Modeling of Icodextrin in PD Adequest® 2.0

Extraneal (Baxter Healthcare, Deerfield, Illinois, USA), a commercially available 7.5% icodextrin solution, has been shown to provide a sustained ultrafiltration (UF) profile for long dwell exchanges (1-7). Such sustainability may have significant clinical benefit in terms of patient outcomes (8,9). While several papers have described the kinetics of icodextrin, these papers are limited to estimation of UF via volume marker data (10,11), or to a description of expected UF behavior via computer simulations (12,13). Little has been done in the way of validating existing kinetic model software in terms of predicting net UF for osmotic agents other than glucose.

The purpose of the present study was to scientifically validate the use of a modified three-pore model for use in predicting net UF for patients undergoing long dwell exchanges using a 7.5% icodextrin solution. Icodextrin is a polydispersed glucose polymer solution consisting of glucose polymers (dextrins) ranging in size from 2 to 1000 carbohydrate units [expressed in terms of degrees of polymerization (DP)]. The distribution of these poly-dispersed glucose polymers serves as osmotic agent for inducing UF during a single peritoneal dialysis exchange. A comparative analysis of modeled versus measured UF in patients undergoing an 8-hour exchange of icodextrin was carried out using data generated by Douma et al. (10). Modeled values of UF were based on a modified three-pore model implemented in the Baxter kinetic modeling software program, PD Adequest 2.0 (Baxter Healthcare) (12,14). Measured values of UF were based on volume marker data from 10 patients undergoing a single 8-hour exchange of icodextrin (10). A comparison was made summarizing how well PD Adequest predicts actual UF as measured using dextran 70 as volume marker.

Kinetic Modeling Assumptions

The basic theory and modeling assumptions used in PD Adequest 2.0 have been extensively described elsewhere (2,14-17). Briefly, PD Adequest 2.0 models solute and fluid removal using a modified three-pore membrane model (12,14). While there is extensive literature validating the use of the three-pore model (12,14,18-20), much of that literature focuses on solute and fluid transport for glucose-containing solutions. The present paper focuses on validating the model and assumptions used to predict UF for exchanges using icodextrin. Icodextrin has a weight average molecular weight (MW) between 12 and 20 kDa and a number average MW between 5 and 6.5 kDa. It is comprised of a mixture of different glucose polymers or dextrin molecules, with the MW of each dextrin determined by its DP, or number of carbohydrate units. Specifically, the MW of a given dextrin is defined as MW = 180.16 + [(DP – 1) x 162.14], where 180.16 is the MW of glucose and 162.14 is the MW of each dextrin addition unit.

The MW distribution of icodextrin has been determined by size exclusion chromatography, and the estimated percent of glucose polymer mass has been determined for each of five glucose polymer size classes across different lots of material (Baxter internal study). Table 1 summarizes the average mass distribution across five glucose polymer size classes. Using the relation between MW and DP, one can compute the DP range and MW bounds for each of the approximate MW cutoff values shown in Table 1. The composition and distribution of mass shown in Table 1 suggest that MW distribution may be described by a log-normal distribution. To confirm this, we plotted the quantiles of a standard normal distribution, corresponding to the cumulative percent mass values, against the corresponding log of the upper bound MW values shown in Table 1. The result, shown in Figure 1, suggests a strong linear relationship exists between the standard normal quantiles and the log(MW) values, indicating that MW distribution is indeed well approximated by a log-normal distribution.

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Table 1

Composition of Extraneal in Terms of Mass

Approximate MW cutoff values (Da)	DP a	MW upper bound a	Percent of mass	Cumulative percent mass	Standard normal quantiles	Log (MW) c
<1638	2–10	1639	5%	5%	–1.64485	7.4
1638–5000	11–31	5044	21%	26%	–0.64335	8.5
5000–20000	32–123	19961	48%	74%	0.64335	9.9
20000–45000	124–277	44931	20%	94%	1.55477	10.7
45000–100000	278–1000	162158	6% b	100%	—	12.0

MW = molecular weight; DP = degree of polymerization.

a

Computed based on MW cutoff values; MW upper bound is calculated based on the DP upper bound. Note there are only small trace elements of glucose in the icodextrin solution.

b

Computed assuming the cumulative % mass adds to 100%.

c

Natural log of the upper bound MW value.

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Figure 1

Plot of log(MW) versus standard normal quantiles. The strong linear trend suggests mass MW distribution may be approximated by a log-normal distribution. MW = molecular weight.

Given that MW distribution is log-normal, one can compute the cumulative number average MW, the cumulative weight average MW, and subsequently the cumulative osmolarity (in milliOsmoles per liter). Based on these values, one can then use properties of the log-normal distribution to compute the number average MW, the weight average MW, and the average osmolarity (mOsm/L) within each glucose polymer class. The results of these calculations are shown in Table 2 along with assumed default baseline blood concentrations of the five representative fractions. Davies (21) reported an average baseline blood concentration for maltose (DP = 2) of 0.04 mg/mL (or 0.12 mmol/L) for 91 patients. This is the average baseline concentration of maltose in patients naïve to icodextrin. In the absence of having either average values or patient-specific values for the blood levels of the five “average” dextrins shown in Table 2, we have assumed default baseline blood levels for the five subfractions that are less than or equal to the average baseline maltose value reported by Davies (21).

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Table 2

Composition of Extraneal ^a in Terms of Cumulative Mass and in Terms of “Average” Dextrins Within Each Class of Glucose Polymers

Glucose polymer (DP) b	Percent mass	Cumulative number avg. MW	Number avg. MW	Cumulative weight avg. MW	Weight avg. MW	Average osmolarity (mOsm/L)	Baseline blood (mmol/L)
2–10	5%	295	1166	64	1272	3.214 b	0.12
11–31	21%	1533	3118	780	3412	5.05092	0.12
32–123	48%	4364	9414	6002	10878	3.82428	0.12
124–277	20%	5543	27466	11779	28886	0.54612	0.12
278–1000	6%	5896	56702	15346	59549	0.07923	0.012

DP = degree of polymerization; MW = molecular weight.

a

Baxter Healthcare, Deerfield, Illinois, USA.

b

0.0042 mOsm/L computed for glucose (DP = 1).

Methods

Scientific validation was done by comparing time-dependent UF values modeled in PD Adequest 2.0 against “actual” values determined by the use of volume marker data. Specifically, we made use of previously published data from an 8-hour icodextrin dwell study carried out on 10 patients new to icodextrin (10). All patients in the study were in a stable clinical condition, without evident signs of overhydration. In 7 of the 10 patients, a 3.86% standard peritoneal permeability analysis (SPA) was done within a year after participation in the study. The mean net UF volume after 4 hours was 669 mL (SD ±195 mL). The total range was 341 – 900 mL. Only 1 patient had UF failure according to the 400 mL/4 hours criterion. Measured or actual UF values at select time points were calculated using total dextran 70 as volume marker in combination with peritoneal fluid kinetics as described by Douma et al. (10). These measured values were then compared against predicted values generated from the PD Adequest 2.0 program. To obtain predicted values, patient-specific data from an 8-hour SPA were entered into the PD Adequest program. Following input of the SPA data, PD Adequest was used to estimate the diffusive mass transfer area coefficients (MTAC or K_PA) for urea, creatinine, and glucose (14). The peritoneal surface area [i.e., the unrestricted pore area over diffusion distance (A₀/Δx)] was then estimated individually for each of these solutes by equating each solute's empirically estimated MTAC to its theoretical value, computed from the three-pore model, and solving for A₀/Δx (14). We then averaged these individual estimates of A₀/Δx across the three solutes to obtain an overall estimate of peritoneal surface area. From this estimate of average surface area, MTAC values and lumped-term reflection coefficients for the five representative “dextrins” were computed using the standard three-pore formula (18-20).

Three additional parameters are required in order to model fluid and solute transport in PD Adequest. These are residual volume (V_R, in mL), fluid absorption rate (Q_L, in mL/minute), and UF coefficient (L_PA, in mL/min/ mmHg). Residual dialysate volume, V_R, was estimated based on the difference between the actual intraperitoneal volumes during the first 10 minutes following infusion. The fluid absorption parameter, Q_L, represents the combined effects of unmeasured Starling forces and lymphatic flow (12,14) and was determined directly on the basis of convective loss of the volume marker over time (10). The UF coefficient, L_PA, was estimated based on post-30 minute data. In particular, the transcapillary UF rate at time t [Q_V(t)] was empirically estimated based on the differences in transcapillary UF (mL) between two successive time points as

e Q v ( t 2 ) = [ T C U F ( t 2 ) − T C U F ( t 1 ) ] / ( t 2 − t 1 ) ,

where TCUF(t) is transcapillary UF (mL) at time t, which is calculated as the dilution of the volume marker dextran 70 (10). Holding the net fluid absorption rate, Q_L, fixed, least squares regression was used to estimate the UF coefficient, L_PA, by fitting the empirically estimated transcapillary UF rates of each patient to the corresponding analytical approximations used in PD Adequest 2.0 (14,15). The kinetically derived estimates of Q_L and the least squares estimates of L_PA were then used as direct input into PD Adequest. Table 3 summarizes the key patient parameters used to model net UF for the 10 patients. The MTACs for urea, creatinine, and glucose in Table 3 differ slightly from those reported by Douma et al. (10). This may be explained partly by the use of different models and partly by different methods for estimating MTAC (10,14).

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Table 3

Summary of Key Patient Parameters for Urea, Creatinine, Glucose, and the Five “Average” Dextrins Used to Represent Each Fraction of Glucose Polymers (GP)

Parameter (n=10)	MW (Da)	Mean	SD
MTAC urea	60.06	19.76	6.96
MTAC creatinine	113.12	12.11	6.61
MTAC glucose	180.16	9.59	5.23
MTAC GP 2–10	1166	2.94	1.28
MTAC GP 11–31	3118	1.35	0.59
MTAC GP 32–123	9414	0.396	0.172
MTAC GP 124–277	27466	0.056	0.024
MTAC GP 278–1000	56702	0.005	0.002
Peritoneal surface area a (cm)	—	26 016	11309
LPA (mL/min/mmHg)	—	0.045	0.028
QL (mL/min)	—	1.032	0.900

MTAC = mass transfer area coefficient; L_PA = ultrafiltration coefficient; Q_L = fluid absorption rate; MW = molecular weight.

a

The unrestricted pore area over the diffusion distance.

Based on the kinetic parameters of Table 3, predicted values of Q_V(t), Q_U(t) = Q_V(t) – Q_L (the net UF rate, mL/ min), V_D(t) and net UF (mL), UF(t), were calculated from PD Adequest 2.0 and compared to values measured based on the disappearance of the dextran 70 marker. Net UF in PD Adequest is modeled as UF(t)_pred = V_D(t) – V_D(0), where V_D(t) is the modeled intraperitoneal volume at time t and V_D(0) = V_F + V_R is the initial fill volume (V_F) plus the residual volume (V_R). Observed UF was calculated as UF(t)_obs = TCUF(t) – LA(t), where TCUF(t) and LA(t) are the values of transcapillary UF and cumulative fluid absorption determined from the volume marker data (10).

Results

To compare measured versus modeled UF over time, we first examined the variability and predictability associated with disappearance of the volume marker over time. Shown in Figure 2 is the mean concentration profile of dextran 70, reflecting both uptake and dilution of the marker over time. There was a bilinear rate of decline in the concentration of dextran 70 over the course of the dwell, with an unusually high rate of decline observed during the first 30 minutes following infusion of icodextrin. This bilinear phase in uptake and dilution results in extreme variation in the measured UF rate (Figure 3). Possible sources for this variation may include variable residual volumes and/or unknown second-order kinetics associated with a distributed model of peritoneal dialysis. Specifically, a distributed model of the peritoneal exchange barrier that includes the effects of adsorption to the cellular glycocalyx of the mesothelium, rapid diffusion into the local interstitium, and initial expansion of the interstitium by convection may all be possible reasons for a sudden uptake of the marker. Likewise, rapid diffusion into the surrounding tissue of the smaller dextrin molecules that comprise icodextrin would affect the Starling forces toward filtration out of the capillaries, resulting in a higher initial UF rate. This would further dilute the dextran 70 in the peritoneal cavity over and beyond the level of dilution associated with variable residual volumes. Since PD Adequest does not incorporate second-order kinetics associated with a distributed model, but rather uses a modified three-pore membrane model to predict fluid and solute removal, it cannot accurately predict the volume-marker based UF rates observed during the first 30 minutes of dwell. However, modeled values of Q_V(t) from PD Adequest do appear to perform reasonably well following those first 30 minutes.

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Figure 2

Disappearance of dextran 70 (mg/L) from the peritoneal cavity following infusion of icodextrin. [Based on data from Ref. (10).]

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Figure 3

Modeled (solid line) versus actual (points) transcapillary ultrafiltration rates [Q_V(t); mL/minute]. Actual Q_V(t) values are based on dividing successive differences in measured transcapillary ultrafiltration by the corresponding elapsed times. [Based on data from Ref. (10).]

In order to assess how well the kinetic model in PD Adequest fits the measured values obtained 30 minutes post infusion, the modified three-pore model was applied assuming a starting volume for the model that is equal to the measured volume observed 30 minutes post infusion. Specifically, the starting volume for the model was set at V(0) = eV_D(30), where eV_D(30) is the empirically measured intraperitoneal volume determined from the volume marker data at 30 minutes post infusion.

Using the 30-minute post infusion volumes as starting values, modeled values were then compared against actual values using the concordance correlation coefficient described by Lin (22). The results of these analyses are summarized in Figures 4 and 5. Specifically, we found there was excellent agreement (concordance correlation = 0.9856) between actual and modeled UF values over the 8-hour dwell (Figure 4). Similarly, we found excellent agreement (concordance correlation = 0.9960) between actual and modeled intraperitoneal volumes (Figure 5). When we computed modeled volumes using the initial post infusion volumes rather than the 30-minute post infusion volumes as starting values, we found a significant reduction in agreement between actual versus modeled UF (concordance correlation = 0.4863), and a moderate reduction in agreement between actual versus modeled intraperitoneal volume (concordance correlation = 0.8498). This is partly explained by the fact that the model does not account for any second-order kinetics associated with the rapid loss of dextran 70 during the first 30 minutes of dwell and, hence, the rapid rise in marker-based UF over the first 30 minutes.

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Figure 4

Modeled (solid line) versus actual (points) net ultraf iltration (UF) values. Actual UF values were determined as the difference between measured transcapillary UF [TCUF(t)] and cumulative fluid absorption [LA(t)]. [Based on data from Ref. (10).]

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Figure 5

Modeled (solid line) versus actual (points) intra-peritoneal volumes (V_d). Actual values were determined based on measured transcapillary ultrafiltration [TCUF(t)] and cumulative fluid absorption [LA(t)]. [Based on data from Ref. (10).]