A Physiologically-Based Pharmacokinetic Model of Endogenous Clotting in Obstetric Patients

Objectives:

According to the CDC’s Pregnancy Mortality Surveillance System, adopted in 1987, pregnancy-related mortality had more than doubled by 2003 and continues to rise. Hemorrhage and venous thromboembolism (VTE), or excessive clotting, combine to account for over 30 percent of maternal deaths (Kuriya et al. 2016). Understanding how activated coagulation factors dynamically distribute and drive clot development during and after pregnancy may provide insight into the mechanisms driving these key morbid outcomes. Physiologically-based pharmacokinetic (PBPK) models provide improved mechanistic understanding of drug distributions throughout the body and the impact of these administrations. PBPK models have been applied to the obstetric population with relative success (Luecke et al. 1994, Kalluri et al. 2017, Zhang et al. 2018). However, to the best of our knowledge, modeling the dynamic coagulation potential over gestation and during childbirth has not been explored and may help bridge the gap between systemic challenges and the mechanisms driving coagulation.

Methods:

The PBPK model includes the following compartments: arteries, central veins, liver, uterus, legs, and a compartment to encompass all other organs (the “organs” compartment). Interacting dynamic equations capturing volume, activated clotting factors (aCFs), and clot were built using mass balance principles using ordinary differential equations (ODEs). Volumetric flow rates were determined from a combination of literature and expert input, and all parameter ranges simulated were restricted to capture the physiological range. Compartmental volumes change as a result of gestational accumulation of volume and increases in specific organ flow rates, particularly in the uterus and organs compartments. Gestational fluid accumulation, and return to the initial blood volume, is accomplished through changes in kidney volume elimination, which is grouped into the organs compartment. Reduced volume elimination drives gestational volume accumulation, and an elimination rate increase after birth provides return to baseline. The model also incorporates the loss of volume occurring immediately post-delivery (simulated over thirty minutes), along with a net shift of blood from the uterus to the venous space that is observed with postpartum uterine contraction. Volume loss is modeled as linearly dependent upon a uterine tone parameter, allowing for simulations of abnormal and insufficient uterine tone leading to increased blood loss during labor and delivery.

During and after delivery, coagulation factor blood concentrations exhibit an increase and return to baseline levels (Gerbasi et al., 1990) and can be associated with a generalized coagulation ability modeled as aCFs. Generation of aCFs is captured in an activation rate parameter, A, which is dependent on the rate of blood loss by the uterus during delivery. The rate of deactivation of aCFs follows liver metabolism, in addition to the fibrinolytic effects in circulation (i.e., tissue plasminogen activator). Specifically, a deactivation parameter, D, serves to decrease concentrations in the liver and system flow in a first-order manner. Lastly, the clot state includes a growth and a breakdown functionality. Clot growth requires exposure to aCFs (residence time in the compartment multiplied by concentration), and a compartment-specific binding affinity parameter. The breakdown or lysis of the clot is linearly dependent on the compartment clot state value and a lysis parameter.

Results:

Model simulations describe compartmental volumes, clotting factor concentrations, as well as the increase in flow to the uterus during gestation. Volume simulations of all organs were parameterized to capture published gestational blood volume changes. Delivery and resulting volume distribution changes resulted in a total loss of 350 mL of blood for a simulated patient with healthy uterine tone. Blood loss increased to 800 mL when uterine tone diminished to a quarter of the healthy value for 30 minutes. This larger volume blood loss qualifies as postpartum hemorrhage. To assess the effect of dynamic volume changes, the magnitude and trajectory of the simulation results for the aCFs and clot state for a healthy and a diminished uterine tone (reduced to 25 percent of the normal value) are compared. Concentration of aCFs simulated for the diminished uterine tone simulation were 1.7 times the concentration of aCFs of the healthy tone simulation in the compartments. The difference between the aCF trajectories includes an extended time that the compartments are exposed to aCFs for the diminished tone simulation. The peak aCF concentration is reached at the end of delivery and hemorrhage (which is extended for the diminished tone simulation). In contrast, the clot state peaks in each compartment at varying times after delivery and hemorrhage. For the leg compartment, the peak clot state occurs approximately 1.2 hours after delivery ends and is 2.2 times higher for diminished uterine tone compared to normal tone. These trajectory differences, including increased exposure marked by increased area under the curves, for both aCFs and clot state might help analyze timing and mechanisms leading to hypercoagulation events including venous thromboembolism that primarily originate in the legs.

Summary:

Our model demonstrates elevated exposure to aCFs, increased clot formation (especially in the legs), and increased blood loss after childbirth as a result of diminished uterine tone. Changes in this model structure and parameterization including uterine tone value, activation and deactivation, clot formation functionality including binding and breakdown, will be assessed with available literature and clinical data. These parameters are expected to vary on a per patient basis, resulting in variability in the expected aCF and clot trajectories. Ongoing work includes testing patient-specific risk factors and characteristics mapped to changes relevant parameters. A higher risk patient will exhibit a lower uterine tone, in addition to an elevated activation rate. Additionally, the resulting exposure to clotting via the clot state may eventually be calibrated to published changes in risk (odds ratio) based on hemorrhage for developing VTE (James 2009). Once validated, this type of model could use patient-specific risk factors to return a timeline of risk as well as recommendations for monitoring coagulation-related challenges.