Protein in Alzheimer Disease

Transcription

1 Reserch Article imedpub Journls Nno Reserch & Applictions ISSN Vol.4 No.:6 DOI: 11767/ Abstrct Theoreticl Clcultion for Removing Tu Protein in Alzheimer Disese Alzheimer's disese (AD) is the most prevlent form of dementi, which ffects people older thn 6 yers nd cuse suffering for more thn 44 million over the world. Plques formtion is one of the first step in the tretment of this illness. The elimintion of the ccumultion of these plques by using the resonnce oscilltion nd het production of ultrsound s bubble cn reduce the side effect of the neurodegenertive disese. In this pper, the resonnce frequency is clculted precisely s function of the required rdius, which is the sme s the rdius of the plques in the brin. The results re in good greement with experimentl dt nd just hve negligible percentge error, less thn.67%. These results cn help in modeling ccurte frequency for mechnicl tretment before in vivo tretment which cn reduce the hrmful side effects nd other helthy cells dmge. Keywords: Alzheimer's disese; Tu protein; Bubble; Ultrsound; Resonnce frequency Behrouz AH, Zreyi H*, Zhour K, Tshori SH nd Vezzdeh M Fculty of Science, Deprtment of Physics, K.N. Toosi University of Technology, Tehrn, Irn *Corresponding uthor: Zreyi H zreyi.h@mil.ntu.c.ir Fculty of Science, Deprtment of Physics, K.N. Toosi University of Technology, Tehrn, Irn. Tel: Received: July 13, 18; Accepted: September 3, 18; Published: September 6, 18 Introduction The Alzheimer disese ws first described by Alois Alzheimer [1]. This illness is processed by formtion of the plques in the brin of the ptient [,3]. Mny vrious methods hve been presented for treting this disese. In spite of the big effort in understnding this illness, few effective tretments nd cures hd been reported []. The recent proposls for solving this problem is not only biologicl method, but lso it tes its wy to physics. One of the most importnt dilemms tht hs been fced is the impermebility of the Blood-Brin Brrier (BBB) [4]. Recently, bubbles produced by focused ultrsound wve bring new methods for pplying sfe, effective, noninvsive nd locl penetrtion in the brin. These bubbles contribute in drug delivery nd removing the plques [5]. The formtion of the ging plques is the most crucil fctor in ppering the AD. These plques form the concentrtion of Amyloid Bet (Aβ) Peptide [6]. Destructive coopertion of these plques strts from the Hippocmpus tht is responsible to form memories, [7,8] s consequence the loss of temporry memory will be the first sign of this disese. After tht, the mutted proteins will ttc the other prts of the brin incresingly leding to specific ltertion of the disese process. The effect of these proteins is relted to the loction of their gthering plce in the brin, for exmple if the proteins re ccumulted in the front prt of Cittion: Behrouz AH, Zreyi H, Zhour K, Tshori SH, Vezzdeh M (18) Theoreticl Clcultion for Removing Tu Protein in Alzheimer Disese. Nno Res Appl Vol.4 No.:6 the brin, the proteins will nnihilte logicl thining bility nd then the feeling control prt which cuse n extreme ltertion in temperment of the ptient, while the ccumultions on the upper prt cn cuse illusion nd prnoi. If the plques rech to the bc of the brin, they remove the deepest memories of the ptient forever. The min reson of neurl string contortion in the AD is Tu protein. Brin neurl cells hve pssges networ tht crries molecules supply. In conditionl mode, Tu protein s role is to me sure this pssge wors properly, but in the of AD, Tu proteins will be trpped in the contortion strings nd the pssges will collpse. Consequently, scientists declre tht AD is cused by deposition of Aβ in plques in brin tissue s shown in Figure 1. Finding hrmless wy for opening the strings is essentil. One of these wys is pplying ultrsound wves. Ultrsound wves re used for scnning inside the body, by using this high frequency sonic wves physicin re ble to crete imges of vrious prt inside the body which is very helpful detecting diseses inside the humn body, nd ctully they my help in the tretment of Alzheimer's disese [9]. However, the min problem is tht thin Under License of Cretive Commons Attribution 3. License This rticle is vilble in: 1

2 ISSN ISSN Vol.4 No.:6 shield of cells, clled Blood Brin Brrier (BBB), protects the brin nd it is very difficult to be crossed by things lie therpeutics or helpful ntibodies. Recent studies showed tht focused sound wves open the blood-brin brriers nd llow the delivery of drugs to the dmged cells in order to chieve gin norml function of brin cells [1]. Since this method hs been the only wy to produce reversible BBB disruption without brin tissue dmge, it hs been extensively investigted by severl reserch groups. Focused ultrsound wves hve the bility to destruct precisely, predetermined volume of chosen tissue without ffecting to other surrounding tissues [11]. This technique is improved in recent decdes to increse the precision nd reduce the side effects [1]. The bltion with ultrsound nd enhncing ultrsound heting effect re importnt pplictions of ultrsound tretment [13,14]. This method genertes cvittion for heting to mtch the cvittion clouds with the heting ptterns for tretment [15] especilly for brin disese nd neurologicl purpose [16,17]. Combining ultrsound with hrmless microscopic bubbles, s ultrsound contrst gents, could be n effective detecting technique. In ddition, the sound wves cuse the bubble to vibrte nd expnd, which cuse friction then explosion tht led to mechnicl impct on the surrounding [18]. The incresing temperture generted in the mbient due to the friction ffects the cell membrne nd the Tu proteins, which cn led to destroy them. The purpose of this wor is to understnd the mechnicl effect of ultrsound recting with the surrounding nd to investigte its pproprite frequency [19] by modeling nd mthemtics, becuse it is the wy for better illustrtion of the methods before tretments. Physicl chrcteristics of biologicl tissue enforce bubble formtion during the propgtion of ultrsound wve, this cse cn lso be studied by modeling nd simultion [-]. Becuse of the bubbly shpe of these proteins, this model is bsed on bubble formtion, nd then these mechnicl effects re considered. Moreover, the effect of the pressure on resonnce frequency hs been investigted in order to chieve more ccurte results. This model helps in treting the diseses with the less side effect nd clculte the more convenient frequency to del with the sitution. This pper focus on the experimentl study ccomplished by Leineng [19] nd coworers to obtin n ccurte theoreticl model tht it bsed on their wor. Our clcultion is bout bubble model surrounded by liquid. Models nd Equtions Minnert M showed tht the bubbles formed when ir escpes from n orifice within flu would give sound by pulstion, becuse ech pulse mes smll cvity in the wter tht it mes sound when closed [3,4]. In this model, the rigid wlls of the bubbles ct s resontor. Therefore, it hs frequency nd it hs been determined s: 1 3 P f = γ π ρ (1) Where is the bubble rdius, P is the mbient pressure, γ is n dibtic index for wter nd ρ is the density of the mbient [4]. The experimentl dt for bubble-lipid shell nd Tu protein hve been obtined from Leineng nd co-worers wor [19]. In this study, we considered 4 μm for bubble rdius, 1.3 for dibtic index in 1 tm pressure, 1.35 g/cm 3 for density. By replcing these vlues in eqution (1) we cn obtin tht the ccurte frequency: 6 f = Hz which is very close to the experimentl dt tht ws reported s.7 MHz. The reltive error percentge for this clcultion is bout.13%. For more ccurte investigtion nother formul is considered, which is one of the best methods for describing the ultrsonic wves in liquid compressibility, this formul ws presented by Figure 1 () Brin s cells in the norml cse nd (b) Shows the ccumultion of protein between these cells which decrese the connections between these cells nd ffect their function. This rticle is vilble in:

3 ISSN ISSN Vol.4 No.:6 Incident ultrsound wve Creted bubble surrounding the protein s ccumultion ccumultion Vibrtion Explosion Figure Cretion of bubble tht surround the protein s ccumultion using n incident ultr sound wve, nd the two possible cses tht cn te plce: Vibrtion or explosion. Keller [5]. This study focuses on Tus proteins, which belongs to group of Microtubules-Associted proteins. For modeling in this sitution disc-shped tretment of Aβ folding is considered [6]. In order to pply ultrsound tretments, micro bubbles must be developed. These bubbles re gs trpped in lipid shell. The bubble will contrct t the frequency of the propgting coustic wve when it psses through the tissue tht exposed to ultrsound, becuse of the cyclic pressure rdition. Consequently, the bubble will strt to oscillte nd forces the surrounding fluid to flow, where the force of the spreding wve is rdil. When the bubble oscilltion mplitude becomes so lrge, nd fter exceeding specific threshold, the bubble will collpse due to the stress pplied by the surrounding fluid, consequently shoc wve will propgte t supersonic speed rdilly from the collpsed site which led to the production of high temperture nd the increse of pressure drmticlly. The frequency of the incident ultrsound wve cretes bubble tht hs the sme dimension of protein s ccumultion nd t the sme time it cuses resonnce vibrtion of the creted bubble. This vibrtion led to increse the temperture due to friction which leds to dmge the Aβ protein. On the other hnd, the bubble cn collpse under effect of the shoc wve introduced by the ultrsound wve which led to mechnicl impct nd consequently the explosion of the ccumultion (Figure ). The coustic field pressure eqution () t the loction of the bubble will be considered s sinusoidl function. P(t) is the ultrsound pressure driving modeled s sptilly homogeneous stnding sound wve with sinusoidl function: Pt ( ) = Pcos( ω t) () d Where p is the pressure mplitude tht is bout 1 to 1 tm nd ω d is the driving ngulr frequency. Recent wors hve shown tht mny fetures of the bubbles cn be expressed within hydrodynmic pproch [7], especilly the bubbles stbility dependence on experimentl prmeters. Furthermore, the Under License of Cretive Commons Attribution 3. License nlysis of bubble wll dynmics gives mny importnt properties. These dynmics re conventionlly described by the Ryleigh- Plesset eqution. A lot of improvement hd been presented for the modeling of the sphericl domin wlls dynmics in liquids, fter Lord Ryleigh modeled the collpse of n empty cvity in liquid. Plesset presented the min step. This step declres the expression of vrible externl driving pressure nd the effect of surfce tension on the bubble dynmics (1949). Nvier-Stoes equtions re utilized for the bubble rdius clcultion with ordinry differentil eqution (ODE) [8]: 3 1 R d R RR σ + R = [ PRt (, ) Pt ( ) P] + [P(R, t) P(t)] 4υ C dt R R (3) ρ ρw w ρw where P(R,t) is the pressure on the liquid side of the interfce, P(t) is the imposed coustic field pressure evluted t the loction of the bubble, P is the sttic mbient pressure, R is the speed of the bubble wll, C w is the sound speed of the liquid nd ρ w is the lipid density, in this cse the surfce tension, σ, will te the vlue of 1.35 g/cm [9]. The bubble moves slowly with respect to the sound velocity in the gs. The pressure in the gs, throughout the bubble, is uniform. In this cse the pressure depends on the bubble volume nd the het trnsfer cross the bubble wll which is produced by friction due to the bubble oscilltion [3]. The clcultion of the pressure cross nd ner the bubble wll cn be given by dopting this reltion s simplified model: σ R h PRt (, ) = (P + )( ) R R h Which is ssumed to obey vn der Wls type process eqution, where R being the mbient bubble rdius, h is the hrd-core vn der Wls rdius nd P is 1 tm [31]. It is necessry to mention tht Eqution (4) presupposes homogeneity of the pressure inside the bubble. h is given by the following reltion. R h = (5) 8.54 (4) 3

4 ISSN ISSN Vol.4 No.:6 Since the velocity of sound in wter is high, the differentil prt of the Ryleigh-Plesset eqution cn be disregrded. And since the rdius is lrge, R 3 h 3, the excluded volume h 3 cn be neglected in the Vn Der Wls formul, therefore Eqution () cn be replced by the idel gs lw under isotherml conditions. Considering the resonnce condition, the bubble rdius will rech its mximum vlue. Therefore, we cn consider tht R (t) =R (1+x(t)) nd by replcing it in eqution (3) the resonnce frequency cn be obtined. The conventionl elstic pendulum model hd been used in this eqution where the oscilltions te plce long the X direction. 3 1 σ R h R (1 + xx ) + R = P + Pcos( ) 3 ωt P ρ R (6) σ 4υ 1 + x ρ R (1 + x ) w Eqution (6) is rewritten s below: 3 x 1 σ R h x= = P + cos( ) 3 p ωt P (1 + x) ρr (1 + x) R (7) σ 4υ 3 w As mentioned before R 3»H 3, 3 so we te R - h R nd Eqution (7) could be rewritten s: 1 σ R h 3 x= P + cos( ) 3 p ωt P ρr (1 + x) R (1 + x) (8) σ 4υ 3 w Therefore, the following eqution cn be obtined: 1 σ 3 3 x= P + (1 + x) pcos( ωt) P ρr (1 + x) R (1 + x) σ 4υ 3 w Furthermore, ll used equtions re for stnding wves creted in finite volume. The initil vlue of bubble rdius is ssumed to be between 1 nd 5 μm nd the sound speed in wter is 1481 m/s [3]. By integrting Eqution (9) with respect to time, the velocity of the wlls is obtined: V P σ σ = + (1 + x) + ( pcos( ωt) + P)( In(1 + x)) ρr R 3 ρwr(1 + x) (1) For x= nd P =, nd by eliminting ll the squred x nd its derivtives terms in eqution (9). (9) P x+ γ + ω x= cos( ω t) (11) ρr Where γ = ʋ/r is the dmping fctor for the lipid shells. 1 σ ω = 3 P + (3 1) ρr R ω =.749MHz (1) With R = (unit) nd =1.3 (unit) nd the resonnce frequency by regrding dmping fctor would be: 1 3σ 8υ ωres = ω γ = 3 P + (3 + 1) 4 (13) ρr R R ω =.744MHz res Therefore, the error percent would be: ω ω res ω =.67% This result shows good greement with experimentl dt for Alzheimer tretment which hs been obtined by Leineng nd his coworer [19]. In ddition, the prediction of conditions for other cses nd pplictions will be used before n opertion nd surgery. Therefore, these clcultions re useful for physicins nd scientist who involve with similr cses for removing protein's disorder. Conclusion In this wor, model ws expnded to predict the ccurte frequency for the predetermined rdius nd the convenient frequency of ultrsound bubble for the tretment of the Alzheimer disese. These bubbles cn help in removing the Amyloid-Bet, which ggregtes in the brin nd cuse disorder intercellulr interction. The obtined results re in good greement with experimentl dt nd just hve negligible percentge error tht is less thn.67%. This cn bring new clcultion for pretretment of Alzheimer. The ppliction of this frequency model before in vivo tretment leds to reduce the hrmful side effects nd other cell dmge, becuse its mechnicl effect focuses only on the bnorml section in the brin. Future scope Sfety issues of ultrsound is mjor chllenges for the ultrsound-bsed strtegies trnsltion for the neurologicl diseses prevention nd tretment by helping modeling nd predetermined pttern of tretment is the future purpose of this wor. 4 This rticle is vilble in:

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