Red blood cell lingering modulates hematocrit distribution in the microcirculation

A icle Red blood cell linge ing modula es hema oc i dis ibu ion in he mic oci cula ion Yazdan Rashidi, 1, *G e a Simiona o, 1,2 Qi Zhou, 3 Thomas John, 1 Alexande Kihm, 1 Mohammed Bendaoud, 1,4,5 Timm K € uge , 3 Miguel O. Be nabeu, 6,7 La s Kaes ne , 1,8 Ma hias W. Laschke, 2 Michael D. Menge , 2 Ch is ian Wagne , 1,9 and Alexis Da as 1, * 1 Expe imen al Physics, Saa land Uni e si y, Saa b uecken, Ge many; 2 Ins i u e o Clinical and Expe imen al Su ge y, Saa land Uni e si y, Hombu g, Ge many; 3 School o Enginee ing, Ins i u e o Mul iscale The mo luids, Uni e si y o Edinbu gh, Edinbu gh, Uni ed Kingdom; 4 Uni e si  e G enoble Alpes, CNRS, LIPhy, G enoble, F ance; 5 LaMCScI, Facul y o Sciences, Mohammed V Uni e si y o Raba , Raba , Mo occo; 6 Cen e o Medical In o ma ics, Ushe Ins i u e, Uni e si y o Edinbu gh, Edinbu gh, Uni ed Kingdom; 7 The Bayes Cen e, Uni e si y o Edinbu gh, Edinbu gh, Uni ed Kingdom; 8 Theo e ical Medicine and Biosciences, Saa land Uni e si y, Hombu g, Ge many; and 9 Physics and Ma e ials Science Resea ch Uni , Uni e si y o Luxembou g, Luxembou g, Luxembou g ABSTRACT The dis ibu ion o ed blood cells (RBCs) in he mic oci cula ion de e mines he oxygen deli e y and solu e ans- po o issues. This p ocess elies on he pa i ioning o RBCs a successi e bi u ca ions h oughou he mic o ascula ne wo k, and i has been known since he las cen u y ha RBCs pa i ion disp opo iona ely o he ac ional blood low a e, he e o e leading o he e ogenei y o he hema oc i (i.e., olume ac ion o RBCs in blood) in mic o essels. Usually, downs eam o a mic o ascula bi u ca ion, he essel b anch wi h a highe ac ion o blood low ecei es an e en highe ac ion o RBC lux. Howe e , bo h empo al and ime-a e age de ia ions om his phase-sepa a ion law ha e been obse ed in ecen s udies. He e, we quan i y how he mic oscopic beha io o RBC linge ing (i.e., RBCs empo a ily esiding nea he bi u ca ion apex wi h diminished eloci y) in luences hei pa i ioning, h ough combined in i o expe imen s and in silico simula ions. We de el- oped an app oach o quan i y he cell linge ing a highly con ined capilla y-le el bi u ca ions and demons a e ha i co ela es wi h de ia ions o he phase-sepa a ion p ocess om es ablished empi ical p edic ions by P ies e al. Fu he mo e, we shed ligh on how he bi u ca ion geome y and cell memb ane igidi y can a ec he linge ing beha io o RBCs; e.g., igid cells end o linge less han so e ones. Taken oge he , RBC linge ing is an impo an mechanism ha should be conside ed when s udying how abno mal RBC igidi y in diseases such as mala ia and sickle-cell disease could hinde he mic oci cula o y blood low o how he ascula ne wo ks a e al e ed unde pa hological condi ions (e.g., h ombosis, umo s, aneu ysm). INTRODUCTION Pa i ioning o ed blood cells (RBCs) h ough bi u ca ions o blood essels de e mines how he oxygen is deli e ed o is- sues and o gans. Ea ly s udies ha e shown ha his pa i ion- ing isa complex phenomenon(1–4) and, since hen, i has been an a ea o in ensi e esea ch, a ac ing a wide ange o expe - imen al (5–13) and nume ical (14–20)s udies.Mo eaccu- a ely, essels wi h a highe low a e end o collec an e en highe p opo ion o RBCs. This ac is known as he Zwei ach-Fung e ec and leads o he e ogenei y in he hema - oc i be ween a ious essels (2). Unco e ing he mechanisms o such a pa i ioning beha io is c ucial o unde s and no only he anspo o oxygen and solu es ac oss ascula ne - wo ks bu also he de elopmen o emodeling o he ne wo ks hemsel es, as RBC dynamics we e ecen ly disco e ed o Submi ed Augus 31, 2022, and accep ed o publica ion Ma ch 13, 2023. *Co espondence: yazdan. ashid[email p o ec ed] o alexis.da as@ uni-saa land.de Yazdan Rashidi, G e a Simiona o, and Qi Zhou con ibu ed equally o his wo k. Edi o : Timo Be z. SIGNIFICANCE We demons a e in i o ha he linge ing beha io o ed blood cells (RBCs) a he apex o bi u ca ions modula es hei pa i ioning in he mic oci cula ion. The in luence o his mechanism opens new ways o unde s anding how al e ed RBC p ope ies in pa hologies can hinde he mic o ascula blood low, o in luence he de elopmen o emodeling o he ascula ne wo ks. Fo ins ance, we show ha igid RBCs linge less a ypical Y-shaped bi u ca ions and mani es a dis ibu ion pa e n close o he well-known Zwei ach-Fung e ec . We also highligh ce ain p ope ies o he bi u ca ion geome y ha con ibu e o he linge ing in ensi y o RBCs. 1526 Biophysical Jou nal 122, 1526–1537, Ap il 18, 2023 h ps://doi.o g/10.1016/j.bpj.2023.03.020 Ó2023 Biophysical Socie y. This is an open access a icle unde he CC BY-NC-ND license (h p:// c ea i ecommons.o g/licenses/by-nc-nd/4.0/). unde pin essel emodeling, p esumably by media ing he wall shea s ess di e ence be ween neighbo ing b anches ia he ou e o e ec i e blood iscosi y (21). An empi ical model ha e ec i ely ecapi ula es he ime-a e age beha io o he Zwei ach-Fung e ec was de eloped by P ies e al. in he 1990s (22–24) and has been widely employed by he esea ch communi y o s udying mic o ascula blood low. Howe e , ecen in i o and in silico s udies demons a ed ha no able de i- a ions om his empi ical model can a ise o a ious ea- sons (5,7,8,10,25,26). In pa icula , i has been shown ha RBC pa i ioning a bi u ca ions in he smalles essels o he mic o ascula ne wo k end o de ia e om he empi - ical p edic ions mo e se e ely (11,12,21,27,28). On he o he hand, i s es ablished h ough nume ical simula ions (25) and subsequen ly alida ed by in i o expe imen s (29), an in iguing beha io o RBCs in he mic o ascula- u e was highligh ed: hey linge a he apex o bi u ca ions (i.e., he cells empo a ily esiding nea he b anching poin o essels wi h diminished eloci y) o ce ain pe iods o ime, consequen ly modi ying he dynamics o cells en e ing downs eam essels and he cha ac e is ic in e -cell dis- ances ea u ing in e mi en oids. P e iously, Bagchi e al. (25) ex ensi ely cha ac e ized he ime-dependen co ela ion be ween single-cell linge ing imes and geome y o he ne wo k, bu he causal ela ion- ship be ween he linge ing pa e n and he a e age beha io o RBC dis ibu ion h ough he bi u ca ion was no explic- i ly in es iga ed. Thei ollowing wo k (28) u he combined a con inuum model wi h he cellula simula ion o dis inguish he e ec s o plasma skimming and cell sc eening. Mo e ecen ly, Bagchi e al. epo ed how changes in he ac ion o linge ing popula ion be ween igidi ied and heal hy cells a e ela ed o de ia ions om iden i y o he RBC low a e and o e all blood low a e (30). No wi hs anding he p og- ess abo e, a mechanis ic unde s anding o he de ia ion om iden i y due o he Zwei ach-Fung e ec as well as he baseline beha io o how such de ia ions a e associa ed wi h he p opo ion o absolu e esidence ime o linge ing cells is ye o be ob ained. In he p esen s udy, we sys ema ically analyze how he linge ing o RBCs in luences hei pa i ioning a highly con ined capilla y-le el bi u ca ions in he mic oci cula ion (whe e he cells li e ally squeeze hemsel es h ough and negligible cell- ee laye exis s con a y o p io s udies; c . (22–24)). Th ough ca e ully designed in i o expe imen s co obo a ed by complemen a y in silico simula ions on ime- scales longe han he linge ing ime and ele an o physio- logical condi ions, we show ha global de ia ions om he empi ical model by P ies e al. (24) a e s ongly co ela ed wi h no malized a e age du a ion o cell linge ing e en s. We u he e eal how linge ing modula es RBCs pa i ioning, wi h a p ima y ocus on mechanis ic unde s anding o he de- ia ion om he baseline beha io o Zwei ach-Fung e ec as pos ula ed by he empi ical model (24). The asymme ic d i e om RBC linge ing is ound o ei he ein o ce o e e he Zwei ach-Fung e ec . In addi ion, gi en ha RBCs usually exhibi la ge de o ma ions when linge ing, we also in es iga e nume ically how cells wi h inc eased s i ness di e om heal hy ones in hei linge ing and pa i ioning beha io . Ou esul s demons a e ha RBC linge ing is a cause o s a is ical de ia ion om he Zwei ach-Fung pa i ioning and p o ide u he e idence ha pa hologically igidi ied cells can impai he dis ibu ion o RBCs ac oss he mic oci cula ion (31–38) due o al e ed linge ing p ope ies. MATERIALS AND METHODS In i o expe imen s Pe missions Expe imen s we e pe o med in Sy ian golden hams e s acco ding o he Ge man legisla ion on p o ec ion o animals and we e app o ed by he local go e nmen al animal p o ec ion commi ee (pe mission numbe 25/2018). Hams e s we e main ained on a s anda d 12/12 h day/nigh cycle and wa e and ood we e p o ided ad libi um. De ailed me hods a e desc ibed below o each ype o in es iga ion. Animal p epa a ion and mic oscopy Hams e s wi h an age o 5–7 weeks, weighing 55–70 g, we e used o he implan a ion o a do sal skin old chambe (39). The su ge y was pe o med unde deep anes hesia (150 mg/kg ke amin (Se umwe ke Be nbu g AG)/ 0.25 mg/kg domi o (O ion Pha ma) in ape i oneal), wi h in aope a i e pain medica ion by ca p o en (10 mg/kg, Zoe is, subcu aneous). A p e i- ously desc ibed p o ocol (39) was ollowed. B ie ly, he back o he ham- s e s was sha ed and a i anium chambe consis ing o wo ames was implan ed on he li ed do sal skin old. On he ame wi h a ci cula obse - a ion window (diame e o 10 mm) he cu is, subcu is, and e ac o muscle we e emo ed o expose he s ia ed skin muscle o la e obse a ion o he mic oci cula ion. The window was closed wi h a co e glass ha was ixed wi h a snap ing. An implan ed do sal skin old chambe is depic ed in Fig. 1 a. Animals we e allowed o eco e o 72 h a e he p ocedu e. Hams e s we e anes he ized as desc ibed abo e be o e in a i al mic o- scopy. A olume o 100 mL o he luo escen plasma ma ke luo escein iso hiocyana e (FITC)-labeled (5%, 150 kDa, Sigma-Ald ich) was injec ed e o-o bi ally and he animals we e ixed on a Plexiglas s age, as illus a ed in Fig. 1 b. Se e al capilla y bi u ca ions in di e en a eas o he chambe window we e chosen o epi luo escence mic oscopy (Axio Examine A1, Zeiss). FITC-labeled dex an was exci ed wi h a 480-nm ligh -emi ing diode (LED) (Colib i 7, Zeiss), and image con as was addi ionally enhanced by simul aneously using ansmi ed blue ligh , which is abso bed by hemoglobin, making RBCs appea da ke . Imaging was pe o med wi h 20(LD A-Plan, NA ¼0.35, Zeiss), 50(LD EC Epiplan-Neo lua , NA ¼ 0.55, Zeiss), o 100(LD C Epiplan-Neo lua 100,NA¼0.75, Zeiss) long-dis ance objec i es. Video acquisi ion was ca ied ou wi h a digi al came a (Hamama su O ca Flash 4.0, C13440) using he so wa e ZEN 3.1 Blue (Zeiss). Fo each ideo, 2000 ames we e eco ded a di e en a es acco ding o low eloci y (100–170 Hz). A 2 2 binning was applied du ing acquisi ion. An example o an ob ained image is gi en in Fig. 1 c. Image analysis and linge ing quan i ica ion Despi e he animal being ixed on he Plexiglas s age, i s b ea hing and/o muscles mo emen caused sligh ansla ions o he mic oscopic ield o iew in he image sequence (Fig. S1 a). To de e mine he mo ion o he RBCs in he essels, we i s co ec hose ansla ions by ansla ing each image by he maximum o i s 2D co ela ion wi h he i s image in RBC linge ing and hema oc i dis ibu ion Biophysical Jou nal 122, 1526–1537, Ap il 18, 2023 1527 he sequence. This p ocess c ea es a mo ie whe e he essels and su ound- ing issues a e s ill ixed (see Fig. S1 b). A Gaussian il e (wi h s anda d de ia ion o wo pixels) is hen applied o despeckel he images, and a mask is d awn a ound he essels. The c ea ion o his mask is acili a ed by also conside ing he image showing he s anda d de ia ion o each pixel in ensi y along ime, which is highe in he essels wi h ansien (da k) RBCs and o e s a guide o he eye o he mask d awing (see Fig. S1 c). The diame e s Do he a ious essels a e compu ed as wice he a e age dis ance om he skele on pixels o he masks o he bo de o he essels, using s anda d Ma lab unc ions bwmo ph and bwdis (see Fig. S1 c). The image se ies is hen in e ed and bina ized inside he mask a ea wi h a h eshold based on a use -de ined ac ion o he O su h eshold (40). The O su h esholding me hod was used because he a e age in ensi y o images is usually sligh ly licke ing. Howe e , he au oma ed h eshold algo i hm o e es ima ed he h eshold equi ed o de ec he whole RBCs; hence, we implemen ed a use -de ined a io o adjus i (see Fig. S1 d). The hema oc i Hwas calcula ed based on he bina ized image: H¼ 4s VRBC ARBCpR , whe e 4sis he measu ed a e age a ea ac ion o RBCs in he essel, VRBC ¼56:5mm3and ARBC a e he cell olume and he su ace a ea (measu ed empi ically in each essel o a selec ion o single cells) o he RBCs espec i ely, and R is he essel adius. This co ec ion, simila o he app oach in p e ious wo k (7), akes in o accoun he de o - ma ion o he cells in he plane while a oiding any coun ing mis ake ha close RBCs (o he segmen a ion algo i hm) could induce (see Suppo ing ma e ial o mo e de ails). This co ec ion is alida ed using 2D p ojec ion slices o he nume ical simula ion, whe e he hema oc i alue is known as simula ion inpu ; he e o o he alida ion is below 1%. Fo de ec ed RBCs, he s anda d Ma lab unc ion Weigh edCen oid was used o calcula e hei cen e o mass. In his unc ion, he cen e o mass is calcu- la ed based on he loca ion and in ensi y ~ R¼PN i¼1PN j¼1½xi;yjIðxi;yjÞ= PN i¼1PN j¼1Iðxi;yjÞ, whe e xand ya e he coo dina es o each pixel and Iðx;yÞ e e s o he in ensi y o he pixel a posi ion ½x;y. A acking algo i hm was hen used o de e mine he eloci y o he de- ec ed RBCs (41). The a ia ions o ligh in ensi y along he essels, in conjunc ion wi h he collisions and ansien agg ega ions o RBCs, did no allow us o eliably ollow all RBCs along hei en i e ajec o ies. How- e e , as we ocused on bi u ca ions whe e he mo he essel ðMÞand he wo daugh e essels ha e a hema oc i low enough o dis inc single RBCs, his acking allowed us o ex ac he spa ial dis ibu ion o he RBC eloci y (i.e., we pe o med pa icle acking elocime y (PTV)), on which we pe o med ou u he analyses. In his a icle, we will e e o he wo daugh e essels as main daugh e ðMDÞand seconda y daugh e ðSDÞ. By de ini ion, MD is he daugh e essel wi h highe ac ional blood low a e and SD is he one wi h lowe alue. To de ec he linge ing o RBCs, we applied a me hod as in ou p io wo k (29) by de ining a ci cle wi h a diame e o 6mm (i.e., he main diame e o a hams e RBC) su ounding he bi u ca ion apex (Fig. 3 a). The cells we e conside ed o linge i hei cen e o mass was loca ed in his ci cle and a he same ime had a eloci y lowe han he local minimum de ec ed in he p obabili y densi y unc ion (PDF) o a collec i e da ase o RBC eloci ies (Fig. 3 b). The eloci y PDF displayed in Fig. 3 bwas ob- ained by conside ing he M essel and he bi u ca ion a ea. In his s udy, low and cell s a is ics we e cha ac e ized wi hin speci ic ime in e als (10–20 s), longe han he ansi ime o indi idual RBCs bu s ill sho enough so ha he low is quasi-s eady (i.e., no sys ema ic end and/o sig- ni ican change in he olume low a es can be iden i ied). Wi hin such in- e als, sel -consis en obse ables could be well de ined. Nume ical simula ions Complemen a y simula ions o ime-dependen RBC low in he ep esen- a i e capilla y bi u ca ions we e un wi h HemeLB (h ps://gi hub.com/ hemelb-codes/hemelb) using he imme sed-bounda y-la ice-Bol zmann me hod ollowing ou p e ious app oach (21). Fi s , h ee-dimensional (3D) luminal su ace models we e econs uc ed om bina y masks o he capilla y bi u ca ions using open-sou ce so wa e PolNe (42), assuming ci cula c oss sec ions o a ying diame e along each essel. Then he low domain enclosed by he luminal su ace was uni o mly disc e ized in o cu- bic la ices o ine oxel size Dx¼0:25 mm, aimed a esol ing cell dy- namics wi h high esolu ion a he bi u ca ion apex. To ini ialize he simula ion, in low/ou low bounda y condi ions based on expe imen al ime-a e age olume low a es we e imposed a he end o he M essel and he MD b anch (simila ly de ined as abo e o he expe imen s) o each bi u ca ion, and a e e ence p essu e o he SD b anch. No-slip bounda y condi ions we e imposed a he essel wall. The physical leng h co esponding o each simula ion ime s ep was D ¼1:04 106s. The simula ion o each bi u ca ion was ini ialized wi h (RBC- ee) plasma low. Once he plasma low became con e ged, RBCs we e andomly inse ed om he M essel h ough a cylind ical low inle wi h cons an eeding hema oc i ðHFÞas measu ed om expe imen s (see Suppo ing ma- e ial sec ion ‘‘simula ion hema oc i and RBC ini ializa ion’’). When RBCs eached he end o MD o SD, hey we e emo ed om he simula ion domain. Each RBC was modeled as a cy osol- illed capsule wi h an iso opic and hype elas ic memb ane consis ing o 5120 iangula ace s. The me- chanical p ope ies o he RBCs we e go e ned by elas ic moduli go e ning di e en ene gy con ibu ions, such as shea ing and bending o he mem- b ane. The cy osol was ea ed as a New onian luid wi h he same iscosi y as he suspending medium (i.e., blood plasma). The iscosi y o he RBC memb ane i sel was no conside ed. To p obe he e ec o con inemen , wo di e en RBC diame e s we e conside ed (D bc ¼6mmco esponding o no mal hams e RBC size and D bc ¼8mmco esponding o la ge cells o simila size o a human RBC). Two di e en memb ane s i ness le els (s ain modulus ks¼5106;5105N=m) we e conside ed o ep e- sen ing a no mal and a ha dened cell, espec i ely. Fo cell-cell and cell- wall in e ac ions, epulsi e po en ials in e sely decaying wi h he dis ance we e implemen ed. High-enough esolu ion was used o ensu e he cell- cell/cell-wall dis ance did no all below one g id poin . RESULTS AND DISCUSSION De e mina ion o low a es and baseline Zwei ach-Fung pa i ioning To de e mine how he linge ing o RBCs in luences hei pa i ioning, we used he empi ical model o P ies e al. abc FIGURE 1 Expe imen al me hods. (a) Do sal skin old chambe implan ed on he back o a ham- s e . (b) Anes he ized hams e placed unde nea h he objec i e o an epi luo escence mic oscope. (c) An exempla mic o ascula ne wo k imaged by luo escence mic oscopy. The dyed plasma appea s b igh ; RBCs in capilla ies (see a ows) and he su - ounding issues a e da k. To see his igu e in colo , go online. Rashidi e al. 1528 Biophysical Jou nal 122, 1526–1537, Ap il 18, 2023 o he Zwei ach-Fung e ec (24) as a baseline. Fo his pu - pose, we i s de e mined he blood low a e Qin each essel. Since he essels we e smalle han he main adius o he RBCs, we assumed a plug low. We also assumed ha he di e ence be ween he ube and discha ge hema oc i s was negligible in ou obse a ions. The low a es wi hin all bi u ca ion segmen s we e he e o e ini ially assessed om he eloci ies (V) and diame e (D) measu emen s o he indi idual segmen s CQD¼CVDpD 22 ;(1) simila ly o p e ious s udies (22,29,43). Mass conse a ion s ipula es ha he o al olume low a e om he M essel QMis di ided in o he daugh e b anches and sa is y QM¼ QMD þQSD. The subsc ip s MD and SD e e o he main daugh e and seconda y daugh e , espec i ely. To obey his conse a ion law and minimize expe imen al e o s, alues ob ained om Eq. 1 we e co ec ed ollowing he no maliza ion p ocess desc ibed by P ies e al. in p e ious simila measu emen s (22). Simila ly, he measu ed e y h o- cy e low a es Ei¼HiQi,Hibeing he local hema oc i , we e also co ec ed o obey EM¼EMD þESD. The empi - ical law o he Zwei ach-Fung e ec de eloped by P ies e al. (22–24) desc ibes he ela ion be ween ac ional blood low, FQb, and he ac ional e y h ocy e lux, FQe, in he mic o ascula bi u ca ion. The ac ional blood lows FQb o bo h daugh e essels we e calcula ed by di iding he low a e Qin he espec i e daugh e by he low a e in he M essel. The ac ional e y h ocy e low a es FQe we e compu ed as he a io o he co ec ed e y h ocy es low a es (e.g., EMD=EM o he MD). Wi h hese de ini- ions, he model om P ies e al. (22–24) s a es whe e logi ðxÞ¼lnðx=ð1xÞÞ and A,B,X0a e ela ed o he bi u ca ion geome y and eeding hema oc i in he M: whe e H e e s o he measu ed hema oc i , calcula ed om he a e age a ea ac ion o RBCs in he mask du ing he expe imen (23,24). The subsc ip s indica e he essel o which he quan i y is conside ed. Due o he he e ogeneous blood low and di e se geome- ies in he mic o ascula u e, he FQeand FQbda a ex- ac ed in i o a e na u ally sca e ed (22,23), which may also apply o egula in i o ascula ne wo ks (10,11). Howe e , P ies e al. de i ed hei empi ical model o obus single-bi u ca ion p edic abili y (see Fig. 4 in Re . (22) and Fig. 2 in Re . (23)) wi h in i o da a ob ained h ough a classic p o ocol ha enabled con inual a ia ion o he hema oc i s in indi idual bi u ca ions. In he p esen s udy, we se ou o in es iga e why indi- idual bi u ca ion cases (a widely adop ed app oach (5–8, 16–18) o s udy he RBC pa i ioning beha io ) would nicely sca e a ound his empi ical limi as de ined by Eq. 2, bea ing in mind ha he e ec s o low a io, essel geome y, and eeding hema oc i we e al eady accoun ed o in he o iginal model. To do his expe imen ally, we conside a se o bi u ca ions selec ed in i o o examine how he RBC pa i ioning in hem de ia es om he base- line spli (as pos ula ed by Eq. 2) and u he co ela e he de ia ion wi h expe imen al ac o s no conside ed by he empi ical model. In pa icula , we ocus on he linge ing beha io , which appea s a po en ial mechanism o such de ia ions in highly con ined capilla ies. Indeed, he ini ial s udy o P ies e al. analyzed a e iola bi u ca ions wi h cha ac e is ic diame e s abou 8mm o la ge (22); i.e., la ge han he main diame e o hams e RBCs. In hei s udies o bi u ca ions wi h lowe con inemen le el, he linge ing beha io (i any) was p obably no playing a signi ican ole in he pa i ioning o cells. In he case p e- sen ed he e, s udied essel diame e s ange be ween 3.5 and 5.6 mm; i.e., conside ably smalle han he diame e o he hams e RBCs. Such high con inemen would a o AMD ¼13:29 D2 MDD2 SD 1 D2 MDD2 SD þ1ð1HMÞDM;ASD ¼AMD;B¼1þ6:981HM DM;X0¼0:9641HM DM; (3) FQe¼ 8 > > > > < > > > > : 0;i FQb<X 0 1;i FQb>1X0 logi 1AþBlogi FQbX0 12X0;o he wise (2) RBC linge ing and hema oc i dis ibu ion Biophysical Jou nal 122, 1526–1537, Ap il 18, 2023 1529 he linge ing o RBCs as he cells canno easily a oid in e - ac ing wi h he essel wall a he bi u ca ion. Linge ing and pa i ioning Global desc ip ion Expe imen s. Fig. 2 a–cshows h ee ep esen a i e bi u - ca ions ( wo Y shaped and one T shaped) whe e all equi ed pa ame e s could be ex ac ed om he image sequences. A cha ac e is ic mo ie is p o ided as Video S1. We calcula ed he empi ical p edic ions by Eq. 2 o each bi u ca ion (nine in o al) and de ined he de ia ions om he model as dZF ¼DFQeEX DFQeZF. Al e na i e de ini ions o he de ia ion (e.g., in signed o m DZF) a e discussed in he Suppo ing ma e ial (Fig. S7). We no ed DFQe¼ FQeðMDÞFQeðSDÞ, he di e ence o ac ional e y h ocy e low a e, and he exp essions EX and ZF e e o he expe - imen al da a and he empi ical p edic ion, espec i ely. The ac ional blood low a e FQbis gi en by he expe imen al measu emen s, and he p edic ed ac ional e y h ocy e low a e FQZF eis compu ed h ough Eq. 2 (see Fig. 4 a o a schema ic). To quan i y he linge ing o RBCs a each bi u ca ion, we i s de e mined he a e age du a ion o he linge ing e en s C D. The o al linge ing ime was conside ed as he sum o he du a ion o all de ec ed linge ing e en s. We hen de e - mined he a io o his o al linge ing ime o he numbe o he RBCs as he cha ac e is ic a e age linge ing ime C D. Since his ime is highly co ela ed wi h he low a e and he ansi ime o an RBC h ough he bi u ca ion (i.e., he ed ci cle de ined in Fig. 3 a), we no malized i by s¼ R=CVMD. The adius R¼3mm is he adius o he ed ci cle de ined in Fig. 3 aand VM he a e age eloci y in he M essel. abc ed FIGURE 2 Rep esen a i e bi u ca ions om expe imen s ha a e simula ed. (a–c) Th ee bi u ca ions selec ed om he expe imen s he ea e e e ed o as BIF-a, BIF-b, and BIF-c, espec i ely. The M essel, he MD, and SD a e anno a ed wi h a ows indica ing he low di ec ion. The plasma was s ained wi h luo escen dye (b igh in he images). Da k a eas in he essels indica e he RBCs. The bo de o he masks used o analyze he bi u ca ions a e depic edin colo ed symbols. Consis en colo s and symbols a e used o hese bi u ca ions h oughou he a icle. (d– ) Simula ed RBC low in he econs uc ed domain o c opped bi u ca ions, espec i ely (a–c) as cha ac e ized expe imen ally. To see his igu e in colo , go online. FIGURE 3 RBC eloci y dis ibu ions in he expe imen and simula ion. (a) Spa ial dis ibu ion o RBC eloci ies ob ained h ough pa icle acking in expe imen o BIF-b. Linge ing is conside ed o occu i a cell is inside he ed ci cle (6mm, size o a ypical hams e RBC) wi h a eloci y lowe han he h eshold eloci y, which is de e mined as a local minimum in he PDF o eloci ies ob ained om he M essel and he bi u ca ion a ea (M þb ), as shown in (b). Fo compa ison, he e- loci y PDFs o he MD and SD b anches and he M essel a e also shown. (c) Co esponding colo map o RBC eloci ies measu ed along simula ed cell ajec o ies in BIF-b. (d) Veloci y PDFs measu ed in di e en essel b anches o he simu- la ed BIF-b as o he expe imen al da a in (b). To see his igu e in colo , go online. Rashidi e al. 1530 Biophysical Jou nal 122, 1526–1537, Ap il 18, 2023 The ime sis hen a cha ac e is ic ad ec ion ime ha a cell would need o go h ough he linge ing de ec ion a ea (whe e he cell eloci ies diminish; Fig. 3 b). We de ined he a io o hese wo cha ac e is ic imes as Pel¼C D= s. The a io Pel de ines he equi alen o a P ecle numbe , since i compa es wo cha ac e is ic imes o di e en anspo modes a he bi u ca ion (linge ing and ad ec ion). As shown in Fig. 4 c o nine di e en bi u ca ions (see expe imen al de ails in Table S1), he de ia ion dZF om he Zwei ach-Fung p edic- ion Eq. 2 s ongly co ela es wi h Pel(Pea son co ela ion co- e icien ¼0:74,p<0:05). In e es ingly, we obse ed in some case ha he de ia ion om he Zwei ach-Fung e ec caused by he linge ing can e e he pa i ioning. Indeed, in he case o he ( ed) cha ac e is ic bi u ca ion highligh ed in Fig. 2 a, he MD (wi h highe FQb) is he b anch wi h lowe FQe.Thisis o en e e ed o in he li e a u e as e e se pa i ioning (7,10,11,26). In ou da a, we only obse ed such e e se pa - i ioning o he highes Pelz1:75. Simula ions. The h ee ep esen a i e bi u ca ions om ex- pe imen s in Fig. 2 a–cwe e also simula ed unde equi alen low condi ions and RBC olume ac ions (see de ails in Table S1), wi h he linge ing phenomenon o RBCs success- ully ep oduced (Fig. 2 d– ). These bi u ca ions we e selec ed o nume ical sc u iny because hei expe imen al coun e - pa s oughly co e he en i e ange o p ima y obse ables (e.g., Pel,dZF,dp ). A compila ion o anima ion ideos gene - a ed om nume ical simula ions a e p o ided as Video S2.To quan i y he linge ing beha io , an equi alen p ocedu e o he expe imen al da a analysis was applied o analyze he simula- ion da a oo. Exempla ajec o ies o RBCs nea he bi u ca- ion apex om simula ions o a ying eeding hema oc i s a e shown in Fig. S3. In line wi h he expe imen al PTV measu emen s, he cell eloci ies diminished as he RBCs app oached he bi u ca- ion apex (Fig. 3 c). A e en e ing one o he daugh e b anches (MD o SD), he ins an aneous eloci y o RBCs would inc ease again. These pa e ns we e well cap u ed by he eloci y PDFs compiled o indi idual essel b anches in each bi u ca ion (Fig. 3 d). Quan i ica ion o linge ing e en s based on he simula ed RBC eloci ies e- ealed ha he pe cen ages o linge ing cells o he h ee bi- u ca ions we e 63%, 85%, and 4%, espec i ely. Fo ha dened RBCs wi h a memb ane s ain modulus 10 imes as la ge, he a ios became 23%, 77%, and 42%. No e ha he p opo ion o linge ing cells does no unequi ocally de e mine Pel; a he , he a e age linge ing ime domina es, conside ed as he sum o ime du a ion (moni o ed om all de ec ed linge ing e en s) di ided by he o al numbe o cell ansi s. In o he wo ds, a highe p opo ion o linge ing cells does no necessa ily lead o a highe P ecle numbe . Fo ins ance, a lowe po ion o cells linge s in BIF-a han in BIF-b, bu hey linge o longe ime compa ed wi h hei ad ec ion ime, he e o e causing a la ge Pel. The co ela ion be ween he linge ing in ensi y o RBCs and hei pa i ioning a he bi u ca ions, namely Peland dZF, was e alua ed simila ly o he expe imen al da a (Fig. 4 d). A s ong associa ion was ound, indica ing a linea inc ease o dZF agains Pel(Pea son- co ela ion coe icien 0.71, p<0:05). Ne e heless, he absolu e magni ude o dZF and Pelwe e subs an ially smalle (al hough in a p opo ional manne ) han hei expe imen al coun e pa in Fig. 4 c.The FIGURE 4 Expe imen al and simula ion esul s o RBC pa i ioning e sus linge ing. (a) Compa i- son o expe imen al RBC pa i ioning agains he empi ical p edic ions o he Zwei ach-Fung e ec ( o BIF-a as in Fig. 2 a). The axes FQeand FQb a e o he ac ional RBC lux and ac ional blood low, espec i ely. The de ia ion om he empi ical p edic ion was calcula ed as dZF ¼DFQeEX  DFQeZF.(b) The ba s show expe imen al esul s agains he lines, ep esen ing empi ical p edic ions by Eq. 2. The da a he e a e o he h ee cha ac e - is ic bi u ca ions in Fig. 2 a–c, wi h consis en colo s and symbols. Dashed lines and hollow symbols he e e e o he SD essel wi h lowe ac ional low a e FQb. No e he in e sion o he Zwei ach-Fung e ec in BIF-a. (c) Expe imen al de ia ion dZF om Eq. 2 as a unc ion o he linge ing P ecle numbe Pel. The poin s wi h e o ba s a e expe imen al da a, and he solid line shows linea eg ession i ing o he da a poin s, wi h he shaded a ea indica ing 95% con i- dence in e al p edic ion om he i . All da a ga h- e ed om nine bi u ca ions (including he h ee bi u ca ions BIF-a, BIF-b, and BIF-c in Fig. 2 a–c) a e included in his g aph. The Pea son- co ela ion coe icien (n ¼9) is ¼0.74 (p¼0.02). E o ba s in (a–c) a e compu ed by e o p opaga ion om he unde lying expe imen al measu emen s. (d) Co - ela ion be ween dZF and Pelin simula ions (n ¼12). The c osses a e simula ion da a and he solid line shows linea eg ession i ing o he da a poin s. The Pea son- co ela ion coe icien is ¼0.71 (p¼0.014). To see his igu e in colo , go online. RBC linge ing and hema oc i dis ibu ion Biophysical Jou nal 122, 1526–1537, Ap il 18, 2023 1531 highes P ecle numbe was only Pel¼0:65 in he simula- ions compa ed wi h a maximum alue o Pel¼1:75 in he expe imen s.This disc epancy may ha e a isen om simu- la ion con igu a ions ha a e di e en om in i o expe i- men s; e.g., absence o endo helial su ace laye (ESL; oughly 0.4–0.5 mm in hickness) and RBC glycocalyx in he nume ical model. Indeed, al hough a epulsi e cell-wall po en ial was implemen ed, i is possible ha he ESL coa ed by cilia ed s uc u es in e ac s wi h he RBCs in mo e complex ways (20,44,45). Fo ins ance, i may con ibu e o enhanced con inemen o gi e ise o an a ac ion o ce. Because hese ad anced cell-wall in e ac ions ha e no been de ini i ely cha ac e ized in he li e a u e, wi hou a angible physical model, we could no cap u e such e ec s in ou simula ions. In any case, he co ela ion be ween he linge ing P ecle num- be Peland he de ia ion om he P ies model was quali a- i ely simila be ween he expe imen and he simula ion. We no e ha no e e se pa i ioning (o in e sion o he Zwei ach-Fung e ec ) wasobse edin ou simula ions, which is in ag eemen wi h he ac ha e e se pa i ioning in expe - imen s only occu ed o bi u ca ions wi h Pel>1:75. Linge ing asymme y in expe imen s Fo insigh s in o how he linge ing beha io could modi y RBC pa i ioning a he bi u ca ion, we u he examined i s symme y be ween he wo daugh e b anches. Indeed, as can be seen om Video S1, he RBCs end o en e he lowe daugh e b anch ðMDÞalmos only i he e is ano he cell al eady linge ing a he bi u ca ion apex. Due o cell collisions a he apex, i was no possible o p ecisely de e - mine he p opo ion o linge ing cells en e ing each daugh e me ely by analyzing hei ajec o ies. The e o e, we calcula ed he a e age ad ec ion ime ao he cells be- ween he (blue) mask in bi u ca ion and he (magen a) mask in he daugh e (Fig. 5 a). This ad ec ion ime was de e mined by calcula ing he con olu ion o he empo al hema oc i in he daugh e mask and ha in he bi u ca ion mask (see Fig. 5 aand Fig. S2 b). We hen checked i he e was a linge ing e en a he bi u ca ion (also moni o ed in a hin mask) a a ime aea lie o each cell de ec ion. We ealized ha , o such so ing, some linge ing e en s a he bi u ca ion could no be a ibu ed o any ad ec ed cell in o he daugh e s. Indeed, he ad ec ion ime o each cell can a y sligh ly, depending on i s in e ac ions wi h o he cells nea he apex. The e o e, a e being empo ally ans- la ed by a, he cell de ec ion can be loca ed close o he linge ing e en bu no exac ly wi hin i s du a ion. Fo mo e accu a e cha ac e iza ion, we he e o e measu ed he p oximi y ime ibe ween he closes linge ing e en and he ansi ime (de ec ion ime in he daugh e minus a) o each cell (Fig. 5 b). Cells wi h a p oximi y ime i¼0 can hen be de e mined as linge ing. We u he de ined dp ¼jpSD pMDjas he di e ence be ween he p opo ion o linge ing cells in he wo daugh e b anches (Fig. 5 ). FIGURE 5 Asymme y in RBC linge ing a he bi u ca ion. (a) Example o mask se used o de e mine he ad ec ion ime ao RBCs om he bi u ca ion (blue mask) o he SD b anch (magen a mask) ia con olu ion o he hema oc i in bo h masks (see main ex and Fig. S2). Equi alen analysis is pe o med independen ly o he MD b anch. (b) Ex ac ion o he p oximi y ime io each cell. The hema oc i a ia ion o e ime, ex ac ed om he daugh e ’s mask, is i s ansla ed by he a e age ad ec ion ime a(see Fig. S2). Then, o each peak o his hema oc i along ime, a p oximi y ime iis ob ained as he empo al dis ance om he closes linge ing e en . This p ocess is pe o med independen ly o he wo daugh e s. (c–e) CDF o he p oximi y ime o linge ing e en s o bo h daugh e s o he h ee cha ac e is ic bi u ca ions. When a signi ican di e ence (conside able dp ) is obse ed in he expe imen s, highe p opo ion o linge ing cells (and a close p oximi y wi h linge ing e en s) is usually ob ained in he daugh e b anch wi h he lowe ac ional RBC lux FQe.( ) The co ela ion be ween expe imen al dp (di e ence in he p opo ion o linge ing cells in SD and MD calcula ed om CDFs a i¼0) and Pel. The Pea son- co ela ion coe icien is 0.59 ðp¼0:09Þ. To see his igu e in colo , go online. E o ba s a e compu ed by e o p opaga ion om he expe imen al unce ain ies o pSD and pMD. Rashidi e al. 1532 Biophysical Jou nal 122, 1526–1537, Ap il 18, 2023 Because cells wi h a small p oximi y ime imigh also ha e been linge ing o migh ha e in e ac ed wi h ano he cell linge ing a he apex, we used he di e ence be ween he i s wo poin s o he cumula i e densi y unc ion (CDF) dis ibu- ion o i(Fig. 5 c–e) as e o ba s o pSD and pMD. As can be seen in Fig. 5 c–e, he p oximi y ime idis ibu ion and he p opo ion o cells iden i ied as linge ing a e dis inc o he wo daugh e s unde la ge Pel. Fo he expe imen ally obse ed cases as highligh ed in Fig. 5 , he asymme y in he p opo ion o linge ing cells is weakly co ela ed wi h he linge ing in ensi y Pel. In simula ion, bo h dp and Pel o he simula ed bi u ca ions ( h ee in o al) a e smalle han hei expe imen al coun e pa bu in a p opo ional manne wi h quali a i e ag eemen (see Fig. S2 c). O igin o linge ing in expe imen s To unde s and wha causes he cells o linge , we iden i ied geome ical ea u es o he bi u ca ions co ela ing wi h he linge ing P ecle numbe Pel. Due o he de ini ion o he linge ing e en s as a signi ican educ ion o he RBC eloc- i y a he bi u ca ion, i is likely ha cells linge a he s agna- ion poin ; i.e., he in e sec ion o he bi u ca ion’s wall and he low di ide plane. No e ha a s agna ion poin is consid- e ed because he 3D essels a e p ojec ed in he mid- essel plane. A his posi ion, he cells will also expe ience he smalles d ag o ce, likely no o push he cell owa d any daugh e essel. The posi ion o he s agna ion poin depends on he ac ional low a e o he daugh e b anches (46). The dis ance o he s agna ion poin om he cen e line Ls, which is depic ed in he Fig. 6 a, can be app oxima ed h ough QMD QSD ¼ 1þ2 pa csinLs RMþ2Ls pR2 Mffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 ML2 s q 12 pa csinLs RM2Ls pR2 Mffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 ML2 s q;(4) whe e RMis he adius o he M b anch (see Suppo ing ma e- ial o u he jus i ica ion). Fo he si ua ions whe e nume i- cal simula ions we e compa ed wi h he expe imen al da a, posi ions o he s agna ion poin de e mined his way we e loca ed wi hin one pixel o dis ance om he posi ion indi- ca ed by he s eamlines (see Fig. S4). This app oxima ion can hen be conside ed o be consis en wi h he a ailable nu- me ical da a. Nume ical simula ions also showed ha he shi o he s agna ion poin due o s udied RBC ansi s we e negli- gible compa ed wi h o he expe imen al unce ain ies (see Fig. S5). Since he cells a he s agna ion poin expe ience he small- es d ag o ce, one can assume ha he domina ing o ces on he cells a ise om hei in e ac ion wi h he endo helial laye . In u n, his in e ac ion p obably depends on he geome y o he wall a his loca ion, whichcan mos ly be desc ibed h ough i s cu a u e. To de e mine he cu a u e o each bi u ca ion, a ci cle was i ed on he neighbo hood o he s agna ion poin FIGURE 6 Po en ial o igin o RBC linge ing. (a) Schema ic highligh ing he low spli and he s agna ion poin a bi u ca ions. Flow in he mo he b anch spli s in o lows QMD and QSD in he MD and SD b anches, espec i ely. The s agna ion poin is indica ed by he g een poin , whose dis ance om he apex Ls is highligh ed wi h he a ow and scale symbol. The illed ci cle shows an idealized c oss sec ion o he mo he essel wi h simpli ied and la low sepa a ix. (b) Co ela ion o he linge ing P ecle numbe Pelwi h he cu a u e zo he bi u ca ion a he s agna ion poin . (c) Co ela ion be ween Peland he low a e a io be ween he SD and MD QSD=QMD.(d) Co ela ion be ween Peland he dis ance be ween he s agna ion poin and he bi u ca ion apex LS.(e) Co - ela ion be ween LSand he cu a u e a he s agna ion poin z.In(b)–(e), he poin s a e expe imen al da a, he solid lines show linea eg ession i ing o he da a poin s, and he shaded a eas indica e he 95% con idence in e al p edic ion om each i . To see his igu e in colo , go online. E o ba s in (b–e) a e compu ed by e o p opaga ion om he unde lying expe imen al measu emen s. RBC linge ing and hema oc i dis ibu ion Biophysical Jou nal 122, 1526–1537, Ap il 18, 2023 1533 (see Fig. S4). The cu a u e is de ined as he in e se o he adius o his ci cle. To es ima e he measu emen unce ain y, we used mul iple i edci cles, each calcula ed using a di e en leng h o he neighbo hood (leng hs be ween 4and 8mm, cen e ed on he s agna ion poin ). The mean alue o he cu a- u es is aken as he bes app oxima ion, whe eas he s anda d de ia ion gi es he e o ba s. The esul s showed ha he cu - a u e o he bi u ca ion a he s agna ion poin co ela es wi h Pel( ¼0:59 and p¼0:09) (see Fig. 6 b). In e es ingly, when es ing co ela ions wi h u he possibly in luencing pa- ame e s, we ound ha he linge ing P ecle numbe Pelalso co ela es wi h he a io o he low a es be ween he SD and MD QSD=QMD (Fig. 6 c). Since his pa ame e de e mines he dis ance LSbe ween he apex o he bi u ca ion and he s agna ion poin h ough Eq. 4, his pa ame e LSalso co e- la es wi h Pel(Fig. 6 d). Fu he mo e, he bi u ca ions whe e he s agna ion poin is u he om he apex gene ally ha e a lowe cu a u e a he s agna ion poin , as shown by Fig. 6 e. We he e o e hypo hesize ha he low a e a io de e mines whe e he cells can linge , whe eas he cu a u e o he endo- helial laye a his linge ing posi ion de e mines he in ensi y o he linge ing. The linge ing P ecle numbe would hen be de e mined by an in e play be ween global pa ame e s o he bi u ca ion ðQSD =QMDÞand local geome ies o he endo he- lial laye ( he cu a u e a he s agna ion poin , z). When i comes o he expe imen al co ela ions, he esul ha a lowe coe icien is ound be ween Peland z han Peland QSD=QMD likely a ises om he ac ha he de e mina ion o zalso elies on he app oxima ion o LSand hen he measu emen o QSD=QMD. The e o p opaga ion on hese successi e quan i- ies hen likely dec eased a i icially he co ela ion be ween Peland he successi ely de e mined pa ame e s LSand z. Mo e geome ical pa ame e s, which ailed o demon- s a e a signi ican co ela ion wi h Pel, a e included in he Suppo ing ma e ial (see Fig. S6). E ec o cell igidi y and hema oc i in simula ions Besides he cu a u e o he s agna ion poin a he apex, o he ac o s may also a ec he in e ac ion be ween he cells and he bi u ca ion, leading o ei he weakened o enhanced RBC linge ing. Taking a ypical Y- ype bi u ca ion o example (Fig. 7 a), h ee physiologically ele an aspec s we e nume ically explo ed: he cell igidi y ks, he eeding hema oc i HF, and he cell size DRBC (D bc ¼6mm unless o he wise speci ied). Inc eased cell igidi y (imi a ing diseased RBCs wi h highe -le el s i ness) a he Y- ype bi u ca ion is ound o in oduce s ong cell-wall and cell-cell s e ic epulsion a he apex (see enla ged gaps nea he b anching poin in Fig. 7 a), hus educing he o e all linge ing equency and a e age du a ion o indi idual linge ing e en s as indi- ca ed by a smalle linge ing P ecle numbe Pel(BIF-a in Fig. 7 b). The same is ound o BIF-b oo (Fig. 7 b). Con a ily, o a T- ype bi u ca ion (less common bi u ca- ion ype in mic o ascula ne wo ks), s i e RBCs end o ge s uck a he apex due o cell collisions and can lead o mo e in ense linge ing ins ead (see BIF-c in Fig. 7 b). The dis inc e ec o RBC de o mabili y on i s linge ing beha io a he Y- ype and T- ype bi u ca ions obse ed he e is in line wi h a ecen epo on capilla y ascula ne wo k (30). On he o he hand, o iden ical low condi ions, an en- iched hema oc i (HF¼33%, ela i e o he baseline HF¼12%basedonexpe imen almeasu emen )in he M b anch has a weakening e ec on RBC linge ing a he bi u ca ion, whe eas a educed hema oc i ðHF¼10%Þhas a s eng hening e ec compa ed wi h he expe imen ally measu ed alue HF¼12% o he same bi u ca ion (Fig. 7 c). The p obable eason behind he dec eased Pelin his case is ha c owded cell a ic educes he possibili y o indi idual RBCs esiding on he apex o ex ended pe iods o ime as hey a e mo e likely o be pushed o wa d by ollowing cells (‘‘he ding’’ e ec as epo ed in (47)). We also conside ed a di e en RBC size gi en he a iabili y o cell mo phology in i o, which is modeled h ough inc easing he de aul cell diame e DRBC ¼6mm om DRBC ¼6mm o DRBC ¼8mm while main aining he same HF(Fig. 7 c). The inc eased RBC size leads o highe le el o cell con inemen in he capilla ies and educes he luc ua ion ampli ude o RBC linge ing caused by hema oc i al e a ion. FIGURE 7 E ec o cell igidi y and eeding he- ma oc i HFon he linge ing o RBCs in simula- ions. (a) S e ic epulsion o ( op) no mal (N) and (bo om) ha dened (H) RBCs a he apex o a Y- ype bi u ca ion co esponding o BIF-a in Fig. 2.(b)Pel e sus cell igidi y o no mal and ha dened RBCs a BIF-a, BIF-b, and BIF-c’’ (see Fig. 2). Solid lines a e o simula ions wi h HF ma ching co esponding expe imen al condi ion, whe eas dashed lines a e simula ions wi h ele a ed hema oc i le els ( wice as high o BIF-a and BIF-b, and h ee imes as high o BIF-c). (c)Pel e sus eeding hema oc i HF o BIF-a wi h no mal RBCs (in de o mabili y) o wo di e en sizes D bc ¼6;8mm. To see his igu e in colo , go online. Rashidi e al. 1534 Biophysical Jou nal 122, 1526–1537, Ap il 18, 2023