Multiscale systems biology of Trauma Induced Coagulopathy

Abstract

Trauma with hypovolemic shock is an extreme pathological state that challenges the body to maintain blood pressure and oxygenation in the face of hemorrhagic blood loss. In conjunction with surgical actions and transfusion therapy, survival requires the patient’s blood to maintain hemostasis to stop bleeding. The physics of the problem are multiscale: (1) the systemic circulation sets the global blood pressure in response to blood loss and resuscitation therapy, (2) local tissue perfusion is altered by localized vasoregulatory mechanisms and bleeding, and (3) altered blood and vessel biology resulting from the trauma as well as local hemodynamics control the assembly of clotting components at the site of injury. Building upon ongoing modeling efforts to simulate arterial or venous thrombosis in a diseased vasculature, computer simulations of trauma induced coagulopathy (TIC) is an emerging approach to understand patient risk and predict response. Despite uncertainties in quantifying the patient’s dynamic injury burden, multiscale systems biology may help link blood biochemistry at the molecular level to multiorgan responses in the bleeding patient. As an important goal of systems modeling, establishing early metrics of a patient’s high dimensional trajectory may help guide transfusion therapy or warn of subsequent later stage bleeding or thrombotic risks.

INTRODUCTION

Modeling the human body’s response to acute hemorrhage and tissue trauma requires an understanding of the microscopic level mechanistic steps of blood coagulation, as well as of the global hemodynamic response to the loss of blood volume. The combination of hypovolemic shock and tissue damage creates the greatest risk of trauma induced coagulopathy (TIC) where excessive bleeding is difficult to manage. Numerous pathways interact to contribute to TIC including: endothelial dysfunction, unregulated inflammation, NETosis, complement activation, fibrinolysis, consumptive coagulopathy, impaired thrombin production, and hypofunctional platelets [17,25,43].

About a quarter of trauma patients display a coagulopathy that greatly increases the risk of death. TIC leaves certain patients at risk for uncontrolled bleeding and “oozing”, a trait often observed by trauma surgeons. The most immediate biochemical changes driven by blood loss are hypothermia, acidosis, tissue hypoxia, and hypotension. Low pH, low temperature, and low oxygen are all linked to deficient coagulation function [35,11].

Blood pressure and blood loss.

At the whole-body scale, the systemic circulation seeks to compensate for blood loss by several mechanisms. Transcapillary fluid shift draws water from the interstitial space to compensate for the first 0.5 to 1 L of blood loss, a beneficial effect that is attenuated in the dehydrated patient [48]. Similarly, the baroreflex modulates cardiac output with declining arterial blood pressure [56]. Slower changes in pressure and volume control involve the hypothalamo-pituitary-adrenal (HPA) axis which may be perturbed by traumatic brain injury (TBI) or during shock [31]. Modeling efforts described in Section 1 are focused on relating the systemic arterial blood pressure, heart rate, and stroke volume to the amount of blood lost via progressing hemorrhage.

Pressure distributions in damaged vascular networks.

At an intermediate length scale of damaged tissue (Section 2), the pressure along a branching arterial or venous network must account for the far upstream pressure condition set by the systemic circulation. The flow through a damaged vessel is different from that of an intact vessel since downstream resistance is lost when a vessel is severed. Specifically, damaged arterial vessels that are bleeding will not be able to maintain high internal pressures since they are directly connected to low pressure environments (P_atm or ~10 mm-Hg (interstitial) or −10 mm-Hg in certain diaphragm cavities below atmospheric pressure). The propagation of a vasoconstriction response to mechanical wounding may have significant effect on bleeding. Damage to veins can prevent filling, allowing for depressurization and leading to some back-drainage and diameter collapse. Blood leakage following damage to capillary beds can be regulated in part by smooth muscle cell contraction of precapillary sphincters. An important attribute of tissue damage to quantify is the instantaneous rate of blood loss relative to the healthy tissue perfusion rate prior to damage.

Changes in blood biology that result in local bleeding.

At the molecular and cellular length scale of vessel damage (Section 3), blood loss is controlled by the instantaneous intravascular pressure, the evolving geometry of the wound and the hemostatic action of clotting, and the extravascular pressure. Distinct from thrombosis in a diseased vessel that is not bleeding, hemostasis requires the rapid and controlled assembly of a clot where flowing blood may either leave the vascular space or continue past the wounded region, depending upon the size of damage. Dysfunction of platelets and thrombin generation and hyperfibrinolysis and increased vascular permeability all increase the risk of a situation where blood clots may be insufficient to support hemostasis. Fortunately, the availability of human blood samples has made it possible to assemble a large database of information related to the kinetics, mechanistic steps, initial conditions, and transport influences of blood coagulation and clot formation. Such blood samples are now obtained routinely from trauma patients, for research and diagnostic purposes, for predicting risk, or for informing transfusion choices (eg. plasma vs. platelets vs. RBC).

Shown in Figure 1 is a summary of the intricate and complex couplings between blood, vessels, heart, and therapeutic intervention that make TIC difficult to simulate, particularly for impacting real time clinical actions. The research field is at an early stage of creating well-annotated patient data sets where hospital monitoring information (HR, BP, O2, pH, T, etc) are coupled with clinical laboratory data (pH, CBC, aPTT, blood gases and ions, etc.) and linked with research data (genome sequences, coagulation and platelet phenotyping data) for each patient. Unique to trauma as a disease state, the onset time of trauma (t = 0) is well defined, which may help modeling efforts. However, a challenge for computer modeling of trauma is that the extent of initial traumatic injury, cumulative blood loss, and interstitial water level are difficult to quantify or monitor.

Figure 1. Multiscale Modeling of Trauma patient over 6 orders of magnitude.

The global hemodynamics model is typically represented as a closed-loop hydraulic circuit that includes lumped, 0-D, descriptions of the various components of the body. Bleeding can be included in these models by connecting the circuit to atmospheric pressure through a “resistance-to-hemorrhage” resistor, as is done in the Reisner-Heldt model [48]. At this scale, cardiovascular output is primarily modulated by the baroreflex and transcapillary fluid shifts. At the tissue level scale (cm), vasculature branching networks are constructed to match physiological conditions before a wound occurs. Once severed, boundary conditions to model blood flow may include inlet pressure/flow conditions and an outlet pressure specification (typically atmospheric pressure). At this scale, modeling efforts should include variable resistance to flow (changing vessel diameter) to divert flow away from the site of injury. At the vessel scale (mm), parabolic flow is assumed in the healthy vessel. In the event of trauma, pressure and flow specifications are both possible, which are set by the global hemodynamic model, with the extrinsic coagulation pathway (tissue factor) being the predominant trigger for maintaining hemostasis. Transfusion, vasopressors, and clotting modulators are standard treatment options.

1. Global hemodynamics during trauma

Quantifying the regulation of systemic blood pressure has been driven by pharmacology research of hypertension, particularly with respect to sodium balance and renal regulation over the course of hours to days. These hypertension models do not account for blood loss but quantify complex interactions between water intake/urine production, renin-angiotensin-aldosterone system, kidney filtering function, the renal sympathetic nerve activity, and ANP (atrial natrietic peptide) and ADH (vasopressin) [20].

In general, understanding the time-dependent global hemodynamics is essential to predicting hemodynamic collapse and mortality during trauma – and must be accounted for in models of a trauma patient. In cases where trauma and hemorrhage lead to shock, relevant changes can occur on a relatively fast time scale and typically involve: transcapillary water shifts, hypoxia/acidosis, the baroreflex, sympathetic nervous system responses, and the hypothalamic-pituitary-adrenal (HPA) triad (especially during traumatic brain injury).

To some extent, models of blood pressure control have started to account for traumatic bleeding. Hemodynamic models of the systemic circulatory system often employ lumped-parameter methods that implicitly assume uniform distributions of pressure, velocity, and hematocrit within a vascular compartment, resulting in a system of ordinary differential equations (ODEs). They often use an analogy with electrical circuits, where blood flow, viscous dissipation, and pressure drop are analogous to current, resistance, and voltage, respectively. Within this analogy, the frictional losses are modeled by resistors, the inertance of blood flow is captured by inductors (typically only significant in relatively large vessels), and vessel elasticity is represented by capacitors. In circuit analysis, Kirchhoff’s current and voltage laws are the primarily tools for determining voltage drops and current flows through every component of the circuit; the former enforces conservation of current and the latter enforces conservation of energy. The early Otto Frank 2-component Windkessel model [31] included a capacitor to capture the storage of stressed blood volume in the large arteries in parallel with a resistor to account for the dissipative losses of blood flow through the vasculature, resulting in the following ODE:

$$F\left(t\right)=\frac{P\left(t\right)}{R}+C\frac{dP\left(t\right)}{dt}$$ (1)

where F(t) is the flowrate of blood (ml/s), P(t) is the mean arterial pressure (mmHg), C is the arterial compliance(mL/mmHg), and R is the peripheral resistance (mmHg*sec/mL). This model has an exponentially decaying solution:

$$P\left(t\right)=P\left(t_o\right)e^{\frac{-\left(t-t_o\right)}{RC}}$$ (2)

which remains useful in medical settings for estimating arterial compliance [59]. However, this model does not provide pressure and flow information in each vascular compartment and does not include regulatory responses to blood loss.

The Guyton-Coleman model [19], the most famous and extensive model of the circulatory system, contains hundreds of equations and parameters with each vascular compartment characterized by its own compliance, inductance, and resistance depending upon its flow characteristics. The models most salient (and perhaps limiting) feature [42] is the dominant role of the kidney in long-term blood pressure control. The model emphasizes the vital importance of renal control of blood volume in maintaining physiological blood pressures in response to any kind of perturbation (blood loss, salt intake/extraction imbalances, etc.) and quantifying the kidney’s response to these changes. The importance of the Sympathetic Nervous System (SNS) to maintain long-term blood pressure control is only marginally captured in the original Guyton-Coleman model [19], and may require extension to include SNS regulation [20].

Particularly relevant to traumatic blood loss, the Ursino model includes an elastic variable description of the heart, a parallel arrangement of splanchnic and extrasplanchnic circulations, and neuroregulation via the baroreflex for short-term arterial pressure control (minutes) [56]. The baroreflex maintains cardiac output and systemic arterial pressure by regulating systemic resistance, heart period via SNS control, end-systolic elastance, and venous unstressed blood volume. Interestingly, a sensitivity analysis of each of these variables has shown that venous unstressed blood volume is the predominant mechanism for protecting the body from acute blood loss. The model was subsequently extended and able to simulate isocapnic hypoxia and hypercapnia [34,54,55]. While other descriptions of the heart have been proposed and included in other models [10,66], the elastic variable description remains the most widely used because of its physical transparency and straightforward implementation [32,63].

In the Reisner-Heldt model [48], a cardiovascular electric circuit model with baroreflex regulation, transcapillary fluid exchange, and lymphatic flow was constructed to model hemorrhage. Parameter values for fluid exchange and lymphatic flow were first tuned with canine blood loss data and then tested against further data sets. To simulate hemorrhage, a resistor was connected to atmospheric pressure and tuned to match blood volume loss as a function of time; once set, the resistance was held constant for the remainder of the simulation. The model predicted that in the initial stages of moderate to severe hemorrhage, transcapillary fluid exchange was significant in limiting hypovolemia and antagonistic to protein return. In the dehydrated patient, hydrostatic pressure in the interstitial tissue was too small to return protein to the vasculature after blood loss and the model predicts an increased risk of hemodynamic collapse.

The Neal-Bassingthwaighte [40] model was the first one with the capability of making trauma episode-specific predictions. The model used the electrical circuit analogy to construct a closed-loop circulation system with baroreceptor regulation. Parameters were determined by tuning the model to match baseline physiology of pigs prior to injury to the heart wall, and then held constant post-injury in the open-loop format. Rather than assuming a hemorrhage rate at a specific location (as in the Reisner-Heldt model), the tuned parameters were used in combination with arterial blood pressure and heart rate measurements (used as inputs to the model) to estimate cardiac output and total blood volume, which were validated via flowprobe measurements and survival/death outcomes of the pigs. Since the model did not explicitly account for diminished sympathetic vasoconstriction or cardiac contractility near the point of death, cardiac output measurements at those points were the most difficult to predict accurately.

The Sterling-Summers model extended the Guyton Model to explore the effects of morbid obesity on Mean Arterial Pressure (MAP) and Cardiac Output (CO) during hemorrhage [52]. Body mass Index (BMI) was used to quantify obesity, parameter values were tuned from known population distributions, and percent changes in hemodynamic quantities were calculated and compared with non-obese patients. Interestingly, the model predicts significant decreases in MAP and CO in response to modest increases in BMI. A systems analysis of the virtual obese patient revealed that an increase in the resistance to venous return that results from increased intra-abdominal pressure is responsible for this. This implies that a greater quantity of fluid during resuscitation is essential to overcoming the resistance to venous return in the obese patient. Since the model is constructed with mean values from population distributions, it is unable to make real-time patient-specific prediction.

The Mazzoni-Skalak microcirculatory network model was based upon the rat spinotrapezius muscle and considered 389 microvessels originating from a single arteriolar tree and converging to a single collecting venule while tracking the flow of leukocytes through the network [36]. Resistance parameter values were calculated by assuming Poiseuille flow through the microvasculature (correcting for viscosity changes using empirical relationships that relate viscosity to diameter, hematocrit, and shear rate) so that flowrate could be calculated in response to an applied pressure. Once a leukocyte attempted to enter a vessel smaller than its diameter, it would deform and increase the resistance to capillary flow. The simulation was used to study the relative importance of mechanisms responsible for slow reperfusion following ischemia and predict blood flowrates and composition in response to measurable changes in pressure, hematocrit, and capillary diameter in the left gastrocnemius muscle of bleeding anesthetized rabbit. Interestingly, the model also predicted that the slow reperfusion that characterizes ischemia is intensified if the leukocytes become active during ischemia.

The Hirshberg-Mattox model incorporated hemodilution into a hemodynamic model to evaluate the transfusion guidelines preventing dilutional coagulopathy in a bleeding patient [21]. Hirshberg et al. argued that plasma and platelet replacement were based upon empirical guidelines derived from a simple mathematical model with assumptions that frequently do not hold in severe trauma patients. For example, the model assumed a stable blood volume and that replacement rate is constant and equal to blood loss rate - in reality, blood loss is a function of blood pressure (not a constant), and replacement follows blood loss (sometimes on the order of many minutes or hours). Furthermore, the original model was derived when whole blood transfusion was the standard protocol – not the packed red blood cell (PRBC) transfusions used today – thus underestimating required concentrations of clotting factors. The model accounted for the heterogeneity of blood by explicitly including red blood cells, plasma, and intravascular water. The circulation system was described with the same nonlinear function relating systolic pressure to blood volume developed by Lewis et al [24]. Interestingly, the model was able to predict that resuscitation with more than 5 units of RBC will unavoidably lead to dilutional coagulopathy, and that the optimal ratio of fresh frozen plasma (FFP) to PRBC is 2:3, with an initial 2:1 ratio being essential to preventing dilutional coagulopathy.

2. Modeling of tissue scale bleeding

Defining vascular networks in silico.

In solving for the flow through a tissue that has been damaged, the hemodynamics of a branching vascular network becomes relevant. Vascular network modeling has been well-studied by numerous researchers. The earliest theoretical analysis for the design of the vasculature network was Murray’s “minimum dissipation principle”, which stated that the parent-vessel bifurcation occurs in such a way as to optimize the balance between the operational costs that arise from viscous energy losses (decreases with increasing diameter) and the capital cost of large blood vessels and large blood volume (increases with increasing diameter) [25]. The most significant equation that arises from this analysis is a rule that governs how the parent vessel bifurcates into daughter vessels:

$$d_0^{\gamma }=d_1^{\gamma }+d_2^{\gamma }$$

Where d₀ is the diameter of the parent vessel, d₁ and d₂ are the diameters of the daughter vessels, and γ is the branching exponent. In Murray’s law γ is set to 3, although other researchers have found that values between 2 and 3 are also physiological in certain vascular beds [16,23]. Other parent-daughter relations for bifurcating network relations are possible for generating realistic vascular tree networks. A constant parent-daughter ratio specification [58] can match measured geometries, as can stochastic sampling of branch/generation distributions [7]. The bifurcation angles are then typically defined, although there is large variability in the angles depending upon the location and target [65]. Realistic vascular networks have been created in silico with these rules in other studies [18,64,47,65], although not in the context of traumatic bleeding. The Westerhof model depicted the systemic arterial tree as an electrical circuit to model the viscoelastic properties of the arterial wall, but this representation is less common [60].

Defining regulatory mechanisms in bleeding tissue

In deploying network models for bleeding by a tissue, a branching network progresses from a large feeding artery to arterioles to capillaries and then de-branches to venules and larger collecting veins. Severing an arteriole or a vein, for example, results in distinct flow changes upstream and downstream of the injury. Arterial injury is characterized by high pressures driving blood loss and disrupted perfusion of all distal vessels. Venous injury is characterized by bleeding driven at lower pressures, with less likely immediate impact on the upstream arterial perfusion of the tissue.

In arterial injuries, the blood vessel’s high pressure is suddenly exposed to atmospheric pressure and bleeding rate becomes a function of pressure difference, oxygen consumption, cardiac output, and resistance to flow towards the exit. In the limit of complete severing of the vascular network, local downstream resistance is entirely lost, further increasing blood loss from the wound. In the event of internal bleeding, which is common following trauma, bruising can often be observed due to blood pooling in the body. In venous injuries, additional complications arise when considering the compliance of the veins -- large vein resistance varies depending upon how compressed they are by their surroundings, or distended due to the flow of blood. However, during trauma, high venous compliance and small filling pressure can lead to venous collapse. This phenomenon was indirectly addressed in Ursino’s model, where an exponential function was used to describe the relationship between pressure and volume in the veins [56]. The body’s immediate response to this perturbation in blood volume is the response of the baroreflex, which attempts to maintain cardiac output by regulating venous blood volume, systemic resistance, and heart rate. Vessel diameters are also varied to divert blood flow away from the site of injury and minimize blood loss. On a larger time-scale (minutes to hours), transcapillary fluid exchange in a well-hydrated patient occurs to diminish, to a limited extent, the effect of hypovolemia [48].

Efforts to model bleeding networks requires inlet/outlet pressure or flow boundary conditions (as functions of time), conservation of flow restrictions at branching points, and regulatory mechanisms to account for the action of the baroreflex and the fluid shifts. Researchers have applied inlet pressure/flow boundary conditions and local vasoregulation effectively to model this phenomenon in the construction of the cardiovascular system and vascular networks [44,65]. In the context of traumatic bleeding, the most natural outlet boundary condition would be a pressure specification since it is held constant at P_atm, although a bleeding rate specification may also be possible. The downstream condition for intact cardiovascular system post-injury could also be pressure/flow specifications [65], although 3-element windkessel boundary conditions [49] and wave reflection coefficient specifications have also been used [53].

Formaggia et al. developed a multiscale model of the circulatory system by coupling a zero-dimensional, lumped parameter model with a carotid bifurcating model [26]. The lumped parameter model provided pressure boundary conditions to the bifurcating model, while the bifurcation model provided flowrates to the global hemodynamic model. Although not used to study traumatic bleeding, a variation of this coupling strategy will be helpful in developing a full multiscale model of a trauma patient [37,45].

3. The hemostatic response in traumatized vessels

In daily life, the routine hemostatic response to vessel injury is well regulated. Platelets are captured by the injured wall and activate to release ADP and synthesize thromboxane (TXA₂) to drive further platelet deposition. The buildup of a platelet mass is highly hemostatic. Additionally, the extrinsic coagulation pathway is initiated when the cofactor Tissue Factor (TF) is exposed to blood near the site of injury and binds Factors VII and VIIa. The TF/FVIIa complex (sometimes called the extrinsic tenase) generates FXa and FXIa [38]. Generation of the intrinsic tenase complex FIXa/FVIIIa results in a burst of FXa, resulting in prothombinase (FXa/FVa) to help drive the generation of thrombin (FIIa). Thrombin is essential for platelet activation and for fibrin polymerization to stabilize the clot structure. Because FXIIa or FXIa deficiency is not associated with hemophilia, the contact pathway is considered nonessential for hemostasis. However, the requirements for hemostasis are substantially more challenging during trauma. Since contact pathway deficiency is associated with some risk for surgical bleeding, TIC risks may exist in trauma patients lacking FXII and FXI. The role of FXII and FXI in traumatic bleeding is not well studied.

From a systems biology perspective, the kinetics modeling of isotropic coagulation protease cascade has progressed over several decades and has been extensively reviewed [9,14,15,2,50]. These models mostly focus on the rate of thrombin generation and the clotting time when a threshold level of thrombin has been reached, although some have progressed towards trauma in silico [1].

Modeling of blood clotting under non-flow conditions.

One of the oldest ODE (lumped) models of coagulation is the Hockin-Mann model [22], which utilized 34 ODEs and 42 kinetic parameters to describe the extrinsic pathway. This model predicted coagulation initiation as [TF] was increased from 1 to 25 pM (zero clotting if TF is absent). A sensitivity analysis performed by Danforth et al. [8] indicated that the model was highly sensitive to parameter choice characterizing FVIIa with TF interactions. Model limitations include implicit assumption of an activated and excess platelet surface for coagulation to begin and did not include the contact pathway, and therefore, could not predict blood clotting in the absence of TF.

The Chatterjee-Diamond “platelet-plasma” ODE model [5] extended the Hockin-Mann model to 76 ODE’s and 105 kinetic parameters to include the extrinsic pathway and characterize the initiation of coagulation in the absence of TF. It also included thrombin and contact mediated feedback of FXIa generation and was able to predict FXIIa generation in the presence of CTI (corn trypsin inhibitor), a feature that was confirmed experimentally. The model included the role of platelet activation to reduce the initiation time for coagulation. Like the Hockin-Mann model, the platelet-plasma model assumes excess platelet surfaces. Recent experiments under flow indicate that the first layer of depositing platelets is sufficient for most of the thrombin produced on a TF bearing surface [67], confirming that platelets are not likely rate-limiting, at least at healthy platelet levels.

Bungay-Gentry model developed an isotropic reaction network model [3] with 73 ODEs and 17 reversible lipid adsorption reactions to explicitly account for lipid binding. While the reaction mechanisms were quite different from the Hockin-Mann model, they both agree with the same experimental study [4]. Their model predicts a threshold value of 25 nM lipid required for thrombin generation with 30–200 nM lipid range being most ideal.

Platelet Models.

Modeling of platelet signaling during clotting often use simple models of platelet activation typically with activation states of platelets as binary, either resting or fully activated depending upon an “activator concentration”, which can be a lumped representation of several species. This approach often is not tested against data sets with individual signaling pathways modulated pharmacologically.

Toward a detailed description of receptor-mediated platelet activation, the Purvis-Diamond model [46] used 77 reactions and 132 parameters to describe ADP-mediated signaling of P2Y1 G-coupled protein receptor activation, phospholipase-Cb activation, protein kinase C activation, phospohoinositol metabolism, and IP3 receptor regulation. The model was able to predict Ca₂₊ levels and ADP dose-responses, phosphoinositide metabolism, and volume of the dense tubular system. This ODE representation of the activation state of a platelet can then be included as a submodel of a larger-scale modeling of platelet aggregation. An ODE reaction network around platelet store-operated calcium entry (Stim1/Orai) predicts calcium mobilization in the presence of extracellular calcium. Lenoci and Hamm [28] used a system of ODE’s to describe kinetics of PAR-1 activation to generate intracellular signals that lead to platelet aggregation.

While these ODE models for P2Y1 and PAR1 signaling are full descriptions, they prove unwieldy in hemostatic clotting with single cell resolution and are difficult to tune to an individual patient. Chatterjee used a high throughput assay to measure [Ca2+] responses to 18 single agonist stimulations (6 agonists * 3 doses) and to 135 pairwise combinations of the agonists, an experimental technique termed pairwise agonist scanning (PAS). The data was used to train a neural network model [6] to make patient-specific platelet intracellular Ca²⁺ predictions in response to pairwise combinations of 6 agonists and to stimulate P2Y1/P2Y12, TP, IP, PAR1/4, GPVI membrane receptors, as well as intracellular guanylate cyclase. This later became an instrumental tool in multi-scale simulations of thrombosis under flow.

Clotting with flow.

The Kuharsky-Fogelson model [24] used 59 ODE’s to describe blood clotting on a Tissue Factor (TF) surface, simultaneously accounting for blood flow and platelet function. The model described blood flow over a TF patch that was small enough to make spatial variations in concentration negligible, enabling an ODE representation. The model was later extended to a PDE formulation [27] to account for concentration gradients in the growing thrombus. The model treated platelets as chemical solutes, and lumped mass-transfer coefficients were used to characterize transport of co-factors, enzymes, platelets, and inhibitors to the injured surface. The model predicted a thrombin generation threshold dependence on surface [TF] that was consistent with experimental results [41]. The PDE formulation of the model was used to calculate concentration variations within the thrombus, with the changing velocity field characterized by solution of the Navier-Stokes equation undergoing Brinkman flow. The model predicted that the thrombus was strongly dependent upon wall shear rate and physical blocking of TF, the latter being a strong inhibitor of coagulation. The model also predicted the classic thrombus architecture of an inner core of fully activated platelets, and an outer shell of less-activated platelets [51]. Importantly, this is a model of clotting on a surface and does not consider boundary conditions associated with bleeding hemodynamics.

Xu et al. used interacting submodels to develop a multiscale simulation of thrombus growth [61]. A coagulation cascade was coupled with a stochastic cellular Potts model of platelet states (motion, adhesion, deformations from the flow, activation state, etc.). Additionally, the Filipovic-Tsuda model used dissipative particle dynamics (DPD) to model thrombosis [12]. The model explicitly accounts for platelet motion and interactions with other platelets and the vessel wall. By integrating the DPD equations in time, the model was able to simulate thrombotic events in small stenotic flow channels while explicitly tracking the behavior of each individual platelet over time. Again, these thrombosis models do not consider the boundary conditions of bleeding and hemostasis.

The Flamm-Diamond model used a patient-specific NN model [14] as one of four interacting submodules of a multi-scale simulation of thrombosis under flow. The model required simultaneous solution of the velocity field in the presence of a growing clot via the Lattice Boltzmann method, solution to the convection-diffusion-reaction equation via the Finite Element Method (FEM) for the concentration profiles of ADP and TXA₂, platelet activation states in response to concentrations of soluble agonists from the NN, and platelet motion and binding via the Lattice Kinetic Monte Carlo (LKMC) method. A platelet drift velocity and an inlet platelet concentration distribution biased to be larger near the walls were included to account for red blood cell motion. The NN was able to provide patient-specific platelet information making it a highly valuable tool for predicting blood clotting under flow, as well as predicting the ranked potency of several drugs. This represented the first instance of patient-specific predictions of platelet deposition under flow and may have consequences in determining responses to therapy in the future. This model was extended (Lu-Diamond model) to include thrombin-dependent platelet signaling during clot buildup in the presence of various pharmacological inhibitors [62]. While no models yet calculate intrathrombus fibrin generation and fibrins anti-thrombin-1 activity, the Lu-Diamond model imposed a biphasic wall flux of thrombin that recapitulates the massive inhibitory action of fibrin against thrombin. Recent measurements prove that most thrombin is captured by intrathrombic fibrin [67].

Current limitations in various clotting models include the difficulty of 3D simulation, lack of pulsatile flow conditions, and difficulty of solving problems on a full arterial length scale. Also for multicomponent reaction systems, different sets of reaction networks and parameterizations may equally fit the data [57], making validation difficult. To date, few mathematical models have been tested for clots growing under diverse flow, biochemical, and pharmacological conditions. Through course graining with an imposed thrombin generation rate at a tissue factor surface, Lu et al. was able to simulate clotting under flow for several relevant pharmacological conditions [62]. However, a full simulation of thrombin generation, platelet activation, and fibrin polymerization has not yet been validated for healthy blood or for trauma blood. Additionally, clotting models have not been tested for boundary conditions of bleeding where clot strength is an important emergent property. Also, flow-clotting models have not yet been parameterized for trauma blood, where platelets are so highly dysfunctional [33].

4. Conclusions and Future Challenges of Model Validation in trauma

A multiscale model of a trauma patient offers the potential to optimize treatment options and quantify difficult to observe mechanisms important to patient outcome. Such a modeling effort would involve coupling of each of the scales discussed in a manner similar to the one presented in Figure 1, with biochemical events being integrated to global hemodynamic responses. Unfortunately, there are important processes that lack suitable biomarkers or measurable attributes, despite their importance. For example, mean arterial pressure is often used as a metric for blood loss since cumulative and instantaneous blood loss are not known quantities in the trauma patient. Patient hydration status is important for quantifying the influence of transcapillary fluid shifts in attenuating hypovolemia, although this is also typically unknown. The pre-trauma pharmacology of a patient is important but typically unknown, particularly antiplatelet and anticoagulant agents or drugs of abuse. Therefore, for models of the trauma patient to be effective they must be able to input/output clinically measurable data. Heart rate, blood pressure, oxygen concentration, pH, and blood gases can all be measured, while prothrombin time, clot strength and retraction, platelet function, and clot time under flow can all be measured in blood samples [30] - whereas cumulative blood loss, bleeding rate, extent of edema, state of baroreflex, quality of transfused blood products, and the state of the blood prior to trauma are important quantities that are difficult to quantify.

Trauma presents complex and rapidly evolving scenarios for clinical decision making. As a patient bleeds, the individual’s life may be at extreme risk if their systemic blood function changes in a manner that is unable to stop further bleeding. The overall goal is to achieve multiscale simulation of the trauma patient by accounting for changes in the systemic circulation and the traumatized blood and tissue so as to better stratify patient bleeding (or clotting) risks, prioritize improved biomarkers of risk, and potentially identify new opportunities for safer treatments. Although at an early stage of development, improved multiscale vessel and blood-tissue models will be broadly useful to other clinical situations of: surgical bleeding, sepsis, consumptive coagulopathies, deep vein thrombosis, acute lung injury, and hemophilic bleeding.