CFD For Blood Transfusions on the Battlefield How the Dynamics of Red Blood Cells in Flow Affects Bleeding Time Andrew Spann Institute for Computational and Mathematical Engineering Eric S. G. Shaqfeh Departments of Chemical and Mechanical Engineering Sean Fitzgibbon, Vivek Narsimhan Department of Chemical Engineering Hong Zhao Exxon-Mobil Upstream Research, Houston, Texas Stanford University June 2, 2014 Red Blood Cell and Platelet Margination Effect on Bleeding Time Zhao, H., E.S.G. Shaqfeh, ``Shear-induced platelet margination in a microchannel'’, PRE 83, 061294, (2011) Zhao, H., E.S.G. Shaqfeh, and V. Narsimhan, ``Shear-induced particle migration and margination in a cellular suspension, '’ Phys. Fluids 24 011902 (2012) Red Blood Cell and Platelet Margination Effect on Bleeding Time Trauma remains the leading cause of mortality for soldiers in combat, and, of trauma vic7ms, 25% to 35% exhibit acute coagulopathy of trauma (ACOTs) characterized by an ini7al bleeding diathesis upon presenta7on to a medical facility. Zhao, H., E.S.G. Shaqfeh, ``Shear-induced platelet margination in a microchannel'’, PRE 83, 061294, (2011) Zhao, H., E.S.G. Shaqfeh, and V. Narsimhan, ``Shear-induced particle migration and margination in a cellular suspension, '’ Phys. Fluids 24 011902 (2012) Hematocrit in Small Vessels PRESENT STUDY Boundary Integral Simulation Details Red Blood Cell/Platelet Mixtures: Margination in a Channel •  Pressure-driven channel flow, height = 34µm •  Ht = 0.1 and 0.2 •  Ca between 0.2 and 2 (max wall shear rate ≈ 4000 s-1) (Zhao & Shaqfeh, Phys Rev E, 2011) Platelet Margination: Evolution in Time In-house experiments for margination P 60x Dichroic mirror In-house experiments for margination P 60x Dichroic mirror Shaqfeh Group Lab Tour 3-4pm Effect of Hematocrit on Platelet Margination d Is this the answer? Effect of Hematocrit on Platelet Adsorption Royal College of Surgeons in Ireland Surface VWF Cross-section of microfluidic device depicting platelet translocation on VWF Dr. James Campbell USAISR Bioflux 1000 Example Experimental Data Platelet Adhesion Model kon ~ 30 / µm2s (weak) k2on ~ 0.05 / µm2s (strong) koff ~ 5 / s L ~ 200nm k2off ~ 0 k ~ 200 pN / µm kon GPIb + vWF ⇔ GPIbvWF koff 2 kon GPIIb /IIIa + vWF ⇔ GPIIb /IIIavWF 2 koff 13 Translocation Paths and Distance γ = 1500s −1 Experiments Simulations Combining Multi-body Calculations and Adhesive Dynamics Comparison of Simulations and Experiments Adhered platelet area versus .me, Ht 30%, Donor 2 run 1 Adhesion rate: slope λ  λ  of bonds per time over first 48 non-dimensional time (roughly 100ms real time) Area occupied by platelets on slide, snapshots taken every 30 seconds λ  Rela%ve adhesion rate, normalized to Ht 30% Extremely encouraging! CONCLUSIONS q  Simulations with a suspension of red blood cells and platelets including all hydrodynamic and interactions have been developed. q  We have examined the concentration distributions and rheology at finite concentrations including wall interactions. We show that the balance between wall lift and collisions produces the clarified Fahraeus-Lindquist layer near the walls. q  Simulations of red blood cell and platelet mixtures have demonstrated platelet margination into the associated FL layer. Recently we have added adsorption to these simulations. We believe this is the key to understanding bleeding time dilation at reduced hematocrit. q  We have used our simulations to choose parameters for margination experiments conducted at Stanford. q  We have compared our simulations to experiments conducted by collaborators at USAISR and found platelet adhesion activity to fall similarly as hematocrit is decreased. q  Ongoing work is underway to improve the performance of the simulations to allow for higher hematocrit, larger geometries, and bifurcations. Acknowledgements • Eric Shaqfeh • Vivek Narsimhan • Sean Fitzgibbon • Hong Zhao • NDSEG Fellowship • NSF Graduate Research Fellowship • Stanford Graduate Research Fellowship • US Army High Performance Compu.ng Research Center • Stanford Certainty Compute Cluster • Stanford HIVE Visualiza.on Center Platelet Adhesion Sequence Aspirin TP TXA2 ADP P2Y12 2-MeSAMP α2BI Ca Mobilization VWF GPIb/V/IX PLCy GPVI α2BI αIIB3 Fibrinogen GPVI Collagen Fibrils Smooth Muscle Cells A Balance Between Lift and Collisional Forces…. Narsimhan, V., H. Zhao, E.S.G. Shaqfeh, “Coarse-grained theory to predict the concentration distribution of red blood cells in wall-bound Couette flow at zero Reynolds number”, Phys. Fluids 25, 061901 (2013) Large scale DNS Collisional Displacements* *Kantsler, V et al. Euro Phys Lett. 82, (2008), 58005 ≈ Theory Lift Velocity** Abkarian, A. and Viallat. Biophys J., 89, (2005), 1055 Model Basics: Lift velocity Lift Velocity (ν = 0.95 vesicle) ∂n ∂ lift + ( u n ) = f coll ∂t ∂z Lift € Calculate ulift from existing Boundary integral simulations*ulift u=γz h *Zhao, H., Spann, A., and Shaqfeh, E.S.G. Phys Fluids, 23, 121901 (2011) **Expt: Callens, N. et al. Euro Phys Lett. 83, (2008), 24002 Comparison with Experiments** Model Basics: Lift velocity Lift Velocity (vesicle & RBC) ∂n ∂ lift + ( u n ) = f coll ∂t ∂z Lift € Calculate ulift from existing Boundary integral simulations*ulift u=γz h *Zhao, H., Spann, A., and Shaqfeh, E.S.G. Phys Fluids, 23, 121901 (2011) **Expt: Callens, N. et al. Euro Phys Lett. 83, (2008), 24002 Comparison with Experiments** Model Basics: Collisional Forces PDE: f coll ∂n ∂ lift coll + (u n) = f ∂t ∂z . (z) = γ *Zurita-Gotor, M. et al. PRL, 108, (2012), 068301 Kumar, A. and Graham, M.D. PRL, 109, (2012), 108102 **Expts: Kantsler, V et al. Euro Phys Lett. 82, (2008), 58005 * ∫∫ [n(z − δ )n(z − δ − k) − n(z)n(z − k)] | k | dkdy channel € δ (k , y) = displacement/collision € Lines = simulation Symbols = expt Simulation Geometry δ Δz Cutoff radius R: Hydrodynamic Screening Collisional Displacement** Comparison with DNS (RBCs) Near-wall: Shear flow! Cell free layer! λ = 1, H/a = 18, φ = 0.1 and 0.2 Theory captures cell-free layer and concentration at core of channel. Underpredicts layering phenomenon Comparison with in-vitro experiments CFL vs Hematocrit Cell free layer (CFL)! Scaling Arguments Bugliarello, G. et al. Trans. Royal Soc. Rheol., 7, 209, (1963) Idea: Pranay, P. et al., .Phys. Fluids 24, (2012), 061902 Bugliarello et al (1963): H = 14.3, Ca ~ 0.4-1.6, Theory H = 14, Ca = 1, R = 2.25-2.75 CFL ~ HCT −1/2 Narsimhan, V., H. Zhao, E.S.G. Shaqfeh, Phys. Fluids 25, 061901 (2013) How the Dynamics of Red Blood Cells in Flow May Affect Your Bleeding Time Andrew Spann Institute for Computational and Mathematical Engineering Eric S. G. Shaqfeh Departments of Chemical and Mechanical Engineering Sean Fitzgibbon, Vivek Narsimhan Department of Chemical Engineering Hong Zhao Exxon-Mobil Upstream Research, Houston, Texas Stanford University June 2, 2014