Table 1.

Dimensional and dynamic parameters for scaling in vitro and in vivo flow models

Parameter	Expression	Meaning	Importance	Typical values
Relative channel height	DRBC/H	Size of channel relative to height of RBC	For values of > 0.05 the viscosity of the blood decreases due to reduced hematocrit	0.01–0.2
Aspect ratio	H/W	Height of channel to width of channel for rectangular channels	Values of < 0.2 are recommended to achieve constant shear stresses across the middle of adhesive surfaces	0.1–1
Relative injury size	L/H	Length of thrombotic trigger or injury relative to channel height	Values > 1 enhance the effectiveness of surface reactions	0.1–10
Reynolds number (Re)	ρUH/μ	Inertial forces/viscous forces	Determines the nature of the flow; laminar, recirculation, turbulent	0.001(capillaries) to 4000 (arteries)
Entrance length (Le)	0.057ReDh*	Distance from the channel inlet where flow is well developed	Prothrombotic triggers should be placed at distance greater than Le	1–100 μm (for ~100 μm channels and physiologic shear rates)
Peclet number (Pe)	UciH/D γH2/6D	Convective velocity/diffusive velocity	Determines the relative rates of solute transport by flow and molecular diffusion	0.01 (interstitial flow in thrombi) to 100 000 (coagulation reactions on surfaces)
Dahmköhler number (Da)†	krxnciH/D (low Pe) krxnciδ‡/D (high Pe)	Reaction velocity/diffusive velocity	Determines whether transport of soluble molecules or their reaction is rate limiting.	0.1 (reaction limited) to 10 000 (transport limited)

D_RBC, diameter of red blood cell; H, height of channel; W, width of channel; SA, surface area of injury; V, volume of channel in injured area; L, length of injury; U, average blood velocity; c_i, concentration of component i; D, diffusivity; γ, wall shear rate; k_rxn, rate constant of first order reaction.

^*D_h, hydraulic diameter [2HW/(H + W)].

^†Note that the expression for the Da depends on the order of the reaction and the mass transfer regime [29].

^‡The boundary layer thickness, δ, depends on the Pe and thus the shear rate [δ = (H2L/Pe)^1/3].