Coagulopathy implications using a multiscale model of traumatic bleeding matching macro- and microcirculation

Abstract

Quantifying the relationship between vascular injury and the dynamic bleeding rate requires a multiscale model that accounts for changing and coupled hemodynamics between the global and microvascular levels. A lumped, global hemodynamic model of the human cardiovascular system with baroreflex control was coupled to a local 24-level bifurcating vascular network that spanned diameters from the muscular artery scale (0.1-1.3 mm) to capillaries (5-10 μm) via conservation of momentum and conservation of mass boundary conditions. For defined injuries of severing all vessels at each nth-level, the changing pressures and flowrates were calculated using prescribed shear-dependent hemostatic clot growth rates (normal or coagulopathic). Key results were as follows: 1) the upstream vascular network rapidly depressurizes to reduce blood loss; 2) wall shear rates at the hemorrhaging wound exit are sufficiently high (~10,000 s^-1) to drive von Willebrand factor unfolding; 3) full coagulopathy results in >2-liter blood loss in 2 h for severing all vessels of 0.13- to 0.005-mm diameter within the bifurcating network, whereas full hemostasis limits blood loss to <100 ml within 2 min; and 4) hemodilution from transcapillary refill increases blood loss and could be implicated in trauma-induced coagulopathy. A sensitivity analysis on length-to-diameter ratio and branching exponent demonstrated that bleeding was strongly dependent on these tissue-dependent network parameters. This is the first bleeding model that prescribes the geometry of the injury to calculate the rate of pressure-driven blood loss and local wall shear rate in the presence or absence of coagulopathic blood. NEW & NOTEWORTHY We developed a multiscale model that couples a lumped, global hemodynamic model of a patient to resolved, single-vessel wounds ranging from the small artery to capillary scale. The model is able to quantify wall shear rates, seal rates, and blood loss rates in the presence and absence of baroreflex control and hemodilution.

Keywords: coagulopathy; hemorrhage; trauma.

Fig. 1.

Global hemodynamic (GH) model. Closed-loop flow diagram of the global hemodynamic model in the absence of bleeding. The patient is represented by interconnected, lumped, compartments, composed of resistances, capacitances, and, in large arteries, inertances. P, pressure; C, capacitance; R, resistance; L, inductance; la, left atrium; lv, left ventricle; sp, splanchnic peripheral; sv, splanchnic venous; ep, extrasplanchnic peripheral; ev, extrasplanchnic venous; bp, brain peripheral; bv, brain venous; hp, heart peripheral; hv, heart venous; mp, muscle peripheral; mv, muscle venous.

Fig. 2.

Bifurcated vasculature network (BVN) and pressure matching. A schematic of a 3-generation BVN is shown (A) along with examples of a 1st generation (1G), second generation (2G), and third generation (3G) vessel sever. The diameter (D), length (L), and the angles between each of the blood vessels within the same plane (θ) are provided for clarity. Traced lines show where severs to the network take place when referring to either a 1G, 2G, or 3G sever. Vessel diameters and flowrates of a 24-generation symmetric branching network (no bleeding) are shown (B). Generations 0–11 represent small arteries, 12–21 represent arterioles, and 22–24 represent capillaries.

Fig. 3.

Multiscale coupling strategy for boundary condition matching where the lumped compartment, macroscale description of resistance (Ursino model) (A) was fully resolved for traumatic bleeding in parallel with an intact tissue (B). The total resistance value R_tot from the Ursino model is divided into a 4-resistance subsystem (R′, R″, R_w, and R_BVN). R′ represents the implicit portion of the compartment and comprises vessels larger than the branching vasculature network (BVN). R″ represent vessels that are of equal size to those of the BVN but were not explicitly resolved. R_w is the resistance to bleeding, effectively infinite in the absence of bleeding but finite in the presence of bleeding. R_BVN is the overall resistance of the BVN computed based on fully developed, steady-state Poiseuille flow with the correction term included (Eq. 11) for all relevant blood vessels. The inlet and outlet pressure boundary conditions for intact vasculature (no bleeding) were set to P_in = 70 mmHg and P_out = 25 mmHg. In simulations of bleeding, the outlet pressure was set to P_atm = 0 for exposure to the atmosphere.

Fig. 4.

Pressure (A) and flowrate (B) profiles in the presence and absence of acute bleeding. For complete severing at t = 0 of 2ⁿ vessels at n = 3, 10, 18, and 23 generation (A), network depressurization was simulated successfully for the pressure matching condition of P_in = 70 mmHg for wounds n = 10, 18, 23 (red curves). For n = 3, depressurization did not allow successful pressure matching and caused a hemodynamic discontinuity by not matching the P_in = 70-mmHg condition. For n = 10–25 generation wounding, the network depressurizes due to the sudden exposure to atmospheric pressure. Under all conditions of wounding, the flow rate (B) through the network increases relative to the intact network as a result of loss of downstream resistance (i.e., P_out = 0). As wounds increase in severity by severing larger vessels, the overall flowrate through the network increases 6-fold from 0.09 ml/s (no wounding) to 0.63 ml/s for n = 10 generation wounding.

Fig. 5.

Model validation in the presence of bleeding. Comparison of multiscale model with normalized in vivo measurements of blood loss rate (BLR; A), mean arterial pressure (MAP; B), and total blood volume (TBV; C) in heparinized bleeding dogs (35). Simulation was performed with the same initial normalized blood loss rate as the reported experimental condition. Excellent agreement can be seen between the two. The initial total blood volume of the dog was estimated assuming a blood volume of 85 ml/kg in the dog (10).

Fig. 6.

Global and local hemodynamics following different injuries (no hemostasis). Arterial blood pressure (ABP; A), blood loss rate (BLR; B), heart rate (HR; C), and total blood volume (TBV; D) evolution as a result of severing all 10th, 13th, 18th, and 23rd generation blood vessels. A moving average was used to remove systole and diastole fluctuations in A–C for visual clarity. As blood is lost, blood pressure drops while heartrate increases due to baroreflex. The rate of blood loss declines with time as the driving force (ABP) declines. The sensitivity of bleeding to prevailing ABP is less pronounced for injury of n = 23 generation vessels due to the added upstream resistance and diameter-dependent viscosity.

Fig. 7.

Global hemodynamics changes in response to severing all generation n = 10 vessels at 0, 1,000, 2,000, and 3,000 s postinjury. Arterial blood pressure (ABP; A–D) and cardiac output (CO; E–H) over a 5-s time interval are shown. As bleeding occurs, the heart rate increases due to the action of the baroreflex (number of pulses in A–H increases from top to bottom). The cardiac cycle curve at the same time points is shown (I): the efficiency of the heart rapidly decreases to <25% in <2 h. All three quantities suggest that the greatest change in the state of the patient occurs in the first 1,500 s, which is when blood loss rate is highest. The effect of the baroreflex (J) is quantified, where the presence of the baroreflex increases blood loss due to its attempts to maintain blood pressure during bleeding. However, if the baroreflex can still initiate vasoconstriction then the added resistance of the shrinking, bleeding, blood vessels can greatly blood loss.

Fig. 8.

Effects of network properties on blood loss. Blood loss profiles for n = 10 wound in the absence of hemostasis due to changes in: branching exponent, k (A), the length-to-diameter ratio, β (B), the ratio, R′/R″ (C), and root diameter at n = 0, d_o (D). The branching exponent has the strongest effect on bleeding as downstream diameters are larger (less resistance) at larger values of K.

Fig. 9.

Global and local hemodynamics with healthy hemostasis. Uniform clotting occurs over the entire length of the severed blood vessel (A) reducing the initial diameter of the blood vessel (D_o) to the effective diameter (D) at a rate given by the seal rate-wall shear rate function parameterized by the experimental measurements of Colace et al. (9) and Bark et al. (1) (B). Wall shear rate (C), blood loss rate (D), seal rate (E), and total blood volume (F), evolution as a result of severing all generation 10 vessels in the presence of shear-dependent clotting. The effect is dramatic, with blood loss ceasing just ~100 s into the simulation.

Fig. 10.

Global and local hemodynamic evolution for different hematocrits. Wall shear rate (WSR; A), blood loss rate (BLR; B), seal rate (C), and total blood volume (TBV; D), evolution as a result of severing all generation 10 vessels in the presence of shear-dependent clotting and for different hematocrits. Local vasoconstriction was not included to examine the sole effect of the hematocrit change. Seal rate function rescaled by data presented by Li et al. (23). While all three have similar wall shear rate profiles, total blood loss dramatically increases by ≈1 liter as a result of a 2-fold decrease in hematocrit. This suggests that hemodilution could be a large component of trauma-induced coagulopathy.

Fig. B1.

Model validation before bleeding. Comparison of multiscale model with in vivo pressure (A) and velocity (B) measurements in the mouse (12) and in the cat (46).

Fig. B2.

Effect of branching exponent variability. To further examine the influence of the branching parameter, k, 1,000 simulations were run with k randomly chosen from a uniform distribution between two and three at each generation. The cumulative blood loss (A) and the blood loss rates (BLR; B) include dashed lines representing the most extreme results and the black line represents the most common result. Small deviations in this geometric parameter can lead to ~3-fold change in these curves.