The successive branching and splitting of the largest vessels into smallest enable efficient blood delivery. In the early development stage, the process of vasculogenesis creates a first primitive network, which is completed during vessel sprouting. In hemodynamic analysis, an analogy with electric circuits can be used. The microcirculation is arranged in a set of in-series and in-parallel vessels, where each vascular segment gives rise to a new generation of microvessels (Figure 1). In this analogy, the blood flow rate and pressure drop are equivalent to an electric current and voltage respectively. Dissipative effects due to blood viscosity stand for a hydraulic resistance (Hu et al., 2012). Intuitively, both design and parallelised architecture of the vascular network guarantee a progressive decrease of the total hydraulic resistance throughout the network and greatly enhance the blood flow, as highlighted by Poiseuille’s law (Liu and Jing, 2021; Pozdin et al., 2021). In addition, blood slows down as the total cross-sectional area increases. Vascular damages such as thrombosis or atherosclerosis affect the flow resistance of individual segments operating a partial or complete blockage (acute thrombosis). When examining the contribution of individual vessels regarding the total hydraulic resistance of the network, one can clearly see how much the site of occlusion affects the viability of the whole system. Circulation models were implemented recently to emulate physiological disruptions including thrombotic events over the entire scales ranges of the vascular network. Through the construction of a tree-shaped network, the study led by Rojas et al., provided novel approaches in liver blood circulation, and shed light on the importance of architecture on blood flow distribution and thus hemodynamics. (Torres Rojas et al., 2021). In such architecture, occlusions in the early generations will dramatically impact the hemodynamic properties of all the dependants vessels due to a reduced blood supply (Rojas et al., 2015), whereas localized events in the smallest capillaries have very little effect on the overall resistance of the system.

Allometric scaling refers to phenomenological relationships that govern the structure and features of an organism according to its body mass. A broad theory of biological allometries have been applied to the human vascular network, which similar to plants, has evolved towards an optimal arrangement of vessels (Hughes, 2015; Razavi et al., 2018; Chaui-Berlinck and Bicudo, 2021). Metabolic allometric scaling, which drives the amount of energy and materials taken from a system, is perhaps the most fundamental assumption (Saghian et al., 2022). Thus, the overall network architecture obeys design principles to minimise energy loss and maximise space-filling to ensure effective distribution of oxygen and nutrients to physiological entities. Two contributions to energy loss can be distinguished and are presented in Figure 2: dissipation and wave reflection. While dissipation accounts for the majority of energy lost in small capillaries where the surface-to-volume ratio is the highest, wave reflection has a greater influence in pulsative flow conditions, such as in arteries (Savage et al., 2008).

First introduced by Hess-Murray in 1926, the principle of minimum work within a vascular system was derived. It accounts for the metabolic costs involved in the maintenance of the blood in the vessel and the dissipation by friction generated by the bifurcations. The theory of dissipation minimisation takes the form of a power law connecting the radii of a parent and n daughter vessels at a branching point with a ratio n − 1 / 3 (Figure 2). It also implies a shear constant (for symmetrical bifurcation) and area-increasing behaviour that is dominant in the smallest vessels (Murray, 1926). In mammals, this feature reduces blood flow in the capillaries to levels allowing adequate oxygenation and metabolite transport. A general model for biological allometries was later developed by West, Brown and Enquist (WBE) and attributes a well-known allometric scaling exponent of 3 / 4 relating metabolic rate to body mass (West et al., 1997). Interestingly, general branching features in biological networks across plants and animals display analogous features under WBE framework, including area-preservation, despite different physiological aims (Brummer et al., 2021). Detailed upon space-filling principle, WBE model gives a description of pulsative networks such as aorta and arteries resulting in branching nodes with a ratio n − 1 / 2 when minimising wave reflection (West et al., 1997). While symmetrical bifurcation was a core assumption of WBE theory, asymmetric branching also shows a convergence to the same metabolic scaling exponent (Brummer et al., 2017).

It is clear that the transition between area-preserving to area-increasing remains an issue in the global description of biological networks. Nevertheless, it is established that blood is much slower to enable oxygenation in the capillaries than in the aorta suggesting area-increasing branching is necessary somewhere in the network. In addition, the mere fact that vascular networks exhibit a non-uniform shear distribution and increased as the vessels reach the capillary size (arteries: 10s^-1, capillaries: 2,000 s^-1 (Doriot et al., 2000; Reneman and Hoeks, 2008; Sakariassen et al., 2015)) confirm the difficulties to predict where the transition would occur regarding the flow regime. Additionally, the observations carried out by Zamir and colleagues pointed out that the cube exponent in the power law proposed by Murray was incompatible with the whole vascular system and was likely varying along the tree (Zamir et al., 1992). Such deviations from the cubic exponent were observed in arterial bifurcations where the velocity is higher than in the rest of the vascular tree. At these junctions, the optimal exponent showed to be closer to two, climbing to three in the arterioles and capillaries, confirming that the predictions of Hess-Murray’s law are closer to reality for the smallest scales of our body (Roy and Woldenberg, 1982; Reneman and Hoeks, 2008; Sciubba, 2016). This range of variation could even be extended in case of vascular damage and severe thrombotic events.

For blood-circulating devices - and more specifically capillaries systems - microfluidics brings novel possibilities in the development of miniaturised, branched architectures. Benefits include micrometric control over geometries including scale reduction, surface of exchanges and mechanical forces. Artificial oxygenators greatly benefit from these principles and display flow distributions arrays in accordance to Murray’s law (Lachaux et al., 2021; Santos et al., 2021; Vedula et al., 2022). These circuits shown in Figures 4A, B achieve a progressive scale reduction from the largest channels to microcapillaries where chemical transport of gas and nutrients will occur faster and more efficiently, contained within a compact manifold. Such geometries enable the maintenance of physiologically relevant shear stress magnitudes and flow rates. A similar approach was applied to the design of a tissue-engineered liver scaffold, integrating a venous scaling throughout the generations of the network (Hoganson et al., 2010; Torres Rojas et al., 2021). Furthermore, novel biomimetic scaffolds based on triply periodic minimal surface (TPMS) theory were developed for fluid-circulation devices. Using a permeability-based design approach, membranes display modules with improved flow distribution overcoming non-uniform and stagnant patterns found in hollow fibres membranes of oxygenators (Hesselmann et al., 2022). TPMS-scaffolds morphology has a markedly high surface area to volume ratio and highly controlled porosity similar to native cellular conditions (Vijayavenkataraman et al., 2018). Two modules are shown in Figure 4C illustrating the permeability-driven optimisation used for a membrane oxygenator design.

Biomimetics can also be applied to bigger implanted devices in contact with blood flow. Currently, a majority of blood devices display macrometric circulation networks where physiological flow is pulsative. The introduction of axial and centrifugal pumps to clinical practice have generated major thrombotic complications (Hastings et al., 2016) Devices with diminished pulsatility create non-physiological continuous flow and likely introduce increased pressure gradients in the circulation (Cheng et al., 2014; Major et al., 2020). Wave membranes blood pump are novel approaches for pulsatile flow integration in which blood is moved by wave propagation systems. Both frequency and amplitude of the waves can be monitored to mimic physiological flow (Martinolli et al., 2022). Bileaflet valves are typically subjected to high flow rates and relative changes in volume throughout the cardiac cycle. Technical designs of the valves are inspired by profiles of a native valve, which is optimised to resist and adapt to natural variations in vessel diameter, blood volume and oscillations (Hofferberth et al., 2020).

Biomimetic features contribute to a safe and durable system. However, the intrinsic architecture of human vasculature naturally disturbs the blood flow which undergoes diverse mechanical constraints (Chistiakov et al., 2017). The development of artificial vasculature would allow high control over hydrodynamic parameters to prevent unsolicited and damaging reactions in the blood.

Platelet margination is monitored by their interaction with RBCs in circulating blood and local fluid dynamics. RBCs density in the blood, their deformability and stiffness participate and are necessary for the margination to occur. Platelets circulating alone or with extremely low hematocrit are less likely accumulate on the vessel walls, indicating that RBCs volume affect platelet trajectories, with a stronger impact under dynamic and stressed conditions (Turitto and Weiss, 1980). Zhao et al. confirmed the contribution of hematocrit to platelet margination, observing a significant difference in platelet probability distribution when hematocrit was doubled from 10% to 20% (Zhao et al., 2012). Platelets have a stiffer membrane compared to RBCs which have an easier faculty to deform. The gradient of stiffness within the cell population enhanced the rate of collisions between deformable red blood cells and stiffer particles (Czaja et al., 2020). This segregation of stiffer particles has been simulated by Zhao et al., in arteriole-like ducts showing that platelet-like spherical beads were pushed due to volume exclusion (Munn and Dupin, 2008; Zhao et al., 2012).

When blood flows through a vessel, the laminar regime reveals a gradient of velocity directed normal to the wall. In response to the non-slip condition (zero speed on the walls), a non-zero mean lateral velocity leads the blood particles to progressively diffuse from the centre of the vessels to the edge. Several corresponding studies demonstrated a remarkable contribution of shear-induced RBC-platelet collisions on the lateral motion of individual platelets (Kotsalos et al., 2022; Li et al., 2023). The analysis of RBC dynamics under flow conditions also suggested that high levels of shear resulted in a 1000-fold increase in platelet diffusivity to the walls (Taylor, 1953; Leighton and Acrivos, 1987; Casa et al., 2015). As Crowl and Fogelson pointed out, margination occurs rapidly in sheared conditions, within a few microseconds at physiological capillaries shear rates (1,100 s^-1) (Crowl and Fogelson, 2010; 2011). Nevertheless, shear stress was found to have a less dramatic impact on platelet lateral margination than hematocrit, even though it clearly enhances the process (Zhao et al., 2007).

Altogether, platelet behaviour and activity is altered in blood circulating devices, with adhesion rates driven by interactions with RBCs, a critical factor for acute thrombus development (Spann et al., 2016). These findings provide useful insight on the influence of hemodynamic environment eon platelet-protein membrane binding and thus adhesion, which are predominant processes initiating thrombus development.

Under low shear rate perfusion in normal physiology (such as venous flow), platelets interact with adsorbed fibrinogen and collagen via their glycoprotein VI (GPVI) receptors. The integrin α I I b β 3 (also known as GPIIb/IIIa) located on platelet membranes enhances the arrest of free platelets onto immobilised fibrinogen (Savage et al., 1998; Maxwell et al., 2016; Xu et al., 2021) (Figure 5). The strong integrin α I I b β 3 —fibrinogen interaction guarantees a firm and immediate adhesion of the platelet on contact with the surface (Savage et al., 1996). The work conducted by Ruggeri et al., in 1996 reveals the contribution of integrins in platelet deposition and adhesion across this range of shear rates. Blood perfused in a parallel plate flow chamber coated with immobilised fibrinogen revealed maximal platelet deposition at lower shear rates, with almost no binding at shear rates reaching 1,500 s^-1. This interaction is selectively engaged under low shear conditions: as the binding rate with integrin α I I b β 3 is considered to be relatively slow, bonds may form if the drag forces do not overcome integrins bond strength (Savage et al., 1996). It is important to mention that shear rate only impacts initial platelet adhesion and the binding of integrins to fibrinogen remained stable at higher levels (Savage et al., 1996). On the biochemical aspect, adhered platelets also tend to activate and demonstrate an upregulation of α I I b β 3 affinity on their membrane enhancing platelet-platelet interactions through soluble fibrinogen. Therefore, the secretion and release of thrombogenic agonists through alpha-granules (ADP, Thromboxane TXA2, Ultra-large von Willebrand factor (ULVWF)) by activated platelets monitors a shift in their phenotype, which progressively exhibits filopodia-like structures (Maxwell et al., 2016).

Investigations on blood circulation in microfluidics at moderate shear rates (exceeding 1,000 s^-1) have shown a two-stage platelet adhesion mechanism. First, as an additional interaction mediating platelet adhesion, glycoproteins GpIb-V-IX (more specifically GPIbα) bridge to immobilized von Willebrand Factor to arrest platelets on the surface (Savage et al., 1996; Reininger et al., 2006). Under moderate shear, VWF molecules unfold to reveal the A1 domain which bonds to platelet receptor GPIb (Siedlecki et al., 1996). A1- GPIb adhesive binding is fast but reversible. The interaction induces a mechanism of platelet translocation whereby flowing platelets can quickly bond/debond, exhibiting a rolling motion on the wall surface (Lackner et al., 2020; Pujos et al., 2022). In the second stage, the rolling motion of platelets prolongs their contact with adsorbed fibrinogen, providing sufficient time for the strong α I I b β 3 —fibrinogen bonds to be established (Figure 5). The surface translocation then generates several morphological switches (Andrews et al., 2003). As the platelet engage into smooth rolling interactions, intermediate shear rates (1,000–10,000 s^-1) introduce membrane tethers. These are smooth cylinders of lipid bilayer derived from the platelet membrane, which function as contact points between integrins GPIIb/IIIa and amino acids in VWF C1 domain. These membrane extensions have the ability to stretch in order to resist the hemodynamic drag forces imposed by the flow and extend the adhesion time of the platelets, further stabilising the emerging aggregate (Dopheide et al., 2002; Reininger et al., 2006; Mountford et al., 2015; Abidin et al., 2022).

It is important to emphasise that aggregate formation does not necessarily require platelet activation (Ruggeri et al., 2006). On the contrary, circulating platelets are able to initiate binding and aggregation without first being activated, which is the case in the presence of pathological shear stress or disturbed flows. VWF binding to the platelet membrane GpIb-V-IX complex triggers activation of platelet GPIIb/IIIa receptors as wells as an accumulation of intracellular calcium. Activated platelets secrete soluble prothrombotic agonists inside the aggregate. These soluble factors include ADP, thromboxane (TxA2) or thrombin and are actively released in the blood plasma, stabilising the plug and promoting the recruitment of flowing platelets (Ruggeri et al., 2006). In addition, high shear rates lead to platelet membrane inversion including the externalisation of phosphatidylserine (PS), a phospholipid normally located in the cytoplasm of resting platelets (Sweedo et al., 2021). This redistribution on activated platelets leads to a 40-fold increase in phosphatidyl serine expression after platelet activation (Thiagarajan and Tait, 1990; Dachary-Prigent et al., 1993; Sun et al., 1993). PS translocation propagates the further platelet activation cascade within the aggregates (Ryan et al., 2020) Finally, pathological conditions including vessel lumen reduction and/or obstruction may cause shear rate rise at extremely high levels above 10,000 s^-1. Under these conditions, platelet thrombus formation is dominated by VWF-dependant interactions, mainly via GPIb-V-IX. Aggregates emerge from soluble VWF multimers, which are in their complete unfolded and fibrous conformation (Figure 5) (Zhussupbekov et al., 2022). The fibres easily bind to already adhered and tethered platelets on immobilized VWF forming a net on the surface. At the same time, the A1 domain mediates the capture of flowing platelets, further activated within the large and unstable aggregate (Colace and Diamond, 2014; Fu et al., 2017; Liu et al., 2022). VWF biomechanical processes have been characterised in silico and bring useful insight in shear-induced platelet activation under flow (Pushin et al., 2020; Kim and Ku, 2022; Belyaev and Kushchenko, 2023).

It is generally accepted that high shear stresses are vectors of platelet aggregation leading to occlusive thrombosis. The different mechanisms of platelet adhesion and aggregation are rather simplified models and descriptions. Blood circulation is not only a laminar flow and will experience local hemodynamic environments, with regions of velocity changes. These can be attributed to the inherent non-Newtonian properties of blood, but also shear rate gradients in cases of vessel constriction where fluid quickly accelerates and decelerates, or turbulences occurring at branching nodes (Chistiakov et al., 2017).

Although the effects of hemodynamic forces on VWF monomeric fibres is demonstrated, there is still no consensus on a critical shear rate needed to initiate platelet aggregation. It is understood that immobilized VWF is likely to remain in its unfolded conformation at shear rates around 3,000 s^-1 whereas an elongation of soluble VWF needs higher shear up to 5,000 s^-1 (Siedlecki et al., 1996; Kuwahara et al., 2002; Schneider et al., 2007). However, recent observations have questioned the existence of such a threshold, showing in particular that VWF could be involved at lower shear magnitudes of, around 1,500 s^-1 (Receveur et al., 2020) and in the context of shear rate gradients (Hoefer et al., 2020; Van Rooij et al., 2021). In a shear gradient context, it was observed that VWF unfolding increased at two-fold lower flow rates when compared to constant shear flows (Zhang, 2009; Sing and Alexander-katz, 2010). Corresponding studies revealed that rapid alterations of the flow through shear microgradients promoted discoid platelet aggregation in the post-stenotic region, or micro-vessel curvatures (Nesbitt et al., 2009; Rooij et al., 2020; Spieker et al., 2021). It suggests that the rapid decrease in shear rate restructures the filamentous membrane tethers and allows integrins α I I b β 3 to considerably stabilise the aggregate. Platelet aggregation has been characterized in microfluidic devices by Receveur et al., suggesting that fibrinogen was responsible only for platelet adhesion in a simple constant shear flow, whereas together with the action of VWF became thrombogenic in an accelerated flow. Thrombosis driven by shear microgradients is bi-phasic: initially slow as platelet are recruited by immobilized VWF and fibrinogen, followed by a dramatic growth of VWF fibres (Receveur et al., 2020).

In the light of the major contribution of platelets in thrombosis, Nobili et al. applied a cumulative damage theory, originally developed for RBC (Yeleswarapu et al., 1995; Grigioni et al., 2005), to quantify platelet activation state (PAS) in dynamic conditions (Table 3). This model relies on a prior activation history term and the instantaneous constant mechanical loading (Nobili et al., 2008). Following the same logic, a new description for the regions of shear gradients was introduced to depict a more accurate description of the mechanical profile along the trajectory (Soares et al., 2013). Furthermore, the PAS formula relates to actual biological markers for platelet degradation. In stressed environment, platelet activation leads to the conversion of prothrombin into thrombin, which acts as a strong agonist generating further activations via a feedback loop. Similarly, modified prothrombin produces acetylated thrombin which does not contribute to any activation and can easily be quantified, assimilated as a direct marker of shear-induced platelet activation (Jesty and Bluestein, 1999). This method combines computational fluid dynamics and biological assessment of platelet activation and provides a direct quantification of a streamline thrombogenicity considering diverse mechanical loading histories (Xenos et al., 2010). The latter study provided some insights into the platelets resilience to shear stress, and their behaviour post-exposure. Interestingly, coupled with experimental results, the model revealed that platelets become activated by very short but strong pulse of shear without recovering their initial and quiescent state under low shear conditions. In addition, an initial pre-exposure to high shear facilitates their activation even at physiological shear. These findings highlight the importance of including previous stress histories in the analysis of platelet sensitivity to activation (Soares et al., 2013).

Stress accumulation (SA) is an additional metric which sums the instantaneous product of shear stress and exposure time between successive nodes of platelet streamline. This parameter indicates the level of activation of a trajectory and should remain lower than 35 dyne s/cm² for save blood transport, according to Hellums criterion (Hellums et al., 1987). Stress accumulation is often integrated in the optimisation procedure as a comparative indicator (Chiu et al., 2019). Girdhar and colleagues led a robust comparison of Left Ventricular Assist devices (LVADs), using the stress accumulation to select the features guaranteeing optimal thrombogenic performances. The optimized version of the VAD was selected after several iterative design modifications on the impeller and showed a markedly reduced stress accumulation among platelet trajectories. More importantly, it caused an order of magnitude lower platelet activation rate when compared with the original design (Girdhar et al., 2012). Similarly, Buck et al. investigated the thrombogenicity of two blood path architectures as part of an implantable artificial kidney (Buck et al., 2018).

Associated with computational fluid dynamics, various numerical models are proposed to predict localised thrombus risks in blood-circulating device designs (Menichini and Yun, 2016; Wu et al., 2020; Bouchnita et al., 2021; Li et al., 2022). The majority of these models integrate a combination of mechanical and biochemical contributions: first the computing velocity, pressure and shear stress fields with Navier-Stokes equations. Utilising the knowledge of the mechanical and physiological environment, a large number of models compute species transport in the system with an Eulerian approach by solving convection-diffusion-reaction equations (Stiehm et al., 2019; Wu et al., 2020). Several components concentrations including the ones of resting or activated platelets, chemical agonists such as adenosine diphosphate (ADP) or thrombin, are processed through a systems of partial differential equations (PDEs) (Sorensen et al., 1999; Leiderman and Fogelson, 2011). Some models have also proposed a direct dependence of these concentrations either with mechanical or chemical cues, through both source terms or diffusivity (Wootton et al., 2001; Menichini and Yun, 2016). Using such models, Blum and colleagues demonstrated that activated platelets concentration in HeartMate II pumps correlated with thrombus events frequency (Figure 7), suggesting that such computational markers have potential as surrogates for thrombus modelling (Blum et al., 2022; Qiao et al., 2022).

Regions with high thrombotic risk are also characterised by their longer residence times. Residence time can be modelled as a passive tracer entering the blood-circulating device and transported with the flow (Figure 7). Along with high activated platelets concentrations, the latter is computed using Eulerian description to evaluate thrombotic clots (Menichini and Yun, 2016; Li et al., 2022). Moreover, Lagrangian methods also provide a valuable description of residence time for individual platelets along their trajectory, but they require extensive computational costs compared with Eulerian methods.