Modelling of Brain Tissue Mechanical Properties: Bi–Phasic Versus Single–Phase Approach
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Rec ent deve lopme nts in Robot− A ided S ur ger y in par t icul ar , the em er genc e of aut omat ic s ur gica l tool s and r obots as w ell as adva nces in V ir tua l Rea lit y te chnique s, ca ll f or cl ose r exa mina tion of the me chani cal pr oper t ies of br ai n ti ss ue. The ult ima te goal of our r es ea r ch is deve lopme nt of cor r e spondi ng, r ea lis ti c ma them ati cal mode ls . The pape r dis cus s es tw o ca ndidat es f or ti ss ue mode ls : s tanda r d, non− li near , bipha si c and single−phase, non−linear, viscoelastic. The me chani cal beha vior of br ai n ti ss ue is highl y nonli near . The s tr es s − s tr ai n cur ve s ar e conc ave upw ar d cont aini ng no li near por ti on f r om w hich a me aningf ul el as tic modul us mi ght be det er mi ned. The ti ss ue r es pons e s tif f e ns as the loa ding s peed increases, indicating a strong stress−strain rate dependence. The s tanda r d me thods of mode ling ti ss ue as a bipha si c cont inuum f ac e s er ious pr oble ms : s tr ong s tr es s – s tr ai nr ate depe ndence ca n not be ea si ly expl aine d. A ccor di ng to our expe r ime nts , f or br ai n ti ss ue the s tr es s es under f as t loa ding ca n be s ix ti mes highe r tha n thos e under s low loa ding. The r ef or e, the us e of the s ingle − phas e mode l is r ec omme nded. The non–li near , vis coe las ti c mode l, bas ed on s tr ai n ene r gy f unct ion w ith ti me depe ndent coe f f ici ents has bee n deve loped. The ma ter i al cons tant s f or the br ai n ti ss ue have bee n eva luat ed. A gr eem ent bet we en the pr opos ed the or eti cal mode l and expe r ime nt is good f or com pr es si on le vels r ea ching 30% and f or loa ding vel ocit ies var yi ng over f ive or der s of ma gnitude . O ne adva ntage of the pr opos ed cons tit utive mode l is tha t it is not dif f i cult to be em ployed in la r ger e s cal e f ini te el eme nt computations.
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