Lingering Dynamics in Microvascular Blood Flow
A. Kihm, S. Quint, M. W. Laschke, M. D. Menger, T. John, L. Kaestner, C. Wagner
LLingering dynamics in microvascular blood flow
A. Kihm, S. Quint,
1, 2
M. W. Laschke, M. D. Menger, T. John, L. Kaestner,
1, 4 and C. Wagner
1, 5, a) Department of Experimental Physics, Saarland University, 66123 Saarbruecken,Germany Cysmic GmbH, 81379 München Institute for Clinical and Experimental Surgery, Saarland University, 66421 Homburg,Germany Theoretical Medicine and Biosciences, Saarland University, 66421 Homburg,Germany Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg (Dated: February 26, 2021)
The microvascular networks in the body of vertebrates consist of the smallest vessels such as arterioles,capillaries, and venules. The flow of RBCs through these networks ensures the gas exchange in as well as thetransport of nutrients to the tissues. Any alterations in this blood flow may have severe implications on thehealth state. Since the vessels in these networks obey dimensions similar to the diameter of RBCs, dynamiceffects on the cellular scale play a key role. The steady progression in the numerical modeling of RBCs, evenin complex networks, has led to novel findings in the field of hemodynamics, especially concerning the impactand the dynamics of lingering events, when a cell meets a branch of the network. However, these resultsare yet to be matched by a detailed analysis of the lingering experiments in vivo. To quantify this lingeringeffect in in vivo experiments, this study analyzes branching vessels in the microvasculature of Syrian goldenhamsters via intravital microscopy and the use of an implanted dorsal skinfold chamber. It also presents adetailed analysis of these lingering effects of cells at the apex of bifurcating vessels, affecting the temporaldistribution of cell-free areas of blood flow in the branches, even causing a partial blockage in severe cases.Keywords: Microvasculature, Lingering, in vivo, blood flow, red blood cells
INTRODUCTION
The steady transport of nutrients to the tissues of thebody, as well as the delivery of oxygen, is crucial for thehealth state in animals and humans. However, in uni-cellular living beings, this task can be achieved by purediffusion. Active transport is necessary to ensure thisexchange in vertebrates. This process is realized by thesynergistic action of the heart, blood, and vasculature .A key setting is the pressure difference between the aortaand the vena cava . In between, the microvasculature ispresent, consisting of the smallest vessels such as the ar-terioles, capillaries, and venules. The diameters of thesevessels in the microcirculation are in the range of thesize of individual RBCs, which highlights the importanceof the deformation ability of RBCs. Due to the over-all length of the microvasculature and the present cross-sections of vessels, it is responsible for the largest re-sistance and hence the largest dissipation of energy inthe blood flow . Since the microcirculation is embed-ded in the tissues and ensures the perfusion of these andthe organs, any alteration in blood flow may have severeconsequences on the actual health state. Indeed, severalpathological states are linked to the disturbance in themicrocirculation, such as Alzheimer’s disease . Angio-genesis and angioadaptation are hereby prone to fulfil themetabolic needs of the respective organs and tissues .The observed architectures range from tree-like networks a) [email protected] to mesh-like networks, where the subsequent diameters ofvessels at bifurcations satisfy, in general, Murray’s law,although deviations are well-known . Compared tomacrovascular blood flow, effects arising from the par-ticulate nature of blood are more pronounced in the mi-crocirculation. Considering the volume fraction of RBCsin whole blood suspensions, the so-called hematocrit, atemporal heterogeneity, is given in the capillary vesselscontrasting a temporal homogeneity ubiquitous in largevessels such as arteries (cf. Movie S2). Similarly, thevessel diameter in which the blood flows has been foundto have an impact on the local hematocrit . Thisso-called Fåhræus effect can be explained by the lateralmigration of RBCs to the vessel centerline, leaving a cell-depleted layer close to the vessel walls. As a result, RBCsobey a higher speed on average in the Poiseuille profilethan the bulk speed of the plasma. In the seminal workby Fåhræus and Lindqvist , the former effect could beidentified as one of the major causes of the dependenceon the vessel diameter of apparent viscosity in blood so-lutions. Apart from these observations, phase separationin the microvasculature becomes apparent, leading to anonhomogeneous distribution of RBCs within the vessels.This phase separation is partially caused by the Fåhræuseffect, especially in conjunction with bifurcations, albeitit is not the only origin. The entirety of the described ef-fects highlighting the significant impact of the bi-phasiccomposition of blood also show the necessity to modelblood in this way.Recent advances in the modeling of the microvascula-ture in mammals have led to findings of the dynamics of a r X i v : . [ phy s i c s . b i o - ph ] F e b RBCs, as well as other cellular components in silico. Thecomplexity of the networks in these studies ranges fromone symmetrical bifurcation to the mimicking of ananatomically accurate in vivo network consisting of an in-terconnected mesh-like structure with various branches,confluences, and bifurcations . In ref. , such com-plex networks have been investigated on a scale thatboth allows for dense suspensions of RBCs as well asyielding discrete datapoints of every single RBC, includ-ing their individual shape. As a result, deformation anddynamic characteristics of RBCs in the vicinity of bifur-cations have been studied, leading to the observation ofthe so-called lingering events. This phenomenon of RBCsresting at the apex of bifurcations is well known in phys-iology; however, to our knowledge, no systematic studieshave been carried out to address this phenomenon. Fur-ther, the results found in ref. are still unmatched byany means in vivo. Thus, this study aims to elucidatethe fundamental dynamics of these lingering events invivo. By means of intravital fluorescence microscopy, itcan extract position data out of flowing RBCs in the mi-crocirculatory system of hamsters. Additionally, we havedeveloped algorithms that allow to separate the effect oflingering on the flow of subsequent RBCs. Specifically,we use this approach to show the impact of lingering onthe void duration, i.e., cell-free areas in the bloodstream. MATERIALS AND METHODSPermissions
All the conducted experiments were approved by thelocal government animal protection committee (permis-sion number: 25/2018) and were performed in accordancewith the German legislation on the protection of animalsand the NIH Guidelines for the Care and Use of Labora-tory Animals.
Animal preparation
We briefly describe the necessary steps in the prepa-ration protocol (for a more detailed description, see ).Syrian golden hamsters ( Mesocricetus auratus ) with abodyweight of 60–80 g are equipped with a dorsal skinfoldchamber, consisting of two symmetrical titanium frameswith a total weight of approx. 4 g. For this purpose, theanimals are anesthetized and from their depilated anddisinfected back, one layer of skin and subcutis with thepanniculus carnosus muscle, as well as the two layers ofthe retractor muscle, are completely removed within thearea of the observation window of the chamber. A total offive hamsters were prepared to neglect any interindivid-ual effects and to observe different phenomena in variousgeometries.
Experimental setup
For intravital microscopic analyses of the microcir-culation, the hamster is anesthetized by an intraperi-toneal injection of 100 mg/kg ketamine and 10 mg/kgxylazine, and 0.1 ml of the blood plasma marker 5 %fluorescein isothiocyanate (FITC)-labeled dextran (150kDa, Sigma-Aldrich, Taufkirchen, Germany) is injectedinto the retrobulbar venous plexus for contrast enhance-ment. Subsequently, the animal is fixed on a stage, al-lowing for horizontal positioning of the desired field ofview under the objective of an upright microscope (ZeissAG, Oberkochen, Germany), as previously described formice . Due to the geometry of the observation window(circular with a diameter of 10 mm) and the attachedsnap ring of the chamber, the use of liquid immersion ob-jectives is provided. To maximize the observation area,one ideally uses narrow objectives since the objective maycollide with the frame by examining an area close to theboundaries of the observation window.In this study, two different objectives are used: a waterimmersion objective for investigations of capillary bloodflow with a magnification of × and an air objective witha magnification of × (both Zeiss). Its high magnifica-tion allows for tracking and analyzing individual RBCs(e.g., the cell shape evolution while passing through con-fluences or bifurcations). On the contrary, an air objec-tive with increased working distance is used to recordblood flow in vessel geometries of bigger dimensions (en-larged field of view) or embedded in deeper tissue lay-ers. The recorded image series consist of up to 6,000images, leading to a time coverage of − s dependingon the actual frame rate of the camera (ORCA-Flash4.0V3, Hamamatsu Photonics K.K., Hamamatsu, Japan). Image processing
Due to the inherent properties of a dynamical system,the amount of fluorescent dye in the field of view is highlytime-dependent. This fact results in a flickering motionin the original footage. Histogram matching has beenapplied for uniform white balance throughout the imagesand to suppress these flickering events. A Gaussian blurwas then applied to despeckle the images before applyinga binary mask to disregard the background and enhancethe contrast of the image series. An example of this maskis depicted in Fig. (2), where the original in vivo geom-etry can be found along with the corresponding mask,created by averaging all images and tracing the resultingmean image. Particle tracking has been carried out via acustom-tailored
Matlab ® (MathWorks, Massachusetts,USA) script (see also ). By this technique, we wereable to extract the position data of the moving cells. Westress that due to abundant breathing movements, not allimages of a series can be analyzed but rather split intosubseries of images where no displacements of the vesselsare visible. However, alterations in tissue thickness maylead to deficiencies in image quality. The same holds forthe fact that vessels are winding in a three-dimensionaltopology, and thus, the focal plane will only capture a cer-tain part of the geometry. Therefore, a complete autom-atized analysis is complicated and possible in only somepeculiar cases. For most analyses, manual adjustmentsand evaluations must be carried out. Since the plasmain the hamsters is stained with a fluorescent dye, the ap-parent RBCs obey lower brightness values than cell-free(plasma rich) areas. From the corresponding temporalbrightness distributions, one can therefore define voidsand the passing RBCs. For uniform characterization ofvoid durations, we binarized the signal with respect tothe mean value, i.e., all the signals above the mean willbe considered as void. In each branch, the mean pas-sage time of RBCs are determined and denoted by τ RBC .For a better comparison within a geometry, we seek toachieve a normalized void duration. Therefore, we havedivided the calculated void durations by τ RBC in the re-spective branch to achieve a normalization by the flowrate. These normalized void durations are then sorted inascending order to obtain the empirical cumulative distri-bution function. We postulate this empirical cumulativedistribution function to be represented by a log-normaldistribution function cdf (cid:16) τ n τ RBC (cid:17) ,cdf (cid:18) τ n τ RBC (cid:19) = 12 erf log (cid:16) τ n τ RBC (cid:17) − ˆ µ √ σ , (1)with the error function erf ( · ) , and parameters ˆ µ, ˆ σ ∈ R , ˆ σ > . These paramaters are estimated based on ourdataset using the maximum-likelihood approach, yielding ˆ µ = 1 N N (cid:88) n =1 log (cid:18) τ n τ RBC (cid:19) , ˆ σ = 1 N − N (cid:88) n =1 (cid:18) log (cid:18) τ n τ RBC (cid:19) − ˆ µ (cid:19) . (2)Probability density distributions of the normalized voiddurations are given by differentiation of Eq. [1]. The pos-tulation of the log-normal distribution of normalized voiddurations has been verified a posteriori by a Kolmogorov-Smirnov test. For the geometry in Fig. 2, the correspond-ing cumulative densities of void durations are depicted inFig. 3. RESULTS
We analyze bifurcating vessels in the microvascularsystem of hamsters (arterioles, capillaries, and venules)with varying diameter and bifurcating angles (details aregiven in the Materials and Methods section). A typicalscenario of a lingering event is shown in Fig. 1, where thetemporal evolution of a lingering RBC in an arteriolar bifurcation has been recorded. We analyzed a varietyof different geometries and hamster models (see Supple-mentary Information). Most of the analyzed geometriesexhibit one apex with two branching vessels; however,we have presented here the interesting data of the morecomplex geometry with four apices and a total of sevenbranching vessels (see Fig. 2). Based on the geometrydepicted in Fig. 2, we calculate the integrated brightnesssignal along a line perpendicular to the respective cen-terline of the vessel.To take the lingering into account, we further applieda particle-tracking algorithm yielding trajectories of indi-vidual RBCs. Out of these tracking data, we can extractdetailed knowledge of the RBC velocities. Since a linger-ing event is defined by an RBC resting at the apex of a bi-furcation, we analyzed the velocity data in a small regionaround the apex of the respective bifurcation. If, in thisregion, the speed of passing RBCs obeys a severe drop,we call this a lingering event. The lingering durationis quantized as a time interval when v RBC < µ m / s.This value is significantly lower than that of typical cellspeeds in the microvasculature, which are in the range of v RBC = 100 µ m / s. We did not set this lingering speedto zero because the detected center of mass may shiftslightly in consecutive images according to fluctuations.We want to stress that the cause of this adaptation isexclusively due to the experimental nature and does notcontradict a lingering event, as defined in .In general, the combined application of both the anal-ysis of brightness signals and particle tracking is neededsince it cannot be guaranteed that the trajectories coverthe whole distance the single RBCs are travelling dueto limited image resolution. On the other hand, the soleevaluation of brightness signals along the vessel centerlinewill not be sufficient to detect lingering events due to thecomplex dynamics of RBCs at the apex. Thus, we used acombination of both techniques in the sense that we ana-lyzed void durations by evaluating brightness signals andapplying the particle tracking data as a filter to separatethe influence of lingering on the distribution of voids ineach branch of the given microvascular network. Due toexperimental restrictions, we have to deal with not allvisible parts of a given vessel being situated in the focalplane since they are exploiting a three-dimensional topol-ogy. To overcome this drawback, we obtained the previ-ously described cumulative brightness signal at a vesselsegment that is in focus and thus corrected for the spatio-temporal shift of lingering RBCs at the bifurcation apexand the influence on the flow field thereof at a positionfurther downstream. This shift is computed by the aver-age flow speed in the vessel segment. As a result, the im-pact of distinct lingering scenarios can be associated withthe formation of voids at a given position in the daugh-ter branches. Using the maximum-likelihood approach,we estimated the parameters of our empirical distribu-tion, cf. Materials and Methods section. In Fig. 3, thegood agreement between the dataset and the estimatedcumulative distribution function is shown. The corre- Figure 1. Time series of a lingering RBC at an arterial bifurcation for a time interval of t = 380 ms. The plasma was fluorescentlylabeled, and therefore, RBCs appear as dark spots. At t = 0 ms, an RBC is touching the apex of the bifurcation, marked bythe arrow. The cell starts to deform and linger around this apex, leading to a partial blockage with decreased flow rate, as canbe seen in the upper daughter vessel for all subsequent images. Finally, the cell is detached from the apex at t = 380 ms. Thescale bar is 10 µ m in width. Additional data is provided in Fig. S1.2.Figure 2. (a) Results of particle tracking of RBCs in the given geometry. The flow is coming from top (mother vessel “M” inFigure (b)) and exits in all other branches. The colorbar corresponds to the tracked velocities and depicted is the superpositionof 500 tracks. (b) Snapshot of the geometry with flowing RBCs (red). To enhance the contrast and visibility, false color imagesare shown. The daughter branches are labeled in ascending order from rightmost to leftmost and will be referred to in themain text. (c) Distribution of voids within a branch (1) of a bifurcation. The graph corresponds to the measured integratedintensity along a perpendicular line segment with respect to the centerline of this branch (red line segment in branch (1) in(b)). Values above the mean value (red dash-dotted line) can be regarded as voids, i.e., an absence of cells, whereas valuesbelow the mean value correspond to passing cells. On average, voids have a duration of approx. 100 ms; however, due to partialblockage caused by lingering RBCs, void formation can exceed multiple times the average duration, as can be seen at t ≈ . s,where a void with a duration of ms is formed. sponding probability density functions of voids for thegeometry in Fig. 2 are given in Figs. 4 and 5, resp. In thefirst case, only void durations associated to non-lingeringevents were taken into account, whereas void durationsexclusively associated with lingering events were takeninto account in the latter case. By comparing the graphsfor each branch in both the figures, the influence of lin-gering on the void durations is obvious. In Fig. 4, the median values of the empirical probability distrubutionfor all graphs are narrowly distributed. Contrasting thisstate, for voids associated with lingering events (Fig. 5),we find a shift of medians toward higher void durations.A severe case of this observation can also be seen in theinset graph of Fig. 5, where the median void durationwas more than double in the lingering case with respectto non-lingering events. Figure 3. Cumulative distribution functions of void durations τ for all branches of the geometry in Fig. 2. The temporallength of the voids is hereby scaled for each branch by theaverage time of a RBC to pass, τ RBC . The data points cor-respond to measured void durations, whereas the solid linecorresponds to the respective log-normal distributions withestimated parameters ˆ µ and ˆ σ , as in Eq. (1).Figure 4. Probability density functions of void durations forall branches as in Fig. 3 in the case of non-lingering events.The temporal length of the voids is hereby scaled for eachbranch by the average time of a RBC to pass, τ RBC . Me-dian values obtained from estimated parameters in Eq. [2] areindicated by filled circles in the respective color code.
In addition to the probability densities of void dura-tions, we can also define a so-called lingering frequency asthe fraction of voids not associated with lingering eventsand the total number of occurring voids in a branch ofthe network. Fig. 6 shows the calculated lingering fre-quencies of all the analyzed vessels in relation to the nor-malized mean flowrate in the respective vessel. The nor-malization factor is given by the mean flowrate of themother or feeding vessel, which is equal to the sum ofthe flowrates of all draining vessels due to the incom-
Figure 5. Probability density functions of scaled void dura-tions for all branches if only lingering events are taken intoaccount. We define a lingering event to occur if the speed of anRBC is lower than v RBC ≤ µ m/s in the vicinity of a bifur-cation apex. The legend is identical to the one in Fig. 3. Theinset graph shows both the probability densities in the caseof lingering and non-lingering, respectively, for the geometryin Fig. 1 to represent extreme cases. Additional informationabout this geometry can also be found in Fig. S1.2. Filledcircles in matching colors denote median values of normal-ized void durations, obtained from estimated parameters inEq. [2]. pressibility of the fluid. Even though the size of RBCs iscomparable to the apparent vessel diameters, their speedmay serve as a good approximation of the mean speed ofthe surrounding fluid (plug flow); hence, we find Q = ∆ V / ∆ t = A v fluid (cid:39)
A l
RBC /τ RBC , (3)with the time-averaged flowrate Q , the volume element ∆ V , the cross-sectional area A , mean speed of the fluid v fluid , the length of the major axis of the circumscribingellipse of RBCs l RBC and the average cell passage time τ RBC , as introduced in previous paragraphs. Among allthe investigated pairs of bifuracting vessels, we find thelingering frequency to be higher in the one with lowerflowrates with respect to its counterpart with a higherflowrate. Apart from lingering at bifurcations, RBCsmay also deform in the vicinity of branches, i.e., bifurca-tions or confluences. While lingering implies the stronginteraction of the vessel walls, the sole presence of junc-tions may induce shape changes for approaching or dis-tancing RBCs. The main difference is the reduction ofthe speed, which is significant in the case of lingering,but adapted to the flow rates in the respective branchin the latter case, although slight deviations may oc-cur. To analyze the spatio-temporal evolution of thisdeformation, we calculated the circumscribing ellipse foreach individual RBC for all consecutive images, yieldingboth the centroid position as well as the eccentricity ofthe cell, given as the ratio of the distance between thetwo foci and the length of its major axis. Fig. 7 shows
Figure 6. Lingering frequencies of the detected voids in re-lation to the normalized mean flowrate in a distinct vessel.The lingering frequency is hereby defined as the fraction ofthe void count associated with a lingering event and the totalvoid count in the vessel. Further, we define the normalizedmean flowrate as a fraction of the flowrate in a daughter ves-sel Q i and the mother vessel Q M . Identical color codes belongto pairs of vessels branching from the same apex; the dashedlines connect the data points of vessels. the measured eccentricity values for the flowing RBCs inthe confluence-bifurcation geometry, both individually aswell as the average curve. The corresponding geometryexhibiting both a bifurcation and a confluence is shownas an inset of Fig. 7. From the average curve, one canclearly see the transition of cell shapes RBCs undergowhile flowing. At the position of the confluence apex x c , the mean eccentricity exhibits the global minimum,implying the roundest obtained shape. Similarly, at theposition of the bifurcation apex x b , the mean eccentric-ity exhibits a local minimum, indicating a transformationfrom an elongated to a more spherical shape when ap-proaching the apex and again elongating when enteringone daughter branch. DISCUSSION
Since we analyzed the void formation downstream ina bifurcating vessel geometry, the apparent increase inmedian void durations originates from two possible sce-narios. One contribution is given by the redistributionof consecutive RBCs into the adjacent daughter vessel.The second contribution is given by a change in voidspeed due to an altered flow rate in the vessel that hasan impact on the temporal void duration. In the lattercase, the spatial distance between the consecutive RBCswould sustain, outmatching the observed state. Indeed,by considering the standard deviation of the speeds ofpassing RBCs in a vessel, variations of the flow ratesare negligible. Thus, temporal void durations and spa-
Figure 7. Eccentricity ε of RBCs as a function of the cen-troid position within the geometry shown as the inset. Theeccentricity is hereby calculated as the ratio of the distancebetween the two foci and the length of its major axis of an el-lipse with identical second moments for each individual RBCfor all consecutive images. The thick red solid line repre-sents the average of all individual graphs (thin lines). For theanalysis, only single RBCs are considered, whereas trains offlowing RBCs are neglected. The offset of the centroid po-sition is chosen in a way that the bifurcation apex x b is atposition zero. tial void lengths are highly correlated, and this impliesa breakup of clusters of RBCs approaching a bifurcationapex. The term cluster hereby implies the state of RBCsmoving in a chain where the intercellular distance is inthe order of the cellular size, where hydrodynamic inter-actions are abundant . However, we emphasize thatthe increase of the median void durations in the case oflingering RBCs does not hold for all the analyzed geome-tries (cf. Supplementary Materials).Further, we also notice a suppression of very shortvoid durations, as can be seen from the comparisonof Figs. 4 and 5. To quantify this statement, we cal-culated the probabilities for void durations being lessthan . τ RBC . In the case of non-lingering, integra-tion of the corresponding probability densities yields forthe probabilities P i ( τ void < . τ RBC ) = { . , . , . , . , . , . , . } , i ∈ { , . . . , } , where i denotes thebranch identifier according to Fig. 2. Similarly, we obtain ˜ P i ( τ void < . τ RBC ) = { . , . , . , . , . , . , . } , i ∈ { , . . . , } with the probabilities ˜ P i in the caseof lingering. If one compares these values for each branch,it is obvious that void durations less than or equal to . τ RBC are suppressed drastically in all but for i = 6 .In some of the graphs showing the probability densi-ties of the void durations, rather long-tailed distributionsare present. We stress that these tails arise inherentlydue to the heterogeneous distribution of RBCs in the mi-crovascular networks, leading to cell-depleted sequencesin branches and thus long void durations in absence oflingering cells.One crucial question is the dependence of the linger-ing frequency on the flow properties. Fig. 6 shows a de-creased frequency for the branch with the higher flowratewith respect to the adjacent vessel. In the prevalentlow Reynolds number regime, RBCs follow merely thestreamlines of the surrounding plasma, and thus, onefinds fewer cells in the vessel transporting less volume.However, the interaction of cellular compounds with theendothelial walls of the vessels is complex , and there-fore, it is highly non-intuitive to observe this circum-stance. It is even more remarkable given the broad distri-bution of opening angles in all the analyzed geometries.For normalized flowrates close to . Q M , we obtainedvery similar lingering frequencies for both the connectedvessels. Nevertheless, the overall magnitude of the lin-gering frequency seems to be unaffected by this observa-tion and rather depends on the cutting angle between thedaughter vessels of the geometry in a way that small an-gles exhibit higher lingering frequencies than large onesin the majority of cases. Other flow parameters such asabsolute flow rates or curvature of the bifurcation apexmay also influence the lingering frequency.So far, we have focused on the impacts of lingeringRBCs on the microvascular blood flow in vivo. However,the physical prerequisites to obey lingering have not beendiscussed yet. RBCs obey an inner network of spectrinfibers, as they are responsible for their biconcave shapeat rest. Due to the flexibility of this spectrin network,RBCs can pass through constrictions much smaller thantheir size at rest . Yet, not only constrictions alter theshape of RBCs, but also the complex structure of the vas-cular network itself, exhibiting merging and bifurcatingvessels. The shape of RBCs undergoes a characteristicdeformation when approaching the apex of a bifurcationor a confluence, respectively (cf. Fig. 7). Recently, thisbehavior was reproduced in silico for a varying numberof passing cells . Whereas this alteration of the shapeis due to increasing or decreasing confinements depend-ing on the geometry, it is responsible for the observedlingering behavior. Particles such as hard spheres obeya less severe coupling with the fluid, and we assume thedeformation and the strong fluid-cell interaction of RBCsis the major cause of lingering . CONCLUSION
We used cutting edge intravital microscopy in conjunc-tion with a combined sophisticated signal processing al-gorithm and particle tracking to obtain detailed informa-tion of flowing RBCs in living hamster models. Based onthis data we define and detect so called lingering events,i.e. RBCs resting at a bifurcation apex of branching ves-sels. We show, that these lingering events particularlycause a redistribution of subsequent RBCs in the adja-cent daughter vessels and lead to a break-up of trainsof RBCs. We further analyze the ratio of lingering cellsand all traversing RBCs, the so called lingering frequency, which is found to be higher in the branching vessel withthe higher flow rate compared to the adjacent vessel. Allthe presented results of our study show a good qualita-tive agreement with in silico results in ref. although, incontrast to the well-defined boundary conditions in silico,the major experimental drawback is the limited insightinto the whole model system. These limitations are givenby a limited field of view and the sheer complexity of theliving hamster model and all its parameters. Neverthe-less, we can assess the impact of lingering RBCs on theflow behavior of subsequent cells in vivo. We can pro-vide evidence to show that these lingering events causea breakup of trains of RBCs as well as redistribution inthe branching vessels. Even though these effects seem tobe rather fine-grained, the impact on the whole organismmay be severe, given the importance of blood flow to thehealth state. AUTHOR CONTRIBUTIONS
M.W.L., M.D.M., L.K., and C.W. designed the re-search; A.K., M.W.L., and S.Q. performed the research;A.K., and T.J. analyzed the data; A.K. and C.W. wrotethe paper; and M.W.L, S.Q., M.D.M., L.K., and T.J.provided feedback and insights.
ACKNOWLEDGMENTS
AK, TJ, LK, and CW gratefully acknowledge supportfrom the research unit DFG FOR 2688 - Wa1336/12 ofthe German Research Foundation. MWL and MDMreceived support from the research unit DFG FOR2688 - LA2682/9-1 of the German Research Founda-tion. This work was supported by the European Union’sHorizon 2020 research and innovation programme un-der the Marie Skłodowska-Curie grant agreement No.860436 – EVIDENCE (SQ, LK, CW). CW, TJ, SQ,and AK kindly acknowledge the support and fundingof the “Deutsch-Französische-Hochschule” (DFH) DFDKCDFA-01-14 “Living fluids”.
SUPPLEMENTARY MATERIAL
The final manuscript including all supplementary datais accessible via doi:10.1016/j.bpj.2020.12.012.
ACKNOWLEDGMENTS
AK, TJ, LK, and CW gratefully acknowledge supportfrom the research unit DFG FOR 2688 - Wa1336/12 ofthe German Research Foundation. MWL and MDMreceived support from the research unit DFG FOR2688 - LA2682/9-1 of the German Research Founda-tion. This work was supported by the European Union’sHorizon 2020 research and innovation programme un-der the Marie Skłodowska-Curie grant agreement No.860436 – EVIDENCE (SQ, LK, CW). CW, TJ, SQ,and AK kindly acknowledge the support and fundingof the “Deutsch-Französische-Hochschule” (DFH) DFDKCDFA-01-14 “Living fluids”.
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