Modelling shear-induced platelet aggregation in general flow

Abstract

Blood-contacting biomedical devices are ubiquitous in current medical practice. Blood is very sensitive to non-physiological conditions, and it can be harmed by the biomedical device in a number of different ways. A very common and frequently fatal consequence of blood damage is thrombosis, which occurs when platelets and fibrin aggregate. Thrombosis occurs after intricate processes involving proteins of the coagulation and immune systems, thrombogenic surfaces, platelets, lymphocytes, and blood flow. This thesis is concerned with mathematical modelling of one aspect of the thrombosis process, namely the aggregation of platelets in shear flow. Yet, most of those models represented the growth of thrombi on thrombogenic surfaces, ignoring the possibility of thrombi forming in the bulk of flowing blood.

A mathematical model for shear-induced platelet aggregation (SIPA) was derived using aggregation and breakup rate equations controlled by shear rate. In this model, activated platelets adhere due to mutual collision caused by the flow of blood. On the other hand, viscous forces of flowing blood can also break up platelet aggregates, which might limit the aggregate growth. The aggregation and breakup effects form a mass-conservative population balance equation (PBE), which transforms cluster mass distribution (CMD) of platelets in time. Model parameters were determined by fitting experimental results from the literature, whose dynamics is determined by a dimensionless number called aggregation-breakup ratio. The aggregation-breakup ratio number is unique for the steady-state CMD, and it depends on shear rate, the total concentration of activated platelets, and empirical parameters. When aggregation rate is stronger than breakup rate, the CMD becomes similar to a log-normal distribution, whose mean value is determined by the aggregation-breakup ratio. On the other hand, when the aggregation ratio is weaker than the breakup ratio, just a relatively low concentration of small aggregates are observed.

Next, this 0-D model is coupled with the transport equation, in order to solve the spatial distribution of platelets aggregates in 3-D. Computational fluid dynamics (CFD) was used to simulated SIPA and aggregate transport in representative cases of blood flow found in medical devices. The 3-D computational model was verified against the 0-D model using a Couette flow simulation. The model was validated by comparing it with an experiment of SIPA in capillary tubes found in the literature, and with a clinical test called light transmission platelet aggregometry, where SIPA occurs in a stirred test tube. Other simulations included a microchannel with a sudden expansion mimicking a stenosis used in an experiment found in the literature, a flow over a crevice case, and flow between two eccentric cylinders. The sudden expansion in the microchannel showed that SIPA is not strong downstream from stenosis if wall adhesion is not occurring as well. In both the flow over a crevice and flow between two eccentric cylinders, platelet aggregates grew in the recirculation zone separated from the main flow field, where platelets got trapped in. The spatial evolution of the CMD was also analysed by dimensionless numbers, such as aggregation Péclet number and cell Damköhler number. The simulations demonstrate that SIPA is directly related to advective transport close to solid walls, where shear rates are highest. In most cases, advection is about three orders of magnitude stronger than SIPA, which generates very low concentration gradients of platelet aggregates. Thus, spatially heterogeneous concentration fields of aggregates are only observed when secondary flow fields, such as recirculation zones are observed. However, platelet aggregates grow intermittently at very slow rates in recirculation zones, because of low shear rates available there.

Finally, an experiment to measure and quantify SIPA in Couette flow is reported in detail. Time-resolved observations of SIPA were observed in a rheoscope, where platelets experienced a peak of high shear rates followed by a period of low shear rate. Platelets were very sensitive to activation when in contact with a viscosity-thickening polymer added to plasma to increase shear stress. Major care to decrease the content of fat in blood plasma had to be taken, because the viscosity-thickening polymer was found to precipitate fat particles which would aggregate with platelets. The CMD was successfully measured by image processing technique, and other measurement uncertainties were assessed and controlled.

The PBE model was able to replicate SIPA experiments, both in Couette flow and in general 3-D flow, where the CMD state could be observed evolving on time. Shear-induced platelet aggregation is a slow process compared to transport of platelets and aggregates, because the volume fraction of platelets in blood is too low for high platelet-platelet collision rates. Significant localised platelet aggregation is only observed for platelets trapped in recirculation zones, whose boundary with the primary flow stream presents high shear rates.

Tá gléasanna bithleighis i dteagmháil le foile le fáil i ngach áit i gcleachtadh leighis. Goilleann coinníolacha neamhfiseolaíocha go mór ar fhuile agus déanann feistí leighis dochar ar fhuile ar go leor bealaí. Tarlaíonn trombóis marfach go minic, mar thoradh dochar do fhuile, nuair a thagann na pláitíni agus fibrin le cheile. Tarlaíonn trombóis tar éis próisis mionsaothraithe a bhain lena proitein téachtadh den córas imghionachta, na dromchlai trombóis, na pláitíni, na limficiti agus imshruthú na fola. Dírionn an tráchtas seo ar na samhaltú matamaitice ar próiseas trombois amháin, an comhbhailiúchán na pláitíni le linn imshruthrú gearr. Áfach, ionadionn an cuid is mo de na samhalacha an fásadh den trombóis ar dhromchlai trombóis. Déanann sé neamhaird ar an deis go bhfuil na trombóisi ag cruthú istigh san imshruthú na fola.

Tháinig samhail matamaitice don comhbhailiúchán pláitín mar thoradh (SIPA), ag baint usáid as comhbhailiúchán agus cothromóidi briste suas, faoi smacht ó ráta gearr.

Greamóinn na pláitín i bhfeidhm mar thoradh bualadh de bharr imshruthu na fola, sa shamail matamaitice seo.

Ar an dtaobh eile, briseann comhbhailiúchán pláitín mar thoradh na fórsaí viscous den fuil ag sileadh, agus ar an t-ábhar sin, b’fhéidir go gcuireann sé teorainn ar fasadh na comhbhailiúcháin.

Cruthaíonn an comhbhailiúchán agus eifeachtai briste imchoimeád na maise cothromód (PBE), mar athraíonn roinnt meal an daonra (CMD) dena pláitíni le h’ama. Socraíonn ar na paraiméadair den samhaltú ag féistiú go triallach na torthaí óna litríocht,...agus socraíonn ar na dynamics by a dimensionless uimhir atá ainmithe comhbhailiúchán breakup ratio.

Bíonn an comhbhailiúchán -breakup number uathúil le haghaidh CMD foistine, agus braitheann se ar shear rate, the total concentration of plaitini activated platelets agus na paraiméadair eimpíreach.

Nuair atá ráta comhbhailiúchán níos láidre ná ráta breakup, éirionn an CMD cosuil lena log normal distribution, a bhfuil an meánluach socraithe ón comhbhailiúchán break up ratio.

Ar an dtaobh eile, nuair a bhíonn an ratio comhbhailiúchán níos laige ná an break up ratio, níl ach cúpla low concentrations of aggregates beaga le feiceáil.

Ina dhiaidh sin, úsáidimíd an samhail 0-D agus an cothromóid iompair le chéile, chun an spatial distribution of plaitini aggregates in mionsamhail thríthoiseach a réiteach. Úsáidtear sreabhmheicnic ríomhaireachtúil (CFD) a bheith cosúil le simulated SIPA agus iompair den combhailiúcháin i ngnáthshamplaí ar shruth na fola i bhfeistí leighis.

Dearbhítear an samhail riomhaireacht thríthoiseach against the samhail 0-D, ag baint usaid as Couette flow simulation.

Bhi an samhail deimhnithe mar deanann comparaid idir e agus an experiment SIPA in capillary tubes, found in literature, agus le scrudu clinical, d’ainm light transmission platelet aggregometry, nuair a tharla SIPA istigh sa stirred test tube.

Usaideann simulations eile a microchannel, ata ag eiri nios mo go tobann, ag mimicking stenosis, a flow over a crevice case agus flow idir 2 eccentric cylinders.