Virtual population development

Prior to simulation of a virtual population, the target population for simulation needs to be defined. Since the observed PK data was obtained in a group of Caucasian Australian men, average height and weight and corresponding coefficients of variations for these anthropometric measurements in non-obese Australian males were obtained from Craig, et al. (2001). As described by Willmann et al., first, height values were randomly drawn from a normal distribution for a population of 1000 male subjects followed by sampling of each organ compartment mass for each individual in the virtual population (Willmann, et al. 2007). To mitigate the likelihood of individuals with the same height being allocated identical organ weights, organ masses were drawn either from a normal or log-normal distribution (Table 1) that was re-centered to the size of the individual employing an allometric scaling factor according to the ¾ power rule (Willmann, et al. 2007). To avoid the selection of extreme outliers, organ mass distributions were symmetrically truncated to the 95^th percentile and, when necessary to prevent negative masses, constrained at the lower bound to one tenth the re-centered mean value. A visual check was then performed to evaluate the impact of truncation and constraining the lower bound by repeating the simulations for all dose levels in the observed data where parameters initially drawn from a normal distribution were then drawn from a log-normal distribution.

Anatomical and physiologic parameters with distributions used in the population PBPK model

^aMean organ mass was obtained from the BioDMET database (Graf, et al. 2012)

All model compartments, with the exception of skin, blood and lymph were scaled according to equation (1), where the mean mass of each organ O, denoted MOmean, is dependent on a single variable, in this case the body height of the individual, H_indiv, via an equation of the form MOmean=cHindivp, where c is a sex- and race-dependent constant and p is a chosen exponent. Organ masses for a reference individual MOref were obtained from the BioDmet database where H_ref is the height of a reference individual weighing 71 kg with a body mass index of 24 kg/m² (corresponding to a height of 172 cm) (Graf, et al. 2012). Where organ volume and or mass were to be interconverted, density values for organs were obtained from ICRP references (2002a).

Body height has been identified previously by de la Grandmaison as a better predictor of organ size in the majority of cases and the formula is rooted in allometric theory (de la Grandmaison, et al. 2001). An exponent of ¾, although previously reported, was largely empiric for the current report, and others have used a range of values, upwards of 2, in a similar fashion (Willmann, et al. 2007; Bosgra, et al. 2012).

Blood and lymph mass means were scaled based on reference body weight (W_ref, equation 2) as blood and lymph vessels are assumed to increase with increasing body weight as opposed to height.

Skin mass was scaled based on body surface area (BSA) as per equation 3 where BSA was estimated based on equation 4 and where the constant values for a, b and c were as proposed by Gehan and George (a = 0.0235, b = 0.515, c = 0.422) (Gehan and George 1970).

The total body mass (BM) of a virtual individual was then calculated as the sum of the bloodless organ masses, lymph mass, skin mass and blood mass and the BM of the final population individuals (n = 1000) included only individuals within the range of 60–80 kg, consistent with the observed population. As previously suggested by Peters blood mass was partitioned as 2/3 venous and 1/3 arterial (Peters 2008).

For the derivation of organ-specific blood flows in each individual, mean perfusion values were first calculated for each organ to serve as a reference value assuming that perfusion rates would be constant across the population. Organ reference perfusion values were obtained by multiplying the cardiac output in a reference 71 kg male (Graf, et al. 2012) by the blood flow fraction to that organ and then dividing the reference blood flow by the mean organ mass. Individual organ blood flows (QB) were then obtained by multiplying the organ weight of the individual by the reference perfusion value. Plasma flow (QP) was derived by multiplying QB by a factor of 1-hematocrit (hct), where hct was assumed to be log-normally distributed (Table 1).

Consistent with the PBPK model for a reference male, lymph flow was set at a constant fraction of blood flow (LO) where the previously employed value of 0.2 % was used for all organs except skin (LS), which was set to 0.1 % (Offman and Edginton 2015). The fraction of 0.2 % corresponds to the upper range of lymph flow reported by Swartz whereas 0.1 % was obtained by optimization in the reference male model (Swartz 2001).

Clearance of the pegylated protein was previously characterized by both renal (RCL) and non-renal clearance (NRCL). RCL was set at 0.1 % of glomerular filtration rate (GFR) consistent with previously investigated PEG-conjugated therapeutics. To allow for incorporation of interindividual variation in GFR, the GFR was derived from the product of renal plasma flow and filtration fraction (FF) where FF was drawn from a log-normal distribution (Table 1) (Baumann, et al. 2014; Offman and Edginton 2015). The acronym FGFR is used to represent the fraction of glomerular filtration attributed to renal clearance. To avoid the risk of including individuals with GFRs in the impaired region of glomerular function, and to avoid extremely large values for GFR, only individuals with a GFR within the range of 90–150 mL/min were used in the simulation (Delanaye, et al. 2012).

For the compound in question, NRCL was assumed to occur by both macrophagic uptake of the non-pegylated moeity and by non-specific cleavage of the pegylated chain (Caliceti and Veronese 2003). NRCL was optimized in primates in our previous model and for the current model NRCL in the primate was scaled to each simulated human based on the body weight ratio of a simulated human individual and the mean weight of the primate (3.4 kg) (Offman and Edginton 2015). The NRCL was then apportioned based on the relative volume of each compartment in which NRCL was assumed to occur.