JOINT CARTILAGE LUBRICATION WITH PHOSPHOLIPID BILAYER

-016 T R I B O L O G I A 145 Krzysztof WIERZCHOLSKI * JOINT CARTILAGE LUBRICATION WITH PHOSPHOLIPID BILAYER SMAROWANIE CHRZĄSTKI STAWOWEJ Z DWUWARSTWĄ FOSFOLIPIDOWĄ Key words: hydrophilic crtilge, lubriction, bi-lyer lmellte phospholipids, geometricl nd physicl dt, vritions of viscosity of synovil fluid, new effect prognosis Słow kluczowe: chłonn chrząstk, smrownie, dwuwrstw fosfolipidow, dne geometryczne, fizyczne, zminy lepkości prognozy nowych efektów Abstrct The surfce of n rticulr crtilge humn joint, coted with phospholipid bilyers or multi-lyers, plys n importnt role in the surfce-ctive phospholipid lubriction, friction, nd wer during humn limb movement. The biologicl bi-lyer is thin polr membrne composed of two lyers of phospholipids tht hve hydrophilic phosphte hed (from the outside) nd hydrophobic til (from the inside) consisting of two ftty cid chins. These membrnes re flt sheets tht form continuous brrier round ll cells. * Technicl University of Koszlin, Institute of Technology nd Eduction, ul. Śnideckich, 75-453 Koszlin, Polnd, phone: +48 94 3478344, fx: +48 94 346753, e-mil: krzysztof.wierzcholski@wp.pl.

146 T R I B O L O G I A -016 Synovil fluid (SF) in the humn joint gp contins glycoprotein, lubricin (proteinglycn 4), nd hyluronidse, i.e. n enzyme tht produces hiluron cid nd ±10% phospholipids. Becuse the mechnism of surfce rticulr phospholipid lubriction (SAPL) hs been frequently controversil subject in the pst decde, this fct requires showing the hydrodynmic description in the form of mthemticl model of the bovementioned problem nd its prticulr solution. To give description of this model, it is necessry to recognize the vritions of the dynmic viscosity of synovil fluid s function of prmeters depending on the presence of mny phospholipid prticles. To these prmeters belong power (exponent) concentrtion of hydrogen ions (ph), crtilge wet bility (We), collgen fibre concentrtion in synovil fluid, nd creted electrosttic field on the phospholipid membrne. Bsed on the Young-Lplce-Kelvin Lw, initil chievements presented in scientific ppers nd our own investigtions illustrted in this pper, the decrements, nd increments of synovil fluid dynmic viscosities versus ph nd wet bility (We) increses, simultneously tking into ccount the influence of the intensity of chrges in the electrosttic field. Moreover, this study considers the influence of collgen fibre concentrtion on the dynmic viscosity of synovil fluid. Bsed on initil considertions performed by virtue of the developed SAPL, it my be stted tht the chrge increments from low to high vlues of the electrosttic field is connected with viscosity increses of synovil fluid but only simultneously with the ph index nd crtilge wet bility vritions. JOINT GAP AND PHOSPHOLIPIDS Synovil fluid in nturl joint gp is limited by the superficil lyer nd its superficil lyer. The lipid bilyers re thin polr membrnes mde of two lyers of lipid molecules. These membrnes re flt sheets tht form continuous brrier round ll cells. The lipid brrier is the brrier tht keeps ions, proteins, nd other molecules where they re needed nd prevents them from diffusing into res where they should not be. Biologicl bilyers re composed of mphiphilic phospholipids tht hve hydrophilic phosphte heds nd hydrophobic til consisting of two ftty cid chins. Synovil fluid contins wter, ions creted fter dissocition, collgen fibres, nd mny vrious viscous elements, for exmple, ctive phospholipids nd proteoglycns contining lubricin, which intercts with the hiluron cid [L. 1 3]. The lipid lyer on the surfce of the norml joint crtilge contins minly Phosphtidylcholine or Phosphtidylserine, which prevents sedimenttion effects. Liposomes re composite structures mde of phospholipids. The gp geometry nd superficil lyer is presented Fig. 1. (Source: Author s mteril). Figure 1 presents the rrngement of forces cting in joint gp filled with synovil fluid between crtilge surfces, which re limited by the membrne coted by the phospholipid s lyer bout 1 to nm height. Moreover, the

-016 T R I B O L O G I A 147 repulsion force R [N] cused by the negtive chrge of hydrted phospholipids covering the membrne surfces is indicted nd re the neutrlized ctions of hydrted sodium occurring in synovil fluid hve been observed [L. 4]. Mutully cooperting crtilge surfces hve curviliner cross sections presented in Fig.. They depended on the shpe of joint bonehed nd consequently to the type of joint. Vrious cross-sections of joint surfces hve been considered in reltion to the joint, porous-deformtions, nd roughness chnges from 1 µm for infnt.30 µm for dult to 5.30 µm for osteorthritis crtilge. Fig. 1. The joint gp limited by the by the phospholipid bilyer Rys. 1. Szczelin stwu ogrniczon dwuwrstwą fosfolipidów Fig.. Phospholipid bilyers on the crtilge surfce: ) the curviliner, b) At the edge of the pore, c) sphericl prbolic (knee): 1 phospholipid lyer, lipid with negtive chrge, synovil fluid, W lod, R repulsion force (own elbortion) Rys.. Dwuwrstwy fosfolipidów n powierzchni chrząstki: ) krzywoliniowej, b) krwędzi prbolicznej pory; c) sferyczno-prbolicznej koln; 1 wrstwy lipidów, fosfolipid z ujemnym łdunkiem, 3 ciecz synowiln, 4 chrząstk, kolgen, W obciążenie, R sił odpychjąc, P sił hydrodynmiczn od wyciskni (źródło: mterił włsny utor) WHAT DETERMINES SYNOVIAL FLUID VISCOSITY? Trditionlly, the pseudoplstic synovil fluid viscosity decreses when the sher rte increses during lubriction flow. However, the synovil fluid viscosity lso depends on the concentrtion of lipids nd phospholipids. The

148 T R I B O L O G I A -016 uthor hs not been ble to find publiction referring to experimentl-lbortory results presenting direct influence of the percentge of the concentrtion of phospholipids on the synovil fluid dynmic viscosity. By virtue of the Young- Lplce-Kelvin eqution nd the uthor s own reserch, referring interfcil energy obtined by Z. Pwlk in experimentl reserch [L. 5 6], the uthor of this pper indictes tht synovil fluid viscosity directly depends on the concentrtion of hydrogen ions determined by the Sörensen index ph from to 10, crtilge superficil lyer wettbility from 40 o to 100 o, nd on the concentrtions of elstic collgen fibres nd lipids nd phospholipids. Of secondry importnce is the influence of the temperture nd electrosttic chrge density on the synovil fluid dynmic viscosity, becuse temperture nd electrosttic chrge density cuses viscosity chnges indirectly mutully through interfcil energy, the ph index, nd the concentrtion of collgen or PL prticles. In the uthor s opinion, the direct influence of temperture nd electric chrge density on the synovil fluid viscosity is negligibly smll. Z. Pwlk [L. 5] hd experimentlly determined the increments of the interfcil energy γ from 1.5 to 3.5 mn/m, for ph from 1 to 4, nd the decrements of the interfcil energy γ from 3.5 to.0 mj/m for ph from 4 to 1. Z. Pwlk comments [L. 5] imply from the non-monotone interfcil energy chnges, tht the mino-group will begin to lose their chrge ( NH + 3 NH ) nd the ( POH) group will begin to lose their proton ( POH PO ), which leves the surfce chrged nd leding to decrese in the interfcil energy. This phenomenon implies, in equtions (1 ) derived by the uthor, new form of trnsformed Young-Lplce-Kelvin eqution, where the interfcil energy γ[mn/m], temperture T [K], wettbility We, index ph, the PL surfce concentrtion s = s PL [mol/m ], synovil fluid viscosity [Ps], nd v-synovil fluid velocity [m/s] re mutully connected nd explicitly indicted. s ( w, p, T ) η L e H = γ ( w, p, T ) e H γ γ RT mx 1 ln 1 + 1 γ ka T ln L ( L k 1) ( w, p,t ) mx + + =, 0 < L e K H + H, L b + H K b, L δ k v v L L b, L L k L + 1 ( L + 1)(L + 1) b ( L + 1)(L + 1) > ( L + 1). b b k < 1, 1, (1) () Synovil fluid dynmic viscosity vries, usully in intervl from 0.003 to 0.5500 Ps. From formule (1) nd (), the following viscosity increments for 1<pH<3.5~4 nd synovil fluid viscosity decrements for 4<p H <10 nd decre-

-016 T R I B O L O G I A 149 ments of viscosity with increments from 70 o to 30 o of crtilge wettbility We cn be determined. These dependences re illustrted in Figs. 3 nd 4 with n isoelectric point, nd re not obtined by virtue of interfcil energy from Z. Pwlk s pper [L. 5], but from interfcil energy obtined bsed on the uthor s own derivtions (1)-(). Chrts of own interfcil energy re not presented. After determining the vlues for interfcil energy, the uthor shows the intensive vritions of the synovil fluid cross the joint gp height presented in Figs. 5 nd 6. Fig. 3. Dynmic viscosity increments for 0<pH<4 nd decrements for 4<pH<10 of synovil fluid versus the concentrtion of hydrogen ions ph for lipids of type PC, PS, for constnt T = 37 o C, crtilge wettbility We = 40 o, verge flow velocity 1.5 m/s, nd collgen concentrtion c c = 500 000 mol/mm 3, IP(γ = 3.5 mj/m, η = 4 Ps). Source: Author Rys. 3. Wzrosty dl 0<pH<4 orz spdki dl 4<pH<10 lepkości dynmicznej cieczy synowilnej ze wzrostem stężeni jonów wodorowych dl molekuł lipidowych typu PC i PS dl ustlonej tempertury człowiek 37 o C, przy stłej zwilżlności chrząstki We = 40 o, stłej koncentrcji włókien kolgenowych c c = 500000 mol/mm 3 orz średniej stłej wrtości prędkości 1,5 m/s, IP (γ = 3,5 mj/m, η = 4 Ps) źródło:bdni włsne Fig. 4. Dynmic viscosity decrements of synovil fluid versus crtilge wettbility for bilyer with phospholipids nd mino groups (visible chrged surfce regions), for constnt temperture of 37 o C, constnt rnges of ph, nd n verge humn limbs velocity of 1.5 m/s, nd collgen concentrtion of c c = 50000 mol/mm 3. Source: Author Rys. 4. Spdki lepkości dynmicznej cieczy synowilnej ze wzrostem wodochłonności We dl dwuwrstwy fosfolipidów z grupą fosftową i minową ze wskzniem obszrów niskiego i wysokiego łdunku elektrosttycznego od PL w temperturze 37 o C, przy ustlonych zkresch ph, stłej koncentrcji włókien kolgenowych c c = 500 000 mol/mm 3 orz średniej prędkości 1,5 m/s

150 T R I B O L O G I A -016 Fig. 5. Comprison of synovil fluid velocity nd its dynmic viscosity distributions between two crtilge surfces in joint gp height direction, for constnt vlue ph = 7.5, for lipids with PC nd PS, for constnt temperture of 37 o C, crtilge wettbility We = 60 o, n verge flow velocity 1.5 m/s, nd collgen concentrtion c c = 500 000 mol/ mm 3. Source: Author s own reserch Rys. 5. Rozkłd prędkości i lepkości dynmicznej cieczy synowilnej między dwom powierzchnimi chrząstek w kierunku wysokości szczeliny stwu dl stłego stężeni jonów ph = 7,5, dl lipidów z PC i PS, dl ustlonej tempertury 37 o C, przy stłej zwilżlności chrząstki We = 60 o, stłej koncentrcji włókien kolgenowych c c = 500000 mol/mm 3 orz średniej stłej wrtości prędkości przepływu 1,5 m/s. Źródło: wyłącznie bdni włsne utor Fig. 6. Comprison of synovil fluid velocity nd its dynmic viscosity distributions between two crtilge surfces in joint gp height direction, for PL bilyer with phosphte groups when We = 66 o, ph = 4.5, nd for PL bilyers with mino-groups when We = 54 o, ph =, t constnt temperture of 37 o C, n verge flow velocity 1.5 m/s, nd collgen concentrtion c c = 500 000 mol/ mm 3. Source: Author s own reserch Rys. 6. Rozkłd prędkości i lepkości dynmicznej cieczy synowilnej z dwuwrstwą fosfolipidów z grupą fosftową gdy We = 66 o, ph = 5,5 z dwuwrstwą fosfolipidów z grupą minową gdy We = 54 o, ph = 3,4, między dwom powierzchnimi chrząstek w kierunku wysokości szczeliny stwu w temperturze 37 o C, dl koncentrcji włókien kolgenowych c c = 500 000 mol/mm 3 orz prędkości przepływu 1,5m/s. Źródło: wyłącznie bdni włsne utor

-016 T R I B O L O G I A 151 In clcultions performed by virtue of equtions (1) nd () we denote the following: gs constnt R = 8.3144598 J/(Kmol), Boltzmn constnt k = 1.38054 (10 3 [J/K], A [m ] crtilge surfce coted with the PL molecule, T = 310K, γ[mj/m ] interfcil energy, We wettbility of crtilge in intervl from 30 o for hydrophilic crtilge to 100 o for hydrophobic crtilge, v-liner velocity of synovil fluid in joint gp (verge limb velocity) from 0.5 to 4.0 [m/s], δ v dimensionless coefficient introduced by the uthor in the rnge (<δ v <6) determining the vritions of the concentrtion of nno-meter long collgen fibres from δ v = for c c = 1,000,000 mol/mm 3 to c c = 100 mol/mm 3 nd less for δ v = 6 in synovil fluid. The clcultions ssumed verge dimensionless vlues of the rtio K /K b = L L b nd the proper dimensionless exponent (power) pk, pk b of K, K b quntities. The K, nd K b denoted by Z. Pwlk s cid nd bse equilibrium constnts re, in relity, K the re compression modulus (how much energy is needed to stretch the bi-lyer), K b bending modulus (how much energy is needed to bend or flex the bi-lyer). The H coefficient describing proton ctivities (hydrogen ion concentrtion) hd been erlier determined by Z. Pwlk. [L. 4 5]. Unfortuntely, the results of clcultions do not imply which vribles independently influence the electrosttic field chrge on the increments of the synovil fluid dynmic viscosity without crtilge wettbility nd without hydrogen ion concentrtion. From the formul (1), it follows tht the PL surfce concentrtion coefficient s PL [T,γ(pH)] decreses when the temperture increses for determined interfcil energy γ in reltion to ph. This phenomenon follows from the fct tht the high temperture increses the mutully repulsion effect between lipid molecules, thus prticle concentrtion decreses. From the second formul (), it follows tht the L function ttins vlues in intervl (0,1); therefore, (T/A)lnL lwys hs negtive vlues. Thus, temperture increments re decresing in the numertor of the frction defining the viscosity, hence viscosity decreses. Anlogously, surfce A increments denote increments of PL concentrtion; hence, the negtive vlue (T/A)lnL decrese. This increses the numertor of the frction describing viscosity, i.e. viscosity increses. Becuse velocity increments of synovil flow denote sher rte increments, the denomintor increses, nd frction defining the viscosity decreses, i.e. viscosity decreses. This fct confirms the well-known lw for pseudo plstic liquids bout viscosity decrements with sher rte increments. The synovil fluid dynmic viscosity vries significntly cross the humn joint gp limited by the PL bilyers. The gp height ttined verge vlues from 10 to 10 micrometres. Dynmic viscosity increses intensively in the proximity of the bi-lyer-phospholipids surfce nd ttined mximum vlues

15 T R I B O L O G I A -016 in these plces. This phenomenon is illustrted in Figs. 5 nd 6. Bsed on hydromechnicl lws, we deduce tht the velocity distribution of synovil fluid during the lubriction flow in the joint bering gp usully hs prbolic profile (shpe) with miniml vlues in the neighbourhood of the superficil lyer, i.e. PL-bilyer. From the second formul (), it follows tht, in these plces, the dynmic viscosity of synovil fluid ttins lrger nd lrger vlues, becuse the denomintor (fluid velocity) of the frction presenting the dynmic viscosity hs smller nd smller vlues. Moreover, in the neighbourhood of the superficil lyer, we observe n increse in the concentrtion of collgen fibres described by the smll vlues of dimensionless coefficient δ v. From the second formul (), it follows tht the smll coefficient δ v, s the denomintor of the frction presenting the dynmic viscosity, implies lrge vlues of the dynmic viscosity of synovil fluid in indicted plces. It is visible in Figs. 5 nd 6 tht the plces of mximl vlues of synovil fluid velocity profiles coincide with the points where the synovil fluid dynmic viscosity ttins the miniml vlues. HYPOTHESIS ABOUT THE MEANING OF ELECTROSTATIC CHARGE The influence of the PL membrne electrosttic field on the functionlity of humn joint will be considered nd exmined by virtue of expressions (1-) s well own nd other uthors scientific clcultions [L. 4, 9]. In the presented exmple, the electrosttic spce chrge in synovil fluid ttins vlues in the intervl 0<ρ e <0.04C/m for 1<pH<3, nd 0.10<ρ e <0 C/m for 4<pH<1. The possible electric current density generted by the electrosttic field in crtilge of norml ptient for ph = 8 hs vlue of J = 1.0 ma/m [L. 10]. If the PL membrne in the joint hs smll electricl conductivity, σ = 10 4 S/m, from Ohm s nd Lorentz s lws, we obtin the electric intensity E nd repulsion force R on the surfce unit in the crtilge in following form: E R = = 3 J 1mA / m 10 A / m A V N = = = 10 = 10 = 10, σ 4 4 10 S / m 10 S / m ms m C N C N µ N E ρ e = 10 ( 0.1) = ( 1.0 ) = 1.0. C m m mm (3) It cn be shown tht the repulsive force R on squre millimetre of the synovil fluid is very smll, one micro-newton, the R-vlue is not tken into ccount during joint lubriction. (Force P>0 for ph>4 nd P<0 for ph<4). The uthor formed the hypothesis tht the synovil fluid viscosity vrition cused by electricl field nd hydrodynmic force P increses. The influence of electric intensity on the fluid dynmic viscosity is described in the following formul [L. 10 11]:

-016 T R I B O L O G I A 153 η ( ph, We,E) = η [ 1+ δ ( ph,e) E ], (4) 0 E where δ E is the coefficient of influence of electric intensity, wettbility nd ph on the synovil fluid dynmic viscosity. This my be the first time tht coefficient δ E for synovil fluid hs been experimentlly mesured. However, from Fig. 3, it is visible tht the ph concentrtion, simultneously with electrosttic chrge, cuses pproximtely 30% viscosity vritions. By virtue of this fct nd the formul (4), we obtin equlity δ E E =0.30. Tking into ccount vlue E from formul (3) for ph=8, we obtin δ E =0.003 m /V. DISCUSSION In recently publisher ppers [L., 3, 5, 7] concerning humn joint lubriction, we cn find numerous ppers presenting experimentl dt referring to the influence of PL concentrtion, crtilge wettbility, nd hydrogen concentrtion ph on the friction coefficient [L. 4]. Reserch indictes tht the decrements of friction coefficients re from 1.00 to 0.01, if the PL concentrtion increses in rbitrry units from 1 to 4. The tril of mthemticl methods of the influence of PL concentrtion on the joint friction coefficient t the moleculr level hs been undertken by A. Gdomski et l. [L. 8], where, fter solving moleculr energy equtions [L. 4], he obtined dependencies determining slow increses of friction coefficient in time, nd bsed on the flexurl dissiption lw, he ws ble to show the dependence of viscosity decresing in time for constnt temperture. It follows tht viscosity is inversely proportionl to the friction coefficient. From clssicl theory of lubriction, it follows tht increments of the dynmic viscosity of lubricnt implies the increments of lod crrying cpcity nd finlly the increment of friction forces. A. Gdomski s reserch leds to the concept tht the increments of phospholipid concentrtion imply friction coefficient decrements. Z. Pwlk nd A. Bojn et l. stipulted tht the locl lrge vlue of dynmic viscosity in synovil fluid could not be in contrdiction with the low vlue of the friction coefficient. Moleculr chemistry nd publictions [L. 4] nd [L. 8], combined with the results of reserch nd the hydrodynmic theory of lubriction nd his own experiences inspired the uthor s further reserch. According to Amontonson s lw, we tke the following simple reltions between friction force F R [N], lod cpcity P[N], nd dimensionless friction coefficient µ: S = Re R ηus Rρ η USρε F = = = µ µ = T R, PN, F R PN, (5) h ε εt ρ ηrρ ρ

154 T R I B O L O G I A -016 where: η dynmic viscosity of biologicl liquid [Ps], U liner velocity of bio-surfce [m/s], S region of cooperting biosurfces [m ], ε T verge vlue of totl gp height in length units in the rnge of cooperting surfces, ρ density of biologicl fluid in rnge from 700 to 1150 kg/m 3, R ρ curvture rdius of cooperting joint surfces in m. From this eqution (5), it follows tht increses of synovil fluid dynmic viscosity implies decreses of the friction coefficient becuse of the decreses in the vlue of the Reynold number Re = Uε T ρ/η. The uthor s opinion s well the simple generl tribologicl nlysis presented by the uthor in expression (5), indictes tht the involved mthemticl nlysis by A. Gdomski bsed on moleculr-chemicl equtions without hydromechnicl nd tribologicl support re not sufficient to solve the hydrodynmic problem of humn joint lubriction with rel phospholipid bilyer. Presently, interesting experimentl mesurements performed by Z. Pwlk nd existing hydrodynmic models of joint lmellr lubriction with numericl solutions for the confirmtion experimentl results will complete the considered problem. CONCLUSIONS This pper presents new clcultion proposl for the humn joint lubriction flow of synovil fluid, tking into ccount its non-newtonin properties nd the morphous joint gp limited by the qusi-impermebility of the phospholipid membrne. To obtin the rel description of the hydrodynmic lubriction of humn joint, this reserch determined the vlues of synovil fluid s dynmic viscosities, tking into ccount the vrious impurities nd vrious rel biologicl dditions nd fctors, including those t the micro nd nno-level, for exmple, lipids, phospholipids, collgen fibres, hydrogen ions, nd other ions fter dissocition. Tking into ccount these fctors, the dynmic viscosity of synovil fluid vries, not only in length nd width, but lso in the direction of gp height. The new results obtined in this reserch re s follows: Joint crtilge wet bility increses (from 70 o to 60 o ), i.e. hydrophobic interctions decrese nd hydrophilic interctions increse, which imply 50% decrements of the dynmic viscosity of synovil fluid for constnt temperture of 37 o C, constnt concentrtion of collgen fibres (δ v = ), nd for hydrogen ion concentrtion vlues of 4<pH<1, nd for n verge synovil fluid flow velocity of v = 1.5m/s in the presence of the phospholipids bilyers with phosphte groups in the synovil fluid. The hydrogen ion concentrtion increses from 1<pH<3 nd cuses the dynmic viscosity of the synovil fluid increments, while the hydrogen ion concentrtion increses from 4<pH<10 cuses decrements of the

-016 T R I B O L O G I A 155 dynmic viscosity of the synovil fluid to bout 50%, if the verge vlue of crtilge wettbility ttined vlue of 40 o for n verge synovil fluid flow velocity of v = 1.5 m/s in the presence of the phospholipids bilyers with phosphte groups in the synovil fluid. The reserch indicted bout 30% vritions in the dynmic viscosity of synovil fluid cross the joint gp height. Mximl synovil fluid viscosity vlues re locted ner the crtilge superficil lyer or PL bilyer, becuse the lrgest vlues of lipids concentrtion, collgen fibres, nd electric chrges ctivities re there. The effects of the electrosttic chrge influence on the synovil fluid dynmic viscosity re cused, if nd only if such effects re considered simultneously with the influences of the hydrogen ion concentrtions on the viscosity chnges during the joint lubriction. After initil prognoses concerning the humn joint lubriction performed with rel phospholipid bi-lyer nd by virtue of the vritions of dynmic viscosity of the synovil fluid visulized in 3D in this reserch, it cn be stted tht the finl determintion of the fundmentl effects of the hydrodynmic humn joint lubriction process in tribologicl spects cn be obtined fter the formultion of hydrodynmic mthemticl model of the humn joint lubriction process. Then numericl solutions of lod crrying cpcities, friction forces, nd friction coefficients cn be obtined. Acknowledgement: The Author wishes to express his grtitude to Professor Z. Pwlk, Tribochemistry Consulting, from Slt Lke City, USA, for numerous discussions during the preprtion of this pper. REFERENCES 1. Bhushn B.: Nnotribology nd nnomechnics of MEMS/NEMS nd BioMEMS/NEMS mterils nd devices, Microel. Eng., 007, 84, pp. 387 41.. Pwlk Z., Figszewski Z.A., Gdomski A., Urbnik A., Oloyede Adekundle:The ultr low friction of the rticulr surfce is ph-dependent nd is built on hydrophobic underly including hypothesis on joint lubriction mechnism. Tribology Interntionl, 43, (010), 1719 175. 3. Hills B.A.: Boundry lubriction in vivo: Proc. Inst. Mech. Eng. Prt H: J. Eng. Med. 14 (000) 83. 4. Pwlk Z., Urbnik W., Hgner-Derengowsk M.W.: The probble explntion for the low friction of nture joints.cell Biochemistry nd Biophysics. vol. 70, 3, 015. 5. Pwlk Z., Urbnik W., Gdomski A., Kehinde Q. Fusuf, Isk O. Afr, Adekundle Oloyede: The role of lmellte phospholipid bilyers in lubriction of joints. Act of Bioengineering nd Biomechnics, Vol, 14, No. 4, 01.

156 T R I B O L O G I A -016 6. Andersen Olf S., Roger E., et.l.: Bilyer thickness nd Membrne Protein Function: An Energetic Perspective.Annulr Review of Biophysics nd Biomoleculr Structure. 36 (1), 107 130, doi:10.1146: nnuref.biophys. 36.040306.13643.Retrieved 1 Decembre 014. 7. Mshghi et.l.:hydrton strongly ffects the moleculr nd electronic structure of membrne phospholipids.136.114709, 01. 8. Gdomski A., Bełdowski P., Miguel Rubi J., Urbnik W., Wyne K. Auge, I.S. Holek, Pwlk Z.: Some conceptul thoughts towrd nno-scle oriented friction in model of rticulr crtilge, Mthemticl Biosciences,44 (013) 188 00. 9. Petelsk Ad., Figszewski Z.A.: Effect of ph on interfcil tension of bilyer lipid membrne.biophys.j. 000, 78, 81-7. 10. Syrek P.: Anliz prmetrów przestrzennych pliktorów młogbrytowych, wykorzystywnych w mgnetoterpii. AGH Krków, prc doktorsk, 010. 11. https://en.wikipedi.org/wiki/electroviscous_effects, Electric_fields. Streszczenie Dwie kostne powierzchnie trące pokryte chrząstką stwową oddzielone są cieczą synowilną w szczelinie stwu. Hydrodynmiczne smrownie stwów z udziłem dwuwrstwy fosfolipidów zkłd, że w wrstwie wierzchniej chrząstki stwowej istnieją dwie wrstwy fosfolipidów o grubości ok. nm w postci dobrze zorgnizownych molekuł. Dwuwrstw lipidow skłd się z dwóch przeciwnie uporządkownych wrstw cząsteczek lipidu z hydrofobowymi końcmi węglowodorowymi zwróconymi do środk wrstwy orz polrnymi hydrofilowymi grupmi fosforytowymi n zewnątrz. Dwuwrstw lipidow jko spontnicznie uksztłtown błon w roztworch wodnych nie przepuszcz związków orgnicznych i nieorgnicznych orz posid zdolność gromdzeni równomiernego łdunku elektrycznego po obu stronch, jeśli w roztworze znjdują się jony nieorgniczne. Ciecz synowiln (SF) zlegjąc w szczelinie stwu zwier glikoproteiny, lubrycynę (proteogikn 4), hiluronidzę, czyli enzym produkujący kws hiluronowy orz mniej jk 10% fosfolipidów uksztłtownych w postci liposomów. N podstwie bdń doświdczlnych dotyczących smrowni stwów nturlnych człowiek z uwzględnieniem fosfolipidów liczni utorzy, wykorzystując przeprowdzone eksperymenty ntury fizykochemicznej sugerują wzrost sił nośnych orz zmniejszenie współczynnik trci. Nie m jednk bdń podstwowych dotyczących zmin lepkości cieczy synowilnej od jej zwilżlności, ph, prędkości deformcji. Dltego też w niniejszej prcy utor przedstwił włsne bdni wstępne odmienne od dotychczsowych. Jko przyczynek do dlszych bdń utor wyzncz lepkość mzi stwowej cieczy synowilnej, ntomist nie koncentruje się

-016 T R I B O L O G I A 157 n wyznczniu energii powierzchniowej celem obliczni poszukiwnych prmetrów tribologicznych. Wyzncz się zminy lepkości cieczy synowilnej w zleżności od koncentrcji jonów ph i od zwilżlności chrząstki orz profile rozkłdu prędkości i lepkości cieczy synowilnej po grubości szczeliny stwu. Prc niniejsz stnowi wstęp do dlszych bdń.

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