A Reference Equation for Objectively Adjusting Dwell Volume to Obtain More Ultrafiltration in Daily Practice of Peritoneal Dialysis

Abstract

Objectives. Few studies mention how to objectively adjust peritoneal dialysis (PD) dwell volume for adult continuous ambulatory peritoneal dialysis (CAPD) patients. We proposed a reference equation composed of parameters from the peritoneal equilibrium test (PET) for adjusting daily dialysate dwell volume to obtain more ultrafiltration volume. Better fluid control could reduce more fluid overload-related complications. Design. We used body mass index, waist circumference, intraperitoneal pressure, and other parameters from peritoneal equilibrium test to compose a reference equation for fine-tuning daily dwell volume. Patients and Setting. Eighty-eight PD patients in one center with laboratory data collected during half-yearly PET evaluations were enrolled. Instilled dialysate was composed of 2.57% glucose PD fluid, either 1500 ml or 2000 ml in volume. In addition to other demographic data, intraperitoneal pressure (IPP) was also measured twice in the supine position four hours apart. We applied statistical multivariate techniques of discrimination analysis and logistic regression to verify the most feasible and optimal formula to determine infill volumes for patients. Results. We determined a novel formula for calculating daily dialysate dwell volume, Z: Z = (0.523 × waist circumference) + (0.852 × body mass index), derived from rotating axes to obtain an accurate prediction rate of 80.68% using the multivariate approach. Conclusion. The novel formula used objective, real-time parameters for determining appropriate dwell volumes for PD patients to optimize maximal ultrafiltration volumes and reduce subjective abdominal discomfort. The novel formula makes frequent adjustment of daily dwell volume by physicians or patients easy to calculate.

Keywords:

• intraperitoneal pressure
• peritoneal dialysis
• ultrafiltration
• peritoneal equilibrium test

INTRODUCTION

Both the incidence and prevalence of end-stage renal disease (ESRD) in Taiwan are highest in the world, with incident ESRD at 418 per million population and prevalent rate at 2,226 per million population, according to the U.S. Renal Data System 2008 Annual Data Report.^[1] The percentage of patients with ESRD on continuous ambulatory peritoneal dialysis (CAPD) is relatively lower, around 7.6%.^[1] Multiple factors cause patients to drop out of peritoneal dialysis treatment, such as feelings of abdominal fullness and decreased appetite resulting from large dialysate volumes or inadequate fluid removal with resulting hypertension, congestive heart failure, and increased mortality.^[2] A previous clinical study confirmed no apparent survival superiority with increasing peritoneal small molecular weight uremic toxin clearances.^[3] On the contrary, inadequate ultrafiltration volume and higher peritoneal transport are associated with increased mortality.^[2] We believe that developing a formula accounting for patient characteristics, peritoneal equilibrium test (PET) data, and intraperitoneal pressure (IPP) for predicting appropriate dialysate volume to achieve maximal ultrafiltration volume is crucial.

Using measurements of intraperitoneal pressure for adjustment of individual dwell volume is extensively applied among pediatric PD patients to obtain maximal volume tolerances and ultrafiltration volumes.^[4,5] Increasing dwell volume recruits more peritoneal membrane surface area for better uremic toxin clearance and larger ultrafiltration volume. Several researchers revealed negative linear correlation between mean IPP and ultrafiltration volume.^[6–8] Maintaining IPP levels of less than 18 cmH₂O is well tolerated by adult and pediatric PD patients, without subjective discomfort, while achieving optimal ultrafiltration volumes.^[7,9] Only a few studies applied IPP measurement as part of adjusting dwell volume in addition to subjective tolerance levels of adult patients and objective observation of a physician.

We studied adult CAPD patients concerned with maximizing ultrafiltration volume during PET evaluations. The waist circumference, body mass index (BMI), and tolerability of patients are usually considered by the physician to decide the infill volume for an individual PD patient. A smaller difference between dialysate/plasma creatinine ratio measured at the second and the fourth hour of PET, as well as a smaller reduction in IPP, reduced the outflow volume for CAPD treatment. The issue of how to determine the appropriate dialysate volume for a CAPD patient is controversial.

In this study, we developed a formula for both physicians and patients to determine and adjust appropriate infill volumes frequently and successfully to attain the maximum ultrafiltration volumes.

METHODS

Subjects

This is a cross-sectional study with consecutive participants on CAPD treatment recruited from a medical center in southern Taiwan. In total, 88 subjects were recruited (66 females, 22 males; age of 18–78 years; duration of dialysis 3.7–121.5 months). Of these, 20 patients used infill volumes of 1500 ml (group 1) and 68 used volumes of 2000 ml (group 2) during PET evaluations. All of the study subjects had been on regular PD treatments for more than three months, and none had a major operation, peritonitis, or acute illness within one month before enrollment.

The protocol of this study was approved by the Research and Ethics Review Board of Chi-Mei Medical Center. All authors certify that there are no known conflicts of interest with any third party.

Study Variables

IPP was measured^[5,10] during routine biannual peritoneal equilibrium test (PET) evaluations. The dwell dialysate was 2.57% glucose solution (Baxter Healthcare SA, Singapore Branch, DIANEAL PD-2 Peritoneal Dialysis Solution in ULTRABAG Container), and dwell volume was either 2000 ml or 1500 ml, which was the same as in the daily exchange regimen. The IPP data were collected at the beginning and end of the PET evaluations.

The PET protocol was performed according to Twardowski's recommendations.^[11] The intraperitoneal pressure was measured in the supine position as previously described,^[5,12] just after instillation of a defined dialysate volume (P₀) and before the dialysate was drained four hours later (P₄). The difference between P₀ and P₄ was defined as ΔIPP. The dwell volume was determined by the physician with consideration of both subjective abdominal discomfort of patients and objective BMI.

Gender, age, height, weight, CAPD duration, infill and dwell volumes, maximum ultrafiltration volume, ΔH4-H2 (the difference between dialysate/plasma creatinine ratio at the second and fourth hours), ΔIPP, waist circumference, and BMI were recorded, and differences between the two experimented groups were examined for statistical significance. The main variables that significantly affected ultrafiltration were then studied to develop the optimal formula to determine the appropriate infill volumes for individual patients.

Formulas and Discriminating Groups

Indentifying the New Axis

Traditionally, a separate independent Student's t-test for two groups based on a univariate approach is done for each variable. A preferred method is to perform a multivariate test in which both variables are tested simultaneously or jointly.

A new axis, Z, in the multivariate approach makes an angle with a variable axis, on which the projection of any point, say patient (p), on Z will be given by:

This equation represents a linear combination of two variables (i.e., waist circumference and BMI in this study) for patient p. The Z-axis gives a new variable Z, which is a linear combination of the original two variables. The ratio of the between-group to the within-group sums of squares for each angle implies that the greatest angle on the new axis provides the maximum separation between the two groups, to which the cutoff value can be decided by the number of observations and the average discriminant score for groups as the following equation^[13]:where ni and Zi bars are the sample sizes and the means of two groups, respectively.

Group Discriminant Analysis

Discriminant analysis is one of the available techniques for separating groups using specific discriminator variables. The first step is to identify a set of variables that best discriminates between groups. The next is to identify a new axis as in Eq. (1) to provide the maximum separation or discrimination between groups. The last step is to classify future observations into one of the groups for suggesting an appropriate dialysate infill-volume adjustment, such that the infill volume for an individual CAPD patient is either 1500 ml or 2000 ml.

The prior probabilities of the groups should be decided before conducting the discriminant analysis. We adopted two ways to examine grouping accuracy by assuming prior probabilities were equal and computing them from sample sizes with either two (waist circumference and BMI) or four variables (the two previous variables plus ΔH4–H2 and ΔIPP). The discriminant function denoting Z1 and Z2 was constructed, assigning observations to a specific group in accordance with the largest classification score.

Logistic Regression

When physicians are interested in determining the probability that a CAPD patient should be assigned to either infill volume group (1500 ml or 2000 ml), discriminant analysis can be used in terms of holding the multivariate normality assumption. Fortunately, the independent variables are a mixture of categorical and continuous variables, in which the logistic regression can be applied without assuming the normality of the distributions of the independent variables. That is, logistical regression is normally recommended when the independent variables do not satisfy the multivariate normality assumption.^[13,14] We showed two approaches for independent variables consisting of two (waist circumference and BMI) or four variables (adding another two variables, ΔH4–H2 and ΔIPP, to waist circumference and BMI) as that in discriminant analysis.

Statistical Analysis

Statistical analyses were performed using MedCalc for Windows, version 9.5.0.0 (MedCalc Software, Mariakerke, Belgium), and using SPSS for Windows (Version 15) (SPSS Inc., Chicago, Illinois, USA).

RESULTS

Eighty-eight peritoneal dialysis patients underwent PET with two infill volumes: 1500 ml (20 patients, group 1) and 2000 ml (68 patients, group 2). There were no differences in the distributions of age and gender between the two groups. Additionally, the differences of underlying diseases and durations of PD treatment between the two groups were insignificant (see Table 1).

Table 1  Demographic data of study subjects (n = 88)

	1500 ml		2000 ml		Total		p
	n	%	N	%	n	%
Gender							0.078
Female	18	90	48	70.6	66	75.0
Male	2	10	20	29.4	22	25.0
Age [year-old]							0.36
<40	4	20	11	16.2	15	17.0
40–50	5	25	29	42.6	34	38.6
>50	11	55	28	41.2	39	44.3
Underlying disease							0.564
DM	2	10	10	14.7	12	13.6
CGN	17	85	54	79.4	71	80.7
CIN	0	0	3	4.4	3	3.4
SLE	1	5	1	1.5	2	2.3
CAPD duration [month]							0.401
<12	8	40	17	25.0	25	28.4
12–36	2	10	17	25.0	19	21.6
36–60	5	25	15	22.1	20	22.7
>60	5	25	19	27.9	24	27.3

*χ² test or Fisher exact test.

Abbreviations: DM = diabetes mellitus, CGN = chronic glomerulonephritis, CIN = chronic interstitial nephritis, SLE = systemic lupus erythematosus.

Discriminant Analysis

Identifying a set of variables that provides the best discrimination between the two groups is the first objective of discriminant analysis. Table 2 shows that the discriminator variables providing the best discrimination are dwell outflow volume (UF is insignificant), waist circumference, and BMI. Only waist circumference and BMI were significantly and practically extracted. That is, Student's t-test suggests that the two groups are statistically different with respect to both waist circumference and BMI at a significant level of 0.05 (see Table 2).

Table 2  Variables compared with two groups of 1500 ml and 2000 ml

	Group 1 (n = 20)		Group 2 (n = 68)		p
	Mean	SD	Mean	SD
Height (cm)	152.0	6.0	159.0	7.2	0.000^†
Weight (kg)	47.5	7.6	59.1	9.5	0.000^†
Waist circumference (cm)	77.6	8.9	86.2	9.3	0.000^†
BMI	20.4	2.9	23.3	3.3	0.001^†
Effluent volume (ml)	1779.0	140.0	2278.0	174.0	0.000^†
ΔH4-H2	0.2	0.2	0.2	0.2	0.158
UF (ml.)	279.0	140.6	278.7	174.7	0.994
Mean IPP0 (cm H2O)	50.4	7.2	48.8	10.5	0.518
Mean IPP4 (cm H2O)	16.6	3.9	18.7	6.1	0.159
ΔIPP (cm H2O)	33.8	8.7	30.1	9.8	0.132

Group 1: inflow volume 1500 ml, Group 2: inflow volume 2000 ml.

*Student's t test.

^†p < 0.05.

Abbreviations: BMI = body mass index, UF = ultrafiltration, IPP = intraperitoneal pressure at the beginning and ending of PET, DH4-H2: difference between dialysate/plasma creatinine level at hour 2 and hour 4.

Formulas Predicting Infill Volume

Indentifying a New Axis

In Figure 1, a new axis, Z, in the two-dimensional space makes an angle of, for example, 58.46° with the waist circumference axis, on which the projection of any point—say, patient (p— on Z will be given according to Eq. (1). This represents a linear combination of the waist circumference and BMI for patient p. Table 3 shows each ratio, λ, of the between-group to the within-group sums of squares for each angle (θ), implying that the greatest λ on the new axis provides the maximum separation between the two groups. We chose an angle of 58.46° as the optimal solution, and cutoffs of 21.5 and 68.5 referred to the BMI and waist circumference scores, respectively. This represents overall accuracy of 80.68%, which is shown as alternative A in Table 4 and Figure 1.

Table 3  Summary statistics for various linear combinations

Angle	Weights		Sum of squares			λ
θ	w1 (Cosθ)	w2 (Sinθ)	SSt	SSw	SSb	(SSb/SSw)	F-value
0	1.000	0.000	8500	7365	1135	0.154	13.251
10	0.985	0.174	9086	7855	1231	0.157	13.483
20	0.940	0.342	9151	7896	1255	0.159	13.673
30	0.866	0.500	8687	7484	1204	0.161	13.831
40	0.766	0.643	7750	6668	1082	0.162	13.961
50	0.643	0.766	6453	5547	907	0.163	14.056
58.46	0.523	0.852	5190	4459	730	0.165	14.089
60	0.500	0.866	4953	4256	697	0.164	14.088
70	0.342	0.940	3430	2950	479	0.162	13.974
80	0.174	0.985	2067	1788	280	0.156	13.448
90	0.000	1.000	1031	909	122	0.134	11.529

Abbreviations: θ = the angle of two variables of waist circumference and body mass index (see Figure 1); w1 = Cosθ, w2 = Sinθ, SSt = total sum of squared deviation between data mean and its observed value, SSw = sum of total squared deviation between group mean and its observed value, SSb = sum of total squared deviation between data mean and its group mean, λ = SSb/SSw, F-value = (SSb ÷ degree of freedom) ÷ (SSw ÷ degree of freedom): as F goes up, P goes down (i.e., more confidence in there being a difference between two means).

Table 4  Six prediction methods for original observed volume

		Observed		Overall percentage	Predicted formula
Alternatives	Predicted	1500	2000
A	Rotation axes				Z = Cos 58.46° * waist + Sin 58.46° * BMI = 0.523 * waist + 0.852 * BMI
	1500	10^†	7	80.68%	Cutoff = 68.5, 21.5 for waist and BMI
	2000	10	61		Z cutoff = 55.65
B	DF (all groups with equal prior probability on two variables)				Z1 = −35.89 + 0.95 * waist − 0.15 * BMI
	1500	14	22	68.20%	Z2 = −44.05 + 1.02 * waist − 0.36 * BMI
	2000	6	46		Selected group = Max(Z1,Z2)
C	DF (prior probability from sample sizes on two variables)				Z1 = −36.69 + 0.95 * waist − 0.15 * BMI
	1500	3	3	77.30%	Z2 = −43.61 + 1.02 * waist − 0.36 * BMI
	2000	17	65		Selected group = Max(Z1,Z2)
D	DF (prior probability from sample sizes on four variables)				Z1 = −41.82 + 0.83 * waist + 0.2 * BMI + 7.35 * D(T4 − T2) + 0.3 * DIPP
	1500	8	3	83.00%	Z2 = −47.31 + 0.92 * waist + 0.25 * BMI + 5.6 * D(T4 − T2) + 0.26 * DIPP
	2000	12	65		Selected group = Max(Z1,Z2)
E	LR with two variables
	1500	4	3	78.40%	Z = −7.68 + 0.07 * waist + 0.16 * BMI
	2000	16	65
F	LR with four variables
	1500	8	4	81.80%	Z = −6.2 + 0.09 * waist + 0.09 * BMI − 1.39 * D (T4 − T2) − 0.05 * DIPP
	2000	12	64

^†counts in the matrix were determined by the respective predicted formula of alternatives.

Abbreviations: DF = discriminant function, LR = logistic regression.

Figure 1.  Plot of study data and new axis of Z (new axis) for alternative A.

Grouping Analysis

We constructed three sets of formulas as alternatives B to D shown in Table 4 with overall percentages of grouping accuracy of 68.20%, 77.30%, and 83.00%, respectively. The highest (i.e., alternative D) is computed from prior probabilities according to the group sample sizes with four discriminator variables.

Logistic Regression

The percentage accuracy of the two and four variables manipulated in logistic regression was 78.40% and 81.80% (as alternatives E and F in Table 4); this indicates that the more variables that are recruited, the higher the classification accuracy obtained. Though logistic regression (LR) with a little lower in percentage accuracy and less visually geometric illustration than discriminant analysis was displayed, the probability that a CAPD patient be assigned to the 1500-ml infill group can be decided when the Z value of LR is less than 5; otherwise, the patient should be assigned to the 2000-ml infill group when Z value of LR greater or equal to 5.

DISCUSSION

We studied the key factors affecting the maximum ultrafiltration volume (i.e., effluent minus instilled dialysate volume for CAPD treatment) as the maximum ultrafiltration volume (see Figure 2), including waist circumference, BMI, ΔH4-H2, and ΔIPP. The highest discriminating probability of those six alternatives in Table 4 is alternative D, with an accuracy percentage of 83.00%, which is arrived at from the four independent variables with prior probabilities decided by sample sizes. Even though the computation can be easily performed at the hospital after obtaining the discrepant values of H4, H2, and IPP measured at beginning and end of the PET evaluation, our recommended novel formula is the one of alternative A derived from rotating axis (see Table 4):

Figure 2.  Relationships of causes and effects obtaining appropriate PD dwell volume to maximum UF volumes for continuous ambulatory peritoneal dialysis (CAPD) treatment.

With only two variables, it can be simply used by patients or their physicians to accurately predict the optimal dialysate infill volume, 1500 ml or 2000 ml, for an individual patient. Traditionally, we decided the infill volume using the two variables of waist circumference and BMI, which showed significant differences in Table 2. Referring to Figure 1, even if using the criterion of waist circumference greater than 68.5 cm and BMI greater than 21.5, we misclassified several patients using the univariate approach. The multivariate method, with the newly calculated axis, obtained a greater success rate for classification whether considering the interception or not.

One of the limitations of this study was that only one set of measurements was obtained during PET, which was performed regularly every six months. That is also the reason why we recommend applying the formula for adjustment of daily dwell volume by patients themselves to obtain maximal ultrafiltration volumes. The sooner adjustments of dwell volumes are made, the better fluid control is, which reduces mortality.

Readers may doubt that only two infill volumes (1500 ml or 2000 ml) would suffice for clinical practice and meet most patients' needs. After performing clustering analyses for the four groups by K-mean of cluster analysis using SPSS for Windows, we suggest that the cutoff threshold values of 57, 65, and 74 of raw scores computed by the formula for axis rotation with alternative A in Table 4, be for four types of infill volumes for individual patients corresponding to 1500, 1700, 1850, and 2000 ml, respectively.

ACKNOWLEDGMENTS

This study was supported by grant CMFHR-9758 from Chi-Mei Medical Center.

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.