluid itself see 8 and prior references therein While the white matter tracts have long been known as preferred pathways of migration for primary brain cancer cells more recently the possible role of the ISF flow in assisting this migration has been pointed out 9 10 The tumor interstitium itself interstitium in this paper is abbreviated INTS instead of IS to avoid confusion with the verb is and the e ect of the flows within it in assisting or hampering drug delivery to tumors have been the subject of intense study within the group of Rakesh Jain and his colleagues 11 12 13 14 15 as well as others 16 The role of the ISF in the transport of morphogens has been described 17 and the e ect of morphogen gradients upon tissue formation and growth regulation has been extensively explored 18 19 20 21 Further neural stem cells deposited in the brain move to sites of injury or pathology such as brain cancer 22 stroke of either kind 23 24 presumably due to the chemoattractants for stem cells released by the pathology 25 Particularly in stroke these observations pertain to stem cells injected into the blood stream but we here concern ourselves only with volume transmission or interstitial transport of the cells The movement of endogenous neural stem cells in the adult is known to relate to CSF flow 26 This movement as well as the migration of brain cancer stem cells 27 is presumably related also to ISF flow Indeed ISF flow is of such importance in brain function that it deserves being called the Fourth Circulation ISF in pathological states 1 INTRODUCTION The purpose of this note is to point out an aspect of interstitial flow and its consequences in certain pathological states The treatment is based upon our mathematical model of the physiology and is therefore in need of test and validaton The sections are as follows In the introduction itself we explain the simplified model for the interaction of fluid flow with tissue mechanics that we shall be employing We conclude the introduction with a list of symbols or glossary along with typical values used for the quantities Then the second section is devoted to the model itself and its predictions for fluid flow in the peritumoral INTS more generally the INTS surrounding a central pathology the transport of chemoattractants in the presence of a pathology and finally the resulting chemoattractant concentration gradient that is assumed to be the driver for stem cell chemotaxis Our description of interstitium is complementary to Jain s work in related areas that focuses on the tumor INTS itself which we assume simply as a source of pressure oncotic serum proteins and of chemoattractants We do not treat the INTS within the tumor Based on our description of pathology induced ISF flow we suggest that the chemoattractant associated migration of stem cells that has been noted in the case of particular pathological states involving compromised blood brain barriers BBB or hemorrhages in the brain can be explained only when the alterations in the INTS are accounted for Only then we claim can one understand how chemoattractants move a su cient distance to develop concentration gradients sensed by neural stem cells in for instance the contralateral hemisphere of human sized brains In the next and concluding section we suggest experiments to test our hypotheses and the potential applications and significance of our model if correct Throughout we neglect endogenous interstitial flow that pertains even in the absence of a pathology in a healthy brain An appendix is devoted to our model for endogenous flow and why its neglect in the main body of the paper is justified We then go beyond the steady flow model to examine the rectified e ects of pulsatility where there is an attributable nonlinear rectification e ect of the oscillatory heartbeat Finally we examine whether our model can support the advection of primary brain tumor cells with interstitial fluid flows as proposed by 9 All quantities are in cgs units unless otherwise stated Also we use the following notation ISF in pathological states 2 THE PERITUMORAL INTERSTITIUM Symbol
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