Kinetics of volume expansion during infusion of Ringer s solution based on two volume model

Transcription

1 Koran J. C. Eng., 3(6, (006 SHORT COMMUNICATION Kinics of volu xpansion during infusion of Ringr s soluion basd on wo volu odl Kyu Tak Coi, Eun Ho L* and Yong Koo Yo*, Dp. of Anssiology and Pain Mdicin, Asan Mdical Cnr, Univrsiy of Ulsan, Soul , Kora *Dp. of Cical Enginring, Hanyang Univrsiy, Soul 33-79, Kora (Rcivd January 006 accpd Jun 006 Absrac In is work aaical odls wr dvlopd o rprsn kinics of volu cangs of fluid spacs associad wi infusion of Ringr s soluion. During infusion of Ringr s soluion, uan body is assud o b caracrizd by wo-fluid spac odl wic as scond volu spac in addiion o firs volu so a fluid xcangs bwn s wo spacs ar possibl. Various infusion yps wr sd o accooda diffrn dical siuaions. Volunrs wr givn Ringr s soluion and cangs in blood oglobin wr dcd. Fro coparison wi xprinal daa, wo-fluid spac odl was found o rprsn adqualy kinics of uan volu xpansion during infusion of Ringr s soluion. Ky words: Volu Expansion, Ringr s Soluion, Two-fluid Spac, Parar Esiaion, Blood Hoglobin INTRODUCTION Ringr s soluion is an lcroly soluion siilar o blood plasa. I is usually usd o supply war and lcroly during pysical opraion or wn uan body is in dydraion sa. Ringr s soluion consiss of 30 illi-quivaln/lir of Na, 4 illiquivaln/lir of K, 3 illi-quivaln/lir of Ca, 09 illi-quivaln/lir of Cl and 8 illi-quivaln/lir of laca. Infusion of Ringr s soluion (or Haran s soluion is an iporan par of pain car in surgry or raua car. I is wll known a aoun of Ringr s soluion ndd o rsor noral blood volus is oug o b r o fiv is volu of blood los. T fluid olculs infusd wiin uan body av bn assud o b disribud wiin a fluid spac of consan volu. Bu i is obvious a volus of fluid spacs cang wn a considrabl aoun of fluid is addd or rovd fro body. T volu xpansion ffc of adinisrd fluid is blivd o b rapuic goal. Howvr, is volu ffc is difficul o sudy. Major diffrncs in volu xpansion bwn infusion fluids ar fairly wll known, bu r is a lack of ods a rprsn ir dynaic propris [Dorbin and Han, 00]. A war olcul nring fluid spac consising of on xpandabl porion and on rigid porion can b found anywr and rfor as a volu of disribuion, bing su of wo porions of nir fluid spac. Bu only xpandabl porion of fluid spac is influncd by addd war olculs. T volu ffc of Ringr s soluion as a i cours a drins opial ra of infusion for fluid. T blood volu is xpandd os during and jus afr infusion, bu xpansion bcos lss pronouncd wi i. Rcnly, sipl singl and wo fluid spac volu odls av bn proposd and sd xprinally [Sal al., 997; Drobin al., 999; Sjosrand al., 00]. Sal al. [997] proposd lnary aaical odls o rprsn cangs in volu of fluid spacs associad wi inravnous adinisraion of a crysalloid soluion. Ty ployd xprinal rsuls o siad odl parars bu faild o sow ffcivnss of proposd odls upon wic our sudy is basd. Svnsn and Han [997] analyzd volu kinics of Ringr s soluion, Dxran 70 and Hypronic salin in al volunrs. Ty confird a disribuion of inravnous fluids can b analyzd by a kinic odl adapd for fluid spacs vn wi sligly diffrn rsuls dpnding on arkr usd o indica diluion of priary fluid spac. Volu kinics of glucos soluions givn by inravnous infusion wr also analyzd by Sjosrand al. [00]. In all volu xpansion odls proposd so far infusion was assud o b rprsnd as a block puls. Bu, in so criical siuaions suc as rgn surgry, infusion of Ringr s soluion can b rprsnd as a sp or an ipuls funcion. T purpos of prsn sudy is o dvlop a clar dscripion of volu xpansion causd by various yps of infusion of Ringr s soluion. In is sudy, w av workd wi kinic odls a allow various yps of infusion and can b applicabl during and afr volu loading. TWO-FLUID SPACE MODEL To wo corrspondnc sould b addrssd. E-ail: [email protected] Fig.. Scaic diagra of wo-fluid spac odl. 867

2 868 K. T. Coi al. T wo-fluid spac odl can b considrd as wo balloons filld wi war and conncd o ac or as sown in Fig.. T priary fluid spac counicas wi a scondary fluid spac. T n ra of fluid xcang bwn xpandabl fluid spacs is proporional o rlaiv diffrnc in dviaion fro arg volus. T sys srivs o ainain arg volus by acing on conrolld ouflow canis in proporion o rlaiv dviaion fro arg volu of priary fluid spac. During infusion, Ringr s soluion nrs an xpandabl fluid spac of volu v a a ra of k i. As in singl-fluid spac odl, funcional for of k i can b block puls, sp, or ipuls. Tr is a scondary xpandabl fluid spac of volu v wic xcangs fluid wi priary fluid spac v i. Bo fluid spacs av arg volus V and V, rspcivly. v cangs wi i du o fflunc of fluid fro fluid spac by prspiraion, basal diursis and conrolld fflux and du o fluid xcang wi scondary fluid spac. v is i dpndn du o fluid xcang wi priary fluid spac. T ra of fluid cang bwn wo fluid spacs is assud o b proporional o diffrnc in rlaiv dviaions fro arg volus wi proporional consan of k. T cobind ra of fluid fflunc fro v du o prspiraion and diursis is rprsnd as. I is assud a conrolld fflux is proporional o rlaiv dviaion of v fro arg volu V wi proporional consan. T bavior of xpandabl volus can b rprsnd by following diffrnial quaions. dv k -- = k i r ( v V - k v V -- v V --- d V dv -- = k v V -- v V --- d V V V v (0=V, v (0=V (3 W assu a V, V, k and ar consan. As in singl-fluid spac odl, parars and k i ar considrd o b known. W now considr r ypical yps as sown in Fig. : block puls, sp and ipuls. Soluions of Eqs. ( and ( for s infusion V ( ( yps ar givn in Appndix. In os cass parars and k i in odl quaions ar known as sad bfor. u or u is asurd diluion of blood and is availabl fro xprinal daa. T raining odl parars, k and wo arg volus V and V sould b siad fro xprinal daa. In ordr o cck firs ffcivnss of odl quaions dvlopd in prsn sudy, w assu valus of odl parars and arg volus as sown in Tabl o prfor nurical siulaions. Siulaions wr prford using MATLAB copuing ool (vrsion 7.0, Ma- Works, U.S.A.. Fig. 3 sows rsuls of siulaions for block puls infusion, sp infusion and ipuls infusion. EXPERIMENTS Ringr s laca soluion was givn o six aly volunrs (four als and wo fals. T ags and wigs of volunrs ar wiin rang of 8-34 yars and kg, rspcivly. T infusion xprins wr approvd by Eics Coi of Asan dical cnr in Soul, Kora and ac volunr gav inford consn. Twlv ours bfor xprinal procdur, food and war wr disconinud. Volunrs wr placd coforably on bds, and 0 inus of quilibraion was allowd bfor fluid adinisraion. Cannula wr placd ino ancubial vin and radial arry. Ringrs laca soluion (Coong wa, Soul, Kora, lcroly conns of wic wr 30 ol/l of Na, 4 ol/l of K, ol/l of Ca, ol/l of Mg, 4 ol/l of laca 4 and 0 ol/l of Cl. T Ringr s soluion was infusd ino a vin a a consan ra of 5 l/kg ovr 30 in wi aid of infusion pups (IVAC 560, San Digo. Sapls ( l ac for asurn of blood oglobin concnraion wr obaind fro radial arrial cannula a 0, 5, 0, 5, 0, 5, 30, 45, 60, 80, 00 and 0 inus afr adinisraion. Afr a blood sapl is drawn, 3 l of Ringr s soluion is injcd o flus cannula and on -l sapl o b discardd is drawn bfor ac blood sapling o avoid undu odiluion causd by is fluid. Bfor infusion of fluid, on sapl is drawn Fig.. Tr yps of infusion. Tabl. Daa for nurical siulaions Infusion yp T (in (l/in k i (l/in (l/in k (l/in V (lir V (lir Block puls Sp Ipuls Novbr, 006

3 Kinics of volu xpansion during infusion of Ringr s soluion basd on wo volu odl 869 Fig. 4. Infusion dynaics xprin. Tabl. Rsuls of block puls infusion xprins for al volunrs (T=30 in, =.94 l/in ID (Mal volunrs Ti (in pc lyj pcw Ljy Avrag Parars Wig (kg Urin (l* (l/in T (in k i (l/in *: Aoun of urin collcd afr 0 inus of infusion. Fig. 3. Rsuls of siulaions for various infusion yps ((a block puls infusion, (b sp infusion, (c ipuls infusion. in duplica and an valu is usd in calculaions. I aks 4 ours o prfor wol procdurs on a volunr. Basic apparaus rquird in xprins ar Haran s soluion ( lir, 4 infusion pups, a prssur bag, an arrial prssur ki, an ar praur prob and a syring ( l. Blood sapling: roug 3- way rou conncd o prssur bag, discard firs l, ak nx l of blood as a sapl and flus wi -l Haran s soluion conncd o prssur bag. Fig. 4 sows a snapso of xprins. Tabls and 3 sow xprinal daa rprsnd as fracional diluions obaind fro infusion xprins for al and fal volunrs, rspcivly. ESTIMATION OF MODEL PARAMETERS For block puls infusion, in wic duraion i is T and = b=consan, volu cang caracrisics ar givn in Appndix. T xprinal daa in Tabl xibis caracrisics of firs volu. Tus w can sia parars, k, V, V for wo volu odl as follows: f = u KA B r C r : 0 <T (4 KA f = u b b KB r - r b T Koran J. C. Eng.(Vol. 3, No. 6

4 870 K. T. Coi al. Tabl 3. Rsuls of block puls infusion xprins for fal volunrs (T=30 in, =.5 l/in ID (Fal volunrs Ti (in swj yo Avrag Parars Wig (kg Urin (l* (l/in T (in k i (l/in *: Aoun of urin collcd afr 0 inus of infusion. Tabl 4. Rsuls of siaion (wo-volu odl Volunrs (l/in k (l/in V (l V (l Mal pc , ,.5 lyj , ,079.0 pcw , ,474.5 ljy ,654.0,973.0 Avrag , ,65. Fal swj ,69.8 0,338.7 yo ,8.7 05,07.4 Avrag ,888. 0,466.5 KC r - r b T : T (5 Valus of parars a iniiz objciv funcion f can asily b found as in singl-fluid odl cas. Tabl 4 sows rsuls of siaion for wo-volu odl. In ordr o valida wo-volu odl, siad parars wr pluggd ino odl and rsuls of copuaions wr copard wi xprinal daa. Fig. 5 sows rsuls of coparison bwn xprinal valus of fracional diluions and copuaional rsuls of odls basd on siad parars for r al volunrs, and Fig. 6 sows os for wo fal volunrs. Caracrisics of als and fals ay b or disinguisabl if w copar avrag valus for als and fals. Fig. 7 sows rsuls of coparison bwn avrag xprinal fracional diluions and copuaional rsuls of odls basd on siad parars using avrag xprinal valus. Fig. 5. Coparison bwn xprinal valus of fracional diluions (Mal volunrs: (a pc, (b lyj, (c pcw. CONCLUSIONS Caracrisics of volu xpansion ffc during infusion of Ringr s soluion wr analyzd by using wo-fluid spac odl. During infusion of Ringr s soluion, uan body is assud o b caracrizd by wo-fluid spac odl ino wic fluid is fd and fro wic fluid lavs. T wo-fluid spac odl as scondary volu spac in addiion o firs volu so a fluid xcangs bwn s wo spacs ar possibl. Various infu- Novbr, 006

5 Kinics of volu xpansion during infusion of Ringr s soluion basd on wo volu odl 87 Fig. 6. Coparison bwn xprinal valus of fracional diluions (Fal volunrs: (a swj, (b yo. Fig. 7. Coparison bwn xprinal valus of fracional diluions (Basd on avrag valus: (a al, (b fal. sion yps wr sd o accooda diffrn dical siuaions. Volunrs wr givn Ringr s soluion and cangs in blood oglobin wr dcd. Fro coparison wi xprinal daa, wo-fluid spac odl was found o rprsn adqualy kinics of uan volu xpansion during infusion of Ringr s soluion. U U wr τ ( s = ( s ( --- { k ( τ s ( τ s k k ( s k i b ( s } ( s = -U ( s = { k i ( s ( s } --- τ s ( k ( τ s ( τ s k (6 APPENDIX v W now inroduc u = V v - and u = V --. Tn w av V u (0=u (0=0, dv =V du, dv =V du. Eqs. (3 and (4 can b rwrin as V du -- k = ( k i u u d k k V du -- = u u d k k A sady-sa w can s a u s = u s = is k --- bs = 0. Fro Laplac ransfor of abov rlaions, w av afr so rarrangn k V V τ = V, τ = k k Cas I: =b=consan and k i =block puls wi agniud of and duraion i T. Tis yp of infusion can b rprsnd as Fig. (a. Subsiuion of k i (s and (s ino Eq. (6 givs afr so rarrangn U ( τ s - Ts b ( s = b -- - τ τ ( k s s τ τ τ τ s --- k τ τ k = -- b A B τ τ ( k C s s r s r - Ts b Koran J. C. Eng.(Vol. 3, No. 6

6 87 K. T. Coi al. wr or Wr : 0 <T : T Siilarly, fro invrs Laplac ransforaion of U (s givs or U ( s = -U ( s τ s = -- b A B τ τ ( k C s s r s r - Ts b r = -- τ τ τ τ r = -- τ τ τ τ τ τ τ τ τ τ τ τ k k τ τ k k τ τ τ A = -, B = r τ --, C = r -- r r r ( r r r ( r r A = A = -, B = --, C = -- r r r ( r r r ( r r Fro invrs Laplac ransforaion w av U = u = KA B r C r K - b A B r ( T C r { T }u s T = KA B r C r KA = b b KB r - r b T u u KC r - r b T K = -- b τ τ ( k = k ( b --- V V U u u = u = KA B r C r K - b A B r ( T C r { T }u s T = KA B r C r KA = b b KB r - r b T KC r r - b T : 0 <T : T Cas II: =b=consan and k i =sp wi agniud of. Tis yp of infusion can b dpicd as Fig. (b. Subsiuion of k i (s and (s ino Eq. (6 givs afr so rarrangn U ( s = b ( τ -- s - τ τ ( k s s τ τ τ τ s --- k τ τ k = -- b A B τ τ ( k C s s r s r (7 (8 U U wr (9 (0 Cas III: =b=consan and k i =ipuls wi agniud of g. Tis yp of infusion can b dpicd as Fig. (c. Subsiuion of k i (s and (s ino Eq. (6 givs afr so rarrangn wr wr ( s = -U ( s = b τ s -- A B τ τ ( k C s s r s r Fro invrs Laplac ransforaion w av U = u = K A B r C r = u = K A B r C r K = -- b τ τ ( k = k ( b - V V U U ( s = ( τ -- s ( gs b - τ τ ( k s s τ τ τ τ s --- k τ τ k = -- A B τ τ ( k 3 3 C 3 s s r s r ( s = -U ( s = τ s -- A B τ τ ( k 4 4 C 4 s s r s r b A 3 = -, B 3 = ( τ r ( gr b -, C 3 = ( τ r ( gr b -- r r r ( r r r ( r r b A 4 = -, B 4 = ( gr b --, C 4 = ( gr b -- r r r ( r r r ( r r Fro invrs Laplac ransforaion of U (s and U (s w av U = u = K A 3 B 3 r C 3 r ( = u = K A 4 B 4 r C 4 r ( U K = -- τ τ ( k NOMENCLATURE A-, B i, C i : parars [-] b : agniud of bas diursis [l/in] g : agniud of ipuls infusion [l/in] : agniud of block infusion [l/in] K, K :gain[-] : bas diursis ra [l/in] : proporional consan for singl fluid odl [l/in] k : proporional consan for wo fluid odl [l/in] : agniud of block infusion [l/in] r, r : consans [-] : i [in] T, T, T : infusion duraion i [in] u, u, u : rlaiv dviaion fro arg volu [-] U, U, U : rlaiv dviaion fro arg volu [-] u s : uni sp funcion [-] Novbr, 006

7 Kinics of volu xpansion during infusion of Ringr s soluion basd on wo volu odl 873 v : volu [l] V, V, V : arg volu [l] Grk Lrs τ, τ, τ : i consan [-] REFERENCES Braur, K. I., Svnsn, C., Han, R. G., Trabr, L. D. and Proug, D. S., Volu kinic analysis of disribuion of 0.9% salin in conscious vrsus isofluran-ansizd sp, Anssiology, 96, 44 (00. Drobin, D. and Han, R. G., Kinics of isoonic and ypronic plasa volu xpandrs, Anssiology 96, 37 (00. Drobin, D. and Han, R. G., Volu kinics of Ringr s soluion in ypovolic volunrs, Anssiology 90, 8 (999. Han, R. G. and Svnsn, C., Plasa diluion and ra of infusion of Ringr s soluion, Briis J. Anassia, 79, 64 (997. Han, R. G., Drobin, D. and Sal, L., Volu kinics of Ringr s soluion in fal volunrs, Briis J. Anassia, 78, 44 (997. Sjosrand, F., Edsbrg, L. and Han, R. G., Volu kinics of glucos soluions givn by inravnous infusion, Briis J. Anassia, 87, 834 (00. Sal, L., Nilsson, A. and Han, R. G., Modlling volu of xpandabl body fluid spacs during I.V. fluid rapy, Briis J. Anassia, 78, 38 (997. Svnsn, C. and Han, R. G., Volu kinics of ringr soluion, Dxran 70, and ypronic salin in al volunrs, Anssiology, 87, 04 (997. Koran J. C. Eng.(Vol. 3, No. 6