÷H(Tue Apr 07 12:21:54 1998) From Nep5.vmfe,*}B~j~j~¼€j~¡7L¿\\È ¼:'&%(#$89,*)+¡Å<>;:cÅ    €?¸(€ö€öL   €ö€ö<   €ö€öºE  "%€ö€ö? , €ö€ö¼Š# €ö€ö;¼ 'Ü€ö€ö¼ ‡*!€ö€ö]¼(/çü"€ö€öŠ ¼(6(­€ö€öI¼ :>& .€ö€öo.¼,>  A£Ò €ö€ö)¼(EL€ö€ö¼ ‡GO4<€ö€öš:¼,J®C Lh@€ö€ö ¼,OȈ\€ö€öˆ6¼,T{KJ€ö€öO!¼,YŒ^€ö€öQ"¼,_¥@ a3µ ¢€ö€ö§@¼ e³k€ö€öv¼(j¿T lý• €ö€ös¼(qD u€ö€ö¶D¼ ~,€ö€ö¼ ‡¥€ö€ö´C¼ ŠL€ö€ö¼ ‡¤Q€ö¼Š‘b€ö¼Š•>Á€ö€ö l(œœýM€ö€ö.l(ž “t€ö€ö–9l  ¬€ö€ö¼ ‡¢¼€ö€ö¼ ‡¤MÌ€ö€öl §Xå€ö€ö#l,ª‘ó>€ö€ö'l ¬C"T€ö€öa'l ¯«#€ö€öS#l,±Mf€ö€öz0l,µ«Ÿ€ö€ö”8l,º3€ö€öW%l ¾ö+€ö€öU$l Á ;€ö€öY&l Ål€ö€ö¼ ‡Ç"XW€ö€öx/l,Éjn€ö€ö|1l Ìuv€ö€ö2l Ï1 Ñv²€ö€ö8L,׺²x€ö€ö£>l(Ù•‹€ö€ö„4l Ý€ƒ€ö€ö‚3l,à°D â[  äƒÁ€ö¼Šçߺ€ö€öm- êêЀö€ö,€î >  òÙ€ö€öi+,÷1é€ö€ög* ü&á€ö€ök, ÌO€ö€öG,<õ&¿€ö€ö, åWõ€ö€öc( Qþ*é€ö€ö  Ì€ö€ö¼ ‡\ /í€ö€ö g6ò€ö€ö r96€ö€ö!,%ÁB€ö€öB *ð_ø€ö€öŽ7 0ûgû€ö€öŸ< 6z&ÿ€ö€ö«A,<€ö¼Š?)€ö€ö²BL,FV˜&€ö€ö:L Ia¤&€ö€ö3L,Qº€ö€öe)L X˜Â€ö€ö¡=L _-   @‰bC€ö¼Šfö€ö€ö†5¼ i¸Ú:€ö€ö%¼ pÃè>€ö€ö,¼,wÜñ&€ö€ö@¼ }0g€ö¼Š×&€ö€ö ¼(0›ò&€ö€ö ¼(0ª €ö€ö ¼,0¹&€ö€ö ¼(0<L,lÜL̼L¬,l L\¼¼¼<Ì,ÜœìüÜÜì<쌬|¼lŒLü  Œ |œ¬ L<\ ìü¬Œl\|,üÜ<|ŒœìÜÌ|Œü|,œ\Ì,œÌ¬¼Ì¬<lü,\<lœ\LìC¡7L¿nnÈÈSUMPRODVMINVMAXTimeINITIAL TIMEFINAL TIMETIME STEP SAVEPER .Nep5Ramp Switch -dmnlNormalized PtPt Proxim Tub PressureInitial PtPhase Angle ARCTANDelayed Pt-rad RadiusSQRT Pt PlotPt Plot SwitchInterpolated PtInterpolated RadiusSINSlice AnglePrevious RadiusZIDZPrevious AngleIF THEN ELSE"T Mac Dens Aff Art Delay Initial -seconds"T Mac Dens Aff Art Delay Final -mmHg.Mosekilde.AfferentRa Afferent Arter ResistdRaRa0-sec-nl Alpha Chg dRad OmegaKPsi InputRa NormalizedK Thresh Max K CoeffK Thresh Min-1PsiPsi max Psi minexpFhen Norm DelayedSPsi Test SW Psi Teststepln .Blood Pg ScaleActual PgFIND ZEROPg DifferencePg Diff ScalePg InitialIndicated PgBF Blood FlowPa Arterial Pressurea-ngbCa Affer Blood Protein ConcCe Effer Blood Protein ConcHa HematocritPv Veinous PressureRe Efferent ResistSNGFR Filtrat Flow .LoopT Mac Dens Aff Art Delay Fhen0Fhen Flow to Loop of HenlePd Distal Tub PressureRhen Henle Loop Resist smOOth3.Proximal Pt DelayCtub Tubule CompliancedPt Chg Prox Tub PressFreab Reabsorb Flow .Control SMOOTH3INSTLV2DLLV16#smOOth3(FhenFlowtoLoopofHenle,TMacDensAffArtDelay)#:#LV2ÜL ,LL¬¼L¬¼L¼l¬"¼¬&L¼Ì*L¼¼ÌÌ/̼6¼L:L¬¡7L¿È¡7L¿ÁÁdL,,¼üœü\|ÌüŒ<<<ŒìÜ\üÜ||L,ì|¼\<ì< Œ\ìü\l|œÜ   Ì<\Üœ|<<<<¬üŒ¬Œ¬Ü|Ì|Ì<|ü|쌜Ü, Ü|,¬Ü\Œ||œœ¬ŒìŒ\ì<\\\ìüܬ¬3.ÿÿÿÿÿÿÿÿ Times New RomanŠModel5/ÿÿÿÿÿÿÿÿ Times New Roman$dPlotting %,3:AHOV]dkry€‹’™ §®µ¼ÃÌÓÚáèïöý  '.5<CJPV\bhntz€†Œ’›¡§­³¹¿ÅËÑ×Ýãéïõû %+17=CIOU[aiou{‡“™Ÿ¥«±·¾ÅËÑ×Ýäêðöý !(/7>DJU[flw}„Š H¡7L¿Èë 0°ÿ ü¸´( 0yÿ <ÉVA ÿ ü{±E ÿ Ü}êN ÿ (^/ ÿ ìZƒ[ ÿ üg2Z ÿ ŒE›( ÿ œÀ¸2 ÿ |[üY ÿ <š  ¼æ! ÿ Üö: ÿ Œƒ}H ÿ œÎ¯L ÿ*( ¯‡$ ÿ€€€€€€  J_A ÿ ,NÑ8 ÿ ¬P? ÿ |Ò[( ÌÁ ÿ ,eŠ0 ÿ Ì ÿ œjà ÿ  \„l- ÿ LÇb ÿ |ç ÿ œ‘ ÿ ¼ˆh@ ÿ lŠ ÿ <ÿu/ ÿ ìXP ÿ ü S ÿ ìŸt ÿ Œ0G ÿ ÌP- ÿ Ì 4 ÿ Üïs( ÿ Ü>°" ì>ÃL ÿ ŒÔ( Œ2" Ü2! ÿ ß8 Ó" ß8 ò Ñ[ ß8 Ó",Yé-‚ ,¬,›î#-? #-?"-J?*Ö× )…*Ò¸*î šÑ qµ Í Ô} {§ ùz ª J¼ Hv˜¥£‘ÈŠ£‘˜¥!镘¥ÈŠ!镘¥'gb°&;Wó%(%((àK$±K(àKh­p ø9ŠohZ Ã)j°)d!°,+,dT ¿  ‚é É  0ÍÊÿ 0͘kÍ€kjdͰ+k±Ð+-è) \®š+  p@qš p@å¬p @à‹ |&à ÿt "à ,X ÿv ?±*( lþ3 ÿ€€€€€€ x  × \ä²S ÿ ¬øe ÿz»‘ <ÀÐd ÿ{z@N×}z@XÁ*( Œ˜Š7 ÿ€€€€€€ €zDœ*( |¶¨< ÿ€€€€€€ ‚z_«*( lR  ÿ€€€€€€ „zí Ì*>+ †z@ þVT ´ž ÿÿ Replicated by Tom Fiddaman (Tom@Vensim.com)*' ªZŒ7ÿÿ From Jensen, K.S., Mosekilde, Erik, and Holstein-Rathlou, N. Self-Sustained Oscillations and Chaotic Behavior in Kidney Pressure Regulation. In I. Prigogine and M. Sanglier, eds., Laws of Nature and Human Conduct. Brussels: Taskforce of Research Informath ")07>EKQW]cipw}„Š–œ¢©¯µ»ÂÈÎÔÚåëH¡7L¿››Èñ <´ $ ÿ Ìs ÿ*( ü¸xS ÿ€€€€€€  |D ÿ üT0 ÿ ŒÖ- ÿ ̸@$ ÿ ã( ÿá½qûÂ1@‘@1ø ¬h=  \ºá @¶¹ Üx"3 @¼B@ß@@5:nP œ:h/ @¤h@ñQ@=F ì" . @sŠ@í @ó¼@º*( ® $ ÿ€€€€€€ !@t žü šH¡7L¿  È;:•lG¦€?•|*•̦r•ìPQ'•ü• R•œ'•ü• B •,'•ì•<b)•\l#(•<¦@(•ì¦@J7W•|S0•Œ•œ¦€öBC•œ%•¬¼•ÌšN"•¬#•Ü%$•\•Üì0$•Ì•ü$••üRa(•ÜPQ•\R•œ•\Òn-•Œ 00* )/••Ì,•ü•Ì)-••Ì.•ü•̦€?¦R‹9•üPQ•R•œ•*˜?•¦@* C•<¦@A*¨H• ¦@A*°L•̦ØI?:¸g•|G•Œ•œ*Çm•̦AâÏq•Ü$ % %%%¦À•ì•ü(• ¦?•Œ%%%•ü•ü• $•|%••œ*îv•ì¦ ×#>:ö|•ŒG•ܦ*•  00.•,•<#¦€?%•L($•,•<¦@ 00,•,•\#¦€?%•L($•\•,¦@¦€?*&‡•L¦D*.‹•<¦À?*6•\¦@?*>“•ü¦®Ga>ªG˜•|$•Œ'$•Œ•œ#¦€?¬%•Ì$•¼•Ìr[Ÿ•#%•Ü•ì%$¦€?•Ü•|*i£•Œ¦À?*q§•œ¦@?Ry«•ì#¦€?ü0¦ÍÌÌ=¦ A*†¯•ܦ*޳•œ¦ff’A:™¸•,'•|•œ’¢¼•Ì$¦€?'  '$¦€?•œ$•Œ¦€?•Ì*µË•,¦ ×£<²½ÐA•<L000 0 0000•,•\•l•|¦€?¦¦oƒ:¦ÈB¦:ÓÕ•\$•<•Œ*ÜÚ•|¦XB*äß•l¦€?Rì䕜'$•¬•<•|*ù야¦yé&>*ñ•ܦí >;*ö•ì¦XB:û•ü%''•¼¦@•Ü$(#¦€?'''$•<•ü•Ü''•¼¦@•Ü''•¼¦@•ܦ?¦€?*=• ¦?bE•Œ#•%•,$•œ•<*R •¬¦ÈB*Z•¦ A*b•,¦`AŠm•<%%•œ$¦€?• $¦€?'•ì•ü²~$•\#•' %%$•<••Ì$•l•|$•Œ•|*“+•l¦@>Rœ/•|'$•ü•Œ•œZ¨4•¼'››¬0•|•\•l*µ9•Œ¦@*½>•œ¦ BRÈH•<PQ•ìR•Ì•ì*ÕN•ܦÍÌÌ>bÞS•ì'$$•<•ü•|•Ü*ìX•ü¦š™™>:õ^•üG•ì• *ÿc•̦ A*q•œ¦€?*u•Œ¦ÈC*y•|¦*}•¬•œ*(‰¬••b/•G'$•••• œh<•G'$•••• œbI•G'$•••• œ:V•'•¦@@ œÚ ¬€8Q9€ö€öƒ€ö€ö…€ö€ö‡ToF€ö€ö‰Ž\€ö€ö‹r‹S€ö€öj4•G'$•,••<•|j4•,G'$•L•,•<•|B4•<'•\¦@@r4•LG'$•|•L•<•|ŒH¡7L¿È_•Ì&®º¦ ‡Ü.•ì&¸P¸®º•ü'• ±•œ±•ü'•  ‡Ü•&®º¸•,•ì'•< ‡L*•\&®º•l•<(¦@#•ì(¦@ ‡Ü"•|&S®º•Œ±•œ±»:NA: ‡Ü•œ&®º•¬%•¼•Ì ‡Ü>•¬&®º•Ü#•\$•Ü%•ì•Ì$•ü±•$•ü ‡Ü&•Ü&¸P¸®º•\±¸•œ±¸•\ ‡Üf•Œ&®º• ¸•¸/¸•̸)¸•ü¸,¸•Ì®º*¸•¸-¸•̸)¸•ü¸.¸•Ì®º±¦€?±¦ ‡Ü&•ü&¸P¸®º•±¸•œ±¸• ‡L•¸&¸¦@ ‡,•<&®º¦@A ‡,• ¸&¸¦@A ‡L•̸&¸¦ØI? ‡L"•|&¸G¸®º•Œ±®ºº¸•œ‡¬%‡L'‡¼•̸&¸¦A ‡ÜV•Ü&®º$¦@%•ì%•ü%• (¦?%•Œ$•ü%•ü%• %•|$•%•œ"‡¬%‡L'‡¼'‡¬'‡¬•ì¸&¸¦ ×#> ‡Ü•Œ¸&¸G•ܱ¸¦‡¬%‡L'‡¼'‡¬z• ¸&• •,.•<±¦€?#•L%¸®•,$•<(¦@±• •,®,•\±¦€?#•L%•\$•,(¦@±¦€? ‡Ü•L¸&¸¦D ‡Ü•<¸&¸¦À? ‡Ü•\¸&¸¦@? ‡Ü•ü¸&¸¦®Ga>‡l'‡¬B•|¸&¸•Œ$•Œ$•œ'¦€?#•¬•Ì%•¼$•Ì ‡Ü*•¸&¸•Ü%•ì#¦€?$•Ü%•| ‡Ü•Œ¸&¸¦À? ‡Ü•œ¸&¸¦@? ‡Ü&•ì¸&¸¦€?#•ü¦ÍÌÌ=±¦ A ‡Ü•ܸ&¸¦ ‡Ü•œ¸&¸¦ff’A‡L%‡¬'‡¼•,¸&¸•|'•œ ‡Ü>•̸&¸¦€?$• ¦€?$•œ'•Œ$¦€?'•Ì ‡Ü•,&®º¦ ×£< ‡LJ•<&®º•L•,±•\±•l±•|±¦€?±¦±¦oƒ:±¦ÈB±¦ ‡L•\&®º•<$•Œ ‡L•|&®º¦XB ‡L•l&®º¦€? ‡L"•œ&®º¸•¬$•<'•|‡¼'‡¬•¼¸&¸¦yé&>‡L%‡¼'‡Ì•ܸ&¸¦í >;&‡L%‡¼%‡¼'‡Ì%‡Ì•ì¸&¸¦XB‡Ì'‡¼r•ü&®º•¼'¦@'•Ü%¦€?#•<$•ü'•Ü'•¼'¦@'•Ü'•¼'¦@'•Ü(¦?¸$¸¦€?‡Ì'‡¼• ¸&¸¦? ‡Ü&•Œ&®º•#•,%•œ$•< ‡L•¬¸&¸¦ÈB ‡L•¸&¸¦ A ‡L•,¸&¸¦`A‡¬%‡L'‡¼2•<&®º•œ%¦€?$• %¦€?$•ì'•ü‡¼'‡¬F•\&®º•¹®º#•<$•®º%•Ì%•l$•|'•Œ$•| ‡,•l¸&¸¦@>‡¼'‡¬•|¸&®•ü$•Œ'•œ‡¼'‡¬&•¼¸&®•¬•|±•\'•l ‡Ü•Œ¸&¸¦@ ‡L•œ¸&¸¦ B‡¬%‡L'‡¼&•<&¸P¸®º•츱•̱•ì¸ ‡Ü•ܸ&¸¦ÍÌÌ>‡¼'‡L&•ì¸&®•<$•ü$•|'•܇L'‡¬•ü¸&¸¦š™™>‡¼'‡¬•ü¸&¸G•챸•  ‡L•̸&¸¦ A ‡,•œ¹&¸¦€? ‡,•Œ¹&¸¦ÈC ‡,•|¹&¸¦ ‡,•¬¹&¸®¹•œ ‡,‰¸šš±š&š&Gš$š'š±š œ&š&Gš$š'š±š œ&š&Gš$š'š±š œš&š'¦@@ œH¡7L¿Èt&Internally defined simulation time.rNormalized PT, delayed by one time step with DELAY FIXED to eliminate inter-TIME STEP values in RK4 integration.6Angle from the origin of the point (Pt, Delayed Pt)6Radius from the origin of the point (Pt, Delayed Pt)FInterpolation to determine value of Pt at crossing of slice angle.ÎPlot switch for taking a section through the Poincare map of Pt vs. Delayed Pt. Returns one when the angle of the slice lies between the current and previous angles of Pt vs. Delayed Pt.FPhase angle delayed by one time step for creating Poincare section.pi/4f Erik Mosekilde's model of chaos in rat kidneys. Replicated from equations presented in Mosekilde's paper by Tom Fiddaman, with help from Bob Eberlein on the use of Vensim's SIMULTANEOUS function. While I have been unable to find chaotic behavior at the exact parameter values specified in the paper, try setting d = 0.10, T_Mac_Dens_Aff_Art_Delay = 10 for a chaotic or at least very high periodicity regime. For chaotic runs, you should extend the final time to 1000 or 2000 seconds and set the time axis controls so that results are plotted only after initial transients have died out - 200 to 500 seconds.: Raising d may increase the amplitude of oscillation!{initialized stationary} {1/s}rNote: there was apparently a mistake in the specification of this logistic-type curve in the article.{mmHg*s/nl}*INITIAL used to save a few clock cycles.î This portion of the model solves a system of simultaneous equations describing the equilibrium glomerular pressure and blood flow. Mosekilde uses a Pascal routine to solve the equations; here the Vensim SIMULTANEOUS function is used.¦Note: the indicated BF and BF loop is a dummy loop inserted to reduce the gain of the Pg->BF->Pg positive loop, so that the convergence routine will work properly.{mmHg*l/g}{mmHg*l^2/g^2} {g/l} {mmHg} {mmHg}{mmHg*s/nl}{ Equation 2 } {mmHg}{mmHg*s/nl}6Delayed value of Pt for creating Poincare section.{nl/mmHg}{nl/sec} nl/sec6{mmHg - guestimate, pg. 92 left side 3rd paragraph} Note: the model MUST be simulated with RK4 integration for reasonable accuracy. Mosekilde uses RK4 with a fixed step of .05; you could probably do better with a variable step of similar or perhaps larger size (.0625 or .125). I haven't tested these in this version.<€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€öyé&>€öAí >;€öXB€ö€öÍÌÌ> ×#>€ö€ö€ö@>ÈCš™™>?€ö@A€ö€ö€öDÀ?@?®Ga>ÈB@€?€öXB ×£<€ö€ö€öÀ?@?€ö A€ö A€öff’A€ö`A B€ö€öØI?€ö€ö@A@€?¡7L¿ È///---\\\ :GRAPH PHASE :TITLE Phase :X-AXIS Pt Proxim Tub Pressure :SCALE :VAR Fhen Norm Delayed :SCALE :VAR Ra Afferent Arter Resist :GRAPH POINCARE :TITLE Poincare :X-AXIS Delayed Pt :X-DIV 4 :Y-DIV 4 :X-MIN 0.5 :X-MAX 1.5 :DOTS :SCALE :VAR Normalized Pt :Y-MIN 0.5 :Y-MAX 1.5 :VAR Pt Plot :GRAPH SECTION :TITLE Section :X-AXIS T Mac Dens Aff Art Delay :X-MIN 0 :X-MAX 16 :DOTS :SCALE :VAR Pt Plot :Y-MIN 0.5 :Y-MAX 1.5 :GRAPH POINCARE_0 :TITLE Poincare :X-DIV 4 :Y-DIV 4 :X-MIN 200 :DOTS :SCALE :VAR Normalized Pt :Y-MIN 0.5 :Y-MAX 1.5 :VAR Pt Plot :L<%^E!@ 9:ramp 22:$,Dollar,Dollars,$s 22:Day,Days 22:dmnl,rad 22:Hour,Hours 22:Month,Months 22:Person,People,Persons 22:sec,secs,second,seconds,s 22:Unit,Units 22:Week,Weeks 22:Year,Years 10:ramp5b.cin, 15:0,0,0,1 19:100,0 4:Time 5:Pt Proxim Tub Pressure