A Physiological Model to Evaluate Drug Kinetics in Patients with Hemorrhagic Shock Followed by Fluid Resuscitation

Abstract

Purpose

To build a physiologically based pharmacokinetic model describing drug kinetics in interstitial fluid in case of hemorrhagic shock, and to propose a simple method to determine the subset of influential parameters that may be estimated with the data at hand.

Methods

The model, which accounts for alterations of regional blood flows and body water distribution, was fitted to amoxicillin and clavulanate kinetic data, assessed in 12 trauma patients with hemorrhagic shock by comparison with 12 healthy volunteers. The predictions were the free concentrations of amoxicillin and clavulanate in 14 organs.

Results

In all tissues of trauma patients, the rate of distribution was lower, but the steady-state level was higher than those in healthy participants. Blood volume was reduced by 25% and blood flow in organs other than lung, brain, and heart were reduced by 18%. Compared with healthy subjects, the time that free amoxicillin concentration remained above 8 mg/L in the interstitial fluid of trauma patients was higher in blood and muscles, and lower in the tendon compartment.

Conclusions

The results and predictions were consistent with the knowledge in this field. The model may be useful to optimize clinical trial designs and drug dosing regimens.

Appendix: Equations of the Model

Base Model

A description of the model equations is presented here. More details and explainations may be found in the article of Levitt (17). The model is written as set of differential equations. Each equation describes the variation of the free drug concentration in the interstitial fluid of an organ (compartment). Each organ i is characterized by its mass V_i (kg), extracellular water fraction wecf_i (L/kg), ratio of interstitial to plasma albumin concentration rcP_i, permeability–surface area product PS_i for free drug (L/min per kg of organ), and blood flow Q_i (L/min per kg of organ).

The unbound fraction of drug in the volume of interstitial fluid (assimilated to the EDTA space) of each organ, fu_Ti, is calculated as :

$${\text{fu}}_{{\text{Ti}}} = \frac{1}{{1 + {\text{Kass}}.\left( {{{{\text{rcP}}_{\text{i}} } \mathord{\left/ {\vphantom {{{\text{rcP}}_{\text{i}} } {{\text{ $ \alpha $ }}_{\text{i}} }}} \right. \kern-\nulldelimiterspace} {{\text{ $ \alpha $ }}_{\text{i}} }}} \right) \cdot \Pr {\text{ot}}}}$$

where Kass is the association constant for drug binding to albumin measured in plasma (L/mol), Prot is albumin concentration in plasma (mol/L), and α_i is the fraction of EDTA interstitial space accessible to the drug in organ i. This parameter allows to take into account steric of electrostatic exclusion of the drug from the interstitial space.

In case of permeability-limited diffusion of the drug into the interstitial space of an organ, the fraction of the arterial drug concentration that diffuses into interstitial fluid during a single pass is calculated as:

$${\text{fclear}}_{\text{i}} = {\text{1}} - {\text{exp}}\left( { - \frac{{{\text{fu}}_{\text{b}} \cdot {\text{PS}}_{\text{i}} }}{{{\text{1}}{\text{.06}}\;{\text{wecf}}_{\text{b}} \cdot {\text{Q}}_{\text{i}} }}} \right)$$

where fu_b is the free fraction of drug in the blood, wecf_b the water fraction of blood in L/kg, and 1.06 is the density of blood in kilograms per liter.

The rate constant for free drug diffusion from blood to interstitial space of each organ, in 1/min, is calculated as:

$${\text{k}}_{{\text{Ti}}} = {\text{1}}{\text{.06}}\;{\text{fclear}}_{\text{i}} \cdot \frac{{{\text{fu}}_{{\text{Ti}}} \cdot {\text{wecf}}_{\text{b}} \cdot {\text{Q}}_{\text{i}} }}{{{\text{fu}}_{\text{b}} \cdot {\text{wecf}}_{\text{i}} }}$$

This equation may be viewed as the ratio of an unbound drug distribution clerarance $1.06{\text{wecf}}_{\text{b}} \cdot {\text{Q}}_{\text{i}} \cdot {{{\text{V}}_{\text{i}} } \mathord{\left/ {\vphantom {{{\text{V}}_{\text{i}} } {{\text{fu}}_{\text{b}} }}} \right. \kern-\nulldelimiterspace} {{\text{fu}}_{\text{b}} }}$ to an unbound drug volume of distribution ${\text{V}}_{\text{i}} \cdot {{{\text{wecf}}_{\text{i}} } \mathord{\left/ {\vphantom {{{\text{wecf}}_{\text{i}} } {{\text{fu}}_{{\text{Ti}}} }}} \right. \kern-\nulldelimiterspace} {{\text{fu}}_{{\text{Ti}}} }}$

The generic equation describing the variation of the free drug concentration in the interstitial fluid of an organ (Cu_Ti) is:

$$\frac{{dCu_{Ti} }}{{dt}} = k_{Ti} (Cu_A - Cu_{Ti} ) - ke.Cu_{Ti}$$

where Cu_A is the free drug concentration in arterial blood, and ke is an elimination rate constant, if any. This rate constant is calculated as the ratio of an unbound drug elimination clerarance ($1.06\;{\text{wecf}}_{\text{b}} \cdot {{{\text{CLi}}} \mathord{\left/ {\vphantom {{{\text{CLi}}} {{\text{fu}}_{\text{b}} }}} \right. \kern-\nulldelimiterspace} {{\text{fu}}_{\text{b}} }}$) to an unbound drug volume of distribution (${\text{V}}_{\text{i}} \cdot {{{\text{wecf}}_{\text{i}} } \mathord{\left/ {\vphantom {{{\text{wecf}}_{\text{i}} } {{\text{fu}}_{{\text{Ti}}} }}} \right. \kern-\nulldelimiterspace} {{\text{fu}}_{{\text{Ti}}} }}$). CLi is the intrinsic clearance of total drug, related to the organ clearance CL_org by a clearance model. In the simple case of a well mixed model, the relationship is:

$${\text{CLi}} = \frac{{{\text{CL}}_{{\text{org}}} }}{{1 - \left( {{{{\text{CL}}_{{\text{org}}} } \mathord{\left/ {\vphantom {{{\text{CL}}_{{\text{org}}} } {{\text{Q}}_{{\text{org}}} }}} \right. \kern-\nulldelimiterspace} {{\text{Q}}_{{\text{org}}} }}} \right)}}$$

The tissue-to-plasma total drug concentration ratios (Kp_i) are calculated as:

$${\text{Kp}}_{\text{i}} = \frac{{{\text{fu}}{\text{.wecf}}_i }}{{0.94\;{\text{fu}}_{{\text{Ti}}} }}$$

where 0.94 is the water fraction of plasma in liters per kilogram.

The volume of distribution of total drug at steady-state is calculated as:

$${\text{Vss}} = {\text{Vp}} + \sum\limits_1^n {{\text{ $ \alpha $ }}_{\text{i}} \cdot {\text{V}}_i \cdot {\text{wecf}}_i \cdot \left( {\lambda _E \cdot \frac{{{\text{fu}}_{\text{p}} }}{{{\text{fu}}_{{\text{Ti}}} }} + \left( {1 - \lambda _E } \right) \cdot {\text{fu}}_{\text{p}} } \right)}$$

where Vp is the volume of water in plasma, λ_E is the fraction of interstitial volume (EDTA space) accessible to albumin (λ_E = 0.45), and the sum is over the n organs.

Characterization of Hemorrhagic Shock and Fluid Resuscitation

The following changes are made to the base model. The volumes (V_i) of venous and arterial blood are multiplied by the factor of variation of blood volume (fbl). The extracellular water fractions (wecf_i) are multiplied by the factor of variation of the water fraction of blood fwbl (venous and arterial blood) or the factor of variation of extracellular water volume fecw (other tissues). The ratios of albumin concentration (rcP_i) are multiplied by a factor fwbl/fecw. The blood flows (Q_i) are multiplied by the factor of reduction of blood flow (fq) in all organs except brain, heart, and lung.