Capillary electrophoresis for the determination of glomerular filtration rate using nonradioactive iohexol

Volumetric absorptive microsampling as alternative sampling technique for renal function assessment in the paediatric population using iohexol

The glomerular filtration rate (GFR) is considered the best overall index for the renal function. Currently, one of the most promising exogenous markers for GFR assessment is iohexol. In this study, the suitability of volumetric absorptive microsampling (VAMS) as alternative for the conventional blood sampling and quantification of iohexol in paediatric plasma was assessed. Therefore, a new, fully validated liquid chromatography-tandem mass spectrometry (LC-MS/MS) method was developed. Subsequently, the clinical suitability was evaluated in 20 paediatric patients by comparing plasma iohexol concentrations and associated GFR values obtained by the VAMS method with those obtained by conventional blood sampling and quantification of iohexol in plasma. The developed, simple and cost-effective LC-MS/MS-method fulfilled all pre-set validation acceptance criteria. Iohexol could be accurately quantified within a haematocrit range of 20-60% and long-term stability of iohexol in VAMS was demonstrated up to 245 days under different storage temperatures. Both iohexol plasma concentrations (r = 0.98, mean bias: -4.20%) and derived GFR values (r = 0.99; mean bias: 1.31%), obtained by a conventional plasma and the VAMS method, demonstrated good correlation and acceptable bias. The agreement between the two methods was especially good for GFR values higher than 60 mL/min/1.73 m². Nevertheless, for GFR values <60 mL/min/1.73 m² the accuracy compared to the plasma method was lower. However, small adjustments to the sampling protocol could probably solve this problem.

Iohexol plasma clearance for measuring glomerular filtration rate in clinical practice and research: a review. Part 1: How to measure glomerular filtration rate with iohexol?

While there is general agreement on the necessity to measure glomerular filtration rate (GFR) in many clinical situations, there is less agreement on the best method to achieve this purpose. As the gold standard method for GFR determination, urinary (or renal) clearance of inulin, fades into the background due to inconvenience and high cost, a diversity of filtration markers and protocols compete to replace it. In this review, we suggest that iohexol, a non-ionic contrast agent, is most suited to replace inulin as the marker of choice for GFR determination. Iohexol comes very close to fulfilling all requirements for an ideal GFR marker in terms of low extra-renal excretion, low protein binding and in being neither secreted nor reabsorbed by the kidney. In addition, iohexol is virtually non-toxic and carries a low cost. As iohexol is stable in plasma, administration and sample analysis can be separated in both space and time, allowing access to GFR determination across different settings. An external proficiency programme operated by Equalis AB, Sweden, exists for iohexol, facilitating interlaboratory comparison of results. Plasma clearance measurement is the protocol of choice as it combines a reliable GFR determination with convenience for the patient. Single-sample protocols dominate, but multiple-sample protocols may be more accurate in specific situations. In low GFRs one or more late samples should be included to improve accuracy. In patients with large oedema or ascites, urinary clearance protocols should be employed. In conclusion, plasma clearance of iohexol may well be the best candidate for a common GFR determination method.

Simple and fast analysis of iohexol in human serums using micro-hydrophilic interaction liquid chromatography with monolithic column

A simple and rapid method based on micro-liquid chromatography using a synthetic monolithic capillary column was developed for determination of iohexol in human serums, a marker to evaluate the glomerular filtration rate. A hydrophilic methacrylic acid-ethylene dimethacrylate monolith provided excellent selectivity and efficiency for iohexol with separation time of 3 min using a mobile phase of 40:60 v/v 50 mM phosphate buffer pH 5/methanol. Four serum protein removal, methods using perchloric acid, 50% acetonitrile, 0.1 M zinc sulfate, and centrifuge membrane filter were examined. The method of zinc sulfate was chosen due to its simplicity, compatibility with the mobile phase system, nontoxicity, and low cost. Interday calibration curves were conducted over iohexol concentrations range of 2-500 mg/L (R(2) = 0.9997 ± 0.0001) with detection limit of 0.44 mg/L. Intra- and interday precisions for peak area and retention time were less than 2.8 and 1.4%, respectively. The method was successfully applied to serum samples with percent recoveries from 102 to 104. The method was applied to monitor released iohexol from healthy subject. Compared with the commercially available reversed-phase high-performance liquid chromatography method, the presented method provided simpler chromatogram, faster separation with higher separation efficiency and much lower sample and solvent consumption.

Biomarkers in chronic kidney disease, from kidney function to kidney damage

Chronic kidney disease (CKD) typically evolves over many years, with a long latent period when the disease is clinically silent and therefore diagnosis, evaluation and treatment is based mainly on biomarkers that assess kidney function. Glomerular filtration rate (GFR) remains the ideal marker of kidney function. Unfortunately measuring GFR is time consuming and therefore GFR is usually estimated from equations that take into account endogenous filtration markers like serum creatinine (SCr) and cystatin C (CysC). Other biomarkers such as albuminuria may precede kidney function decline and have demonstrated to have strong associations with disease progression and outcomes. New potential biomarkers have arisen with the promise of detecting kidney damage prior to the currently used markers. The aim of this review is to discuss the utility of the GFR estimating equations and biomarkers in CKD and the different clinical settings where these should be applied. The CKD-Epidemiology Collaboration equation performs better than the modification of diet in renal disease equation, especially at GFR above 60 mL/min per 1.73 m². Equations combining CysC and SCr perform better than the equations using either CysC or SCr alone and are recommended in situations where CKD needs to be confirmed. Combining creatinine, CysC and urine albumin to creatinine ratio improves risk stratification for kidney disease progression and mortality. Kidney injury molecule and neutrophil gelatinase-associated lipocalin are considered reasonable biomarkers in urine and plasma to determine severity and prognosis of CKD.

Estimating glomerular filtration rate in older people

We aimed at reviewing age-related changes in kidney structure and function, methods for estimating kidney function, and impact of reduced kidney function on geriatric outcomes, as well as the reliability and applicability of equations for estimating glomerular filtration rate (eGFR) in older patients. CKD is associated with different comorbidities and adverse outcomes such as disability and premature death in older populations. Creatinine clearance and other methods for estimating kidney function are not easy to apply in older subjects. Thus, an accurate and reliable method for calculating eGFR would be highly desirable for early detection and management of CKD in this vulnerable population. Equations based on serum creatinine, age, race, and gender have been widely used. However, these equations have their own limitations, and no equation seems better than the other ones in older people. New equations specifically developed for use in older populations, especially those based on serum cystatin C, hold promises. However, further studies are needed to definitely accept them as the reference method to estimate kidney function in older patients in the clinical setting.

Measured GFR as a confirmatory test for estimated GFR

Clinical assessment of kidney function is central to the practice of medicine. GFR is widely accepted as the best index of kidney function in health and disease, and accurate values are required for optimal decision making. Estimated GFR based on serum creatinine is now widely reported by clinical laboratories, and in most circumstances, estimated GFR is sufficient for clinical decision making. GFR estimates may be inaccurate in the non-steady state and in people in whom non-GFR determinants differ greatly from those in whom the estimating equation was developed. If GFR estimates are likely inaccurate or if decisions based on inaccurate estimates may have adverse consequences, a measured GFR is an important confirmatory test. Endogenous creatinine clearance is the most common method used to measure GFR in clinical practice but may be difficult to obtain or fraught with error. We review methods for GFR measurement using urinary and plasma clearance of exogenous filtration markers and focus on urinary clearance of iothalamate and plasma clearance of iohexol compared with inulin clearance. We suggest plasma clearance of nonradioactive markers be more widely implemented in clinical settings. Further research is necessary on the impact of the use of measured GFR as a confirmatory test.

Serum iohexol analysis by micellar electrokinetic capillary chromatography

A simple and rapid ( approximately 4 min) method for the measurement of iohexol in serum for assessing the glomerular filtration rate is described. It is based on direct serum injection on the capillary by MEKC. The method is linear between 8 and 260 mg/L, with an RSD of peak height of 2.9%. Several simple steps have contributed to an improved daily precision, such as choosing a high pH buffer, increasing the SDS concentration, frequent standardization, and eliminating any sample pretreatment.

Determination of iohexol clearance by high-performance liquid chromatography-tandem mass spectrometry (HPLC-MS/MS)

We have developed a simple, rapid, and accurate HPLC-MS/MS method for the determination of iohexol in serum. The column used was a Zorbax Eclipse XDB-C8 (100 mm x 2.1 mm i.d., 3.5 microm). Mobile phases consisted of water containing 2mM ammonium acetate and 0.1% formic acid (A) and methanol containing 2 mM ammonium acetate and 0.1% formic acid (B). After simple protein precipitation with ZnSO4, serum samples were mixed with I.S. (bromperidol) and centrifuged for 3 min. The obtained extraction recovery at three levels was 94.6-107.4%. Quantitative analysis was performed in the multiple reaction-monitoring mode (m/z 822.0-->804.0 for iohexol, 420.1-->122.7 for I.S.) with the total running time of 3 min for each sample. The assay was linear between 0.5 and 1500 microg/mL (r2 > 0.997). The intra- and inter-assay coefficient of variations were 2.4-6.2% and 5.5-6.5%, respectively. Our method provided sufficient analytical range and specificity for the 210 clinical samples analyzed.

Development and validation of an HPLC-UV method for determination of iohexol in human plasma

An HPLC-UV analytical method for estimation of iohexol in human plasma was developed and validated. Protein precipitation and iohexol extraction from plasma (100 microl) was carried out by adding 800 microl perchloric acid (5%, v/v in water) containing iohexol related compound B as the internal standard followed by vortex mixing and centrifugation. The supernatant (90 microl) was then injected onto a microBondapak C(18) column (150 mm x 3.9 mm, 10 microm) maintained at 30 degrees C. The mobile phase comprised of various proportions of acetonitrile and water with a total run time of 12 min and the wavelength of the UV detector was set at 254 nm. The extraction recovery of iohexol from plasma was >95% and the calibration curve was linear (r(2)=0.99) over iohexol concentrations ranging from 10 to 750 microg/ml (n=8). The method had an accuracy of >92% and intra- and inter-day CV of <3.7% and <3.6%, respectively. The method reported is simple, reliable, precise, accurate and has the capability of being used for determination of iohexol in clinical settings.

Measured and estimated GFR in healthy potential kidney donors

BACKGROUND

Nonradiolabeled iothalamate clearance is an accurate way to determine glomerular filtration rate (GFR). Objectives of this study are to define the normal range of nonradiolabeled iothalamate clearance in potential kidney donors and assess whether creatinine-based GFR estimates are accurate in this population.

METHODS

Medical records of 365 potential kidney donors were reviewed. GFR was measured using clearance of nonradiolabeled iothalamate. Linear regression analysis was used to determine age- and sex-specific normal range values for GFR and serum creatinine. The abbreviated Modification of Diet in Renal Disease (MDRD) and Cockcroft-Gault prediction equations were used to estimate GFR from serum creatinine levels.

RESULTS

GFR declined significantly with increasing age (P < 0.001) and was lower in women than men (P < 0.001). Men at the age of 20 years had an estimated mean GFR of 129 mL/min that declined by 4.6 mL/min/decade. Women at the age of 20 years had a mean GFR of 123 mL/min that declined by 7.1 mL/min/decade. Regression analysis of GFR normalized to body surface area (nGFR) was significant for age (P < 0.001), but not sex (P = 0.826). A 20-year-old had a mean nGFR of 111 mL/min/1.73 m2 that declined by 4.9 mL/min/1.73 m2/decade. Correlation between measured nGFR and estimated GFR was weak (r = 0.26 for abbreviated MDRD equation; r = 0.35 for Cockcroft-Gault equation).

CONCLUSION

This study of nonradiolabeled iothalamate clearance for the measurement of GFR in potential kidney donors established age-adjusted normal values. In healthy individuals, GFR cannot be estimated accurately using the abbreviated MDRD or Cockcroft-Gault prediction equations.

Method development for determining the iohexol in human serum by micellar electrokinetic capillary chromatography

Iohexol is widely used in clinical laboratories as a non-ionic radiographic contrast medium. Determination of its concentration in blood has a vital meaning in preventing its side effects caused by its retention in the system. A method for determining iohexol in serum by micellar electrokinetic capillary chromatography (MECC) requiring no pretreatment is developed. Electrophoresis is performed for serum samples at 25 kV with a borate buffer (50mM; pH 9.5) containing sodium dodecyl sulfate (50mM) and detection is carried out at 245 nm. Migration time of iohexol is 7.4 min. Linearity (0-1000 mg/l) is good and detection limit is 0.5mg/l (S/N=3). CV of intra-assay precision at a measurement concentration range of 6.2-200.1mg/l is 1.38-4.68% and recovery rate is 96-102%. CV of inter-assay precision is 2.06-5.94% at a measurement concentration range of 10.3-155.4 mg/l. This method is characterized by determination through direct injection of serum samples of super micro-quantity into the capillary, which simplifies the determination procedure in a significant manner and improves the precision and accuracy of determination.

Guidelines for the Reporting of Renal Artery Revascularization in Clinical Trials

Although the treatment of atherosclerotic renal artery stenosis with use of percutaneous angioplasty, stent placement, and surgical revascularization has gained widespread use, there exist few prospective randomized controlled trials (RCTs) comparing these techniques to each other or against the standard of medical management alone. To facilitate this process as well as help answer many important questions regarding the appropriate application of renal revascularization, well-designed and rigorously conducted trials are needed. These trials must have clearly defined goals and must be sufficiently sized and performed so as to withstand intensive outcomes assessment. Toward this end, this document provides guidelines and definitions for the design, conduct, evaluation, and reporting of renal artery revascularization RCTs. In addition, areas of critically necessary renal artery revascularization investigation are identified. It is hoped that this information will be valuable to the investigator wishing to conduct research in this important area.

Neutron-activation analysis: a novel method for the assay of iohexol

Accurate measurement of glomerular filtration rate (GFR) is of great importance in both research and clinical medicine. Available methods require radiation exposure or are technically difficult, thereby limiting their utility. Recent work has validated plasma clearance of nonradioactive contrast agents (iohexol and iothalamate) for the measurement of GFR. However, their clinical utility has been restricted by the difficulties associated with the detection of contrast agents in serum. In this investigation, we evaluate the sensitivity, accuracy and precision of neutron activation analysis (NAA) to measure serum iohexol at concentrations necessary for estimating GFR. We subjected aliquots of serum containing 0 to 6470 microg/mL iohexol to neutron activation by placing them in a neutron beam for 1 minute. The activation process resulted in the elevation of iohexol's naturally abundant iodine 127 to iodine 128. The spontaneous decay of (128)I to xenon 128 (proportional to the amount of total iodine in the sample) was calculated by means of spectrographic analysis. The correlation between the predetermined elemental mass of iodine in the sample and that measured on NAA was then determined. A similar analysis was performed to establish the intra- and interday accuracy and precision, with multiple measurements taken over a single day and over the course of a month. We noted excellent correlation between iodine measured on NAA and the known elemental mass (r(2) =.99). Measurements were highly accurate (mean accuracy 2.4% +/- 1.8%), with excellent intra- and interday reliability (mean coefficient of variation 4.1% +/- 1.6%). NAA is a feasible and reproducible method of detecting iohexol for the purpose of measuring GFR.

Guidelines for the reporting of renal artery revascularization in clinical trials

Although the treatment of atherosclerotic renal artery stenosis with use of percutaneous angioplasty, stent placement, and surgical revascularization has gained widespread use, there exist few prospective randomized controlled trials (RCTs) comparing these techniques to each other or against the standard of medical management alone. To facilitate this process as well as help answer many important questions regarding the appropriate application of renal revascularization, well-designed and rigorously conducted trials are needed. These trials must have clearly defined goals and must be sufficiently sized and performed so as to withstand intensive outcomes assessment. Toward this end, this document provides guidelines and definitions for the design, conduct, evaluation, and reporting of renal artery revascularization RCTs. In addition, areas of critically necessary renal artery revascularization investigation are identified. It is hoped that this information will be valuable to the investigator wishing to conduct research in this important area.

Measurement of iohexol by capillary electrophoresis: minimizing practical problems encountered

Iohexol is a non-ionic contrast agent, which has been widely described in recent literature as an accurate marker for the measurement of glomerular filtration rate (GFR). Our aim was to establish a capillary electrophoresis assay, based on a previously described method, that had adequate reproducibility to be used as part of a clinical trial. In this paper, we examine the practical aspects, pitfalls and steps we took to achieve a precise and reproducible assay. To minimize laboratory variation, we examined properties such as the use of an internal standard in a capillary electrophoresis separation, alternative deproteinization methods for serum, the most suitable matrix for the dilution of standards and the implementation of suitable quality control material to ensure that run-to-run variability was minimized. The optimized capillary electrophoretic assay of iohexol was found to be robust, with over 860 runs from the one capillary over a 9-month period. Excluding capital costs of the instrument, the consumable cost of the assay is less than A$0.25 per test, with a run time of 5.25 min and a coefficient of variation (CV) of 4.3% at 80 mg/L. The GFR, calculated from the plasma clearance, had a reproducibility of 5.47%.

A comparison of the plasma disappearance of iohexol and 99mTc-DTPA for the measurement of glomerular filtration rate (GFR) in diabetes

BACKGROUND

Changes in glomerular filtration rate (GFR) provide a valuable indicator of the progression of diabetic nephropathy. GFR is most commonly measured by the plasma clearance of radioisotopes, however, use of iohexol, a non-ionic radiocontrast medium, is a recently described alternative and has shown good agreement with inulin clearance. A one-compartment model is used for calculating GFR in most Australian centres but a two-compartment model is more accurate.

AIMS

To set up a non-radioisotopic method for assessment of GFR using iohexol, and to compare this with the currently used 99mTc-diethylene-triamine-penta-acetic acid (DTPA) method. Secondly, to compare GFR results using an unmodified one-compartment model with a one-compartment model subjected to the Brochner-Mortensen modification.

METHODS

Twenty-one patients with diabetes had assessment of GFR with simultaneous measurements of 99mTc-DTPA and iohexol plasma clearance. Plasma clearance was determined by the slope intercept method and then modified according to the Brochner-Mortensen equation. Plasma iohexol concentrations were determined by capillary electrophoresis.

RESULTS

There was no significant difference between iohexol and 99mTc-DTPA derived GFR values, difference 4.3+/-7.7 mL/minute (mean+/-SD). This was despite 99mTc-DTPA protein binding demonstrated in the range of 5-10%. Comparison of GFR results using an unmodified one-compartment model with a Brochner-Mortensen corrected one-compartment model showed higher GFR values with the former, in the range of 20-30% for GFR values > 100 mL/minute.

CONCLUSION

Iohexol provides an efficient alternative to radioisotopic methods for serial measurement of GFR in diabetic patients with hyperfiltration, incipient and overt nephropathy. A one-compartment model with its inherent overestimation of GFR should be replaced by the Brochner-Mortensen modified one-compartment model.

Pharmacokinetic aspects of measurement of glomerular filtration rate in the dog: a review

Glomerular filtration rate (GFR) is estimated by means of clearance, defined as the volume of plasma that has been cleared of a particular substance per unit time. Glomerular filtration rate may be estimated by measuring the renal clearance of a filtration marker using data from both urine and plasma or by plasma clearance using only plasma data. Several alternative pharmacokinetic models are used for the calculation of clearance using various filtration markers with slightly different pharmacokinetic properties. The purpose of this article is to discuss how the choice of marker and pharmacokinetic model may influence estimated GFR values and to elucidate commonly used methods and reported GFR values in the dog.

Application of newer clearance techniques for the determination of glomerular filtration rate

Glomerular filtration rate (GFR) is the standard measure of renal function and is critical for the management of renal diseases. Rigorous assessment of GFR requires the measurement of renal clearance of a filtration marker, such as inulin. This method, however, is not suitable for routine clinical practice. Labelled compounds as alternative filtration markers provide accurate and precise GFR measurement, but their use may be limited for safety reasons. Thus investigators have proposed clearance procedures using minute doses of non-radioactive contrast agents, including iothalamate and iohexol. Their renal clearance provides similar accuracy as inulin clearance in GFR estimation, but the need of urine collection again poses certain limitations to the procedure. Thus, plasma clearance of suitable exogenous markers, such X-ray contrast media, has been suggested for measuring renal function, in which the elimination rate of the tracer after a single intravenous injection is evaluated. Plasma clearance of these markers estimated by multiple blood samples provides precise information, but repeated sampling makes this method cumbersome. Abbreviated kinetic profiles have been proposed to predict GFR from the plasma disappearance curve. The simplified method that uses a one-compartment model corrected by the Bröchner-Mortensen formula gives an excellent correlation with inulin clearance and is currently employed for measuring GFR in multi-centre clinical trials.

Capillary electrophoresis in clinical and forensic analysis

During the past decade, capillary electrophoresis (CE) emerged as a promising, effective and economic approach for separation of a large variety of substances, including those encountered in clinical and forensic analysis. Reliable and automated CE instruments became commercially available and promoted the exploration of an increasing number of CE methods and fields of application. The widespread applicability of CE, its enormous separation power and high-sensitivity detection schemes make this technology an attractive and promising tool. This review discusses the principles and important aspects of CE-based assays and provides an overview of the key achievements encountered with CE in clinical and forensic analysis, including those associated with the analysis of serum proteins, hemoglobin variants, drugs and nucleic acids. Validated assays, interesting applications and future trends in clinical and forensic analysis are also discussed.

GFR determined by nonradiolabeled iothalamate using capillary electrophoresis

Traditional measurements of glomerular filtration rate (GFR) in clinical practice include the measurement of serum creatinine or creatinine clearance. Increasing evidence concerning the limitation of these measurements in clinical practice and clinical trials has resulted in efforts to develop technologies that improve measurement of GFR. Recent efforts in that regard have used radioisotopic labeling of markers of GFR, such as 125I-iothalamate, and 51Cr-ethylenediaminetetraacetic acid. Limitations of these technologies include radiation exposure as well as cost considerations for the management of radioisotopes, including safety, disposal, mailing, and deteriorating activity that results in short shelf life. We report a test that used 0.5 mL Conray dye injected subcutaneously and subsequent measurement of the nonisotopic (cold) iothalamate by capillary electrophoresis in blood and urine. GFR using cold iothalamate compared with standard clearance using 125I-iothalamate was 0.99. The method is cost-effective and allows for avoiding exposure to isotopes, as well as problems such as the disposal and short shelf life of isotopes. This technology could allow for replacement of 125I-iothalamate as a marker for GFR.

Development of a nonisotopic capillary electrophoresis-based method for measuring glomerular filtration rate

The conditions for quantitative measurement of nonisotopic iothalamate meglumine (Conray) in urine and plasma by capillary zone electrophoresis (CE) have been developed. The impetus for developing this methodology was to replace the traditional [125I]iothalamate glomerular filtration rate (GFR) marker assay, a routine tool in the measurement of kidney function. This new approach for measuring kidney function is attractive since it avoids the cost of administration of radioisotopic compounds to patients, as well as the cost associated with purchase and disposal of isotopic compounds and contaminated samples. The concentration of iothalamate in urine and plasma determined by CE can be used directly to calculate GFR. The GFR in patients injected with [125I]iothalamate and nonisotopic iothalamate simultaneously showed an excellent correlation (0.998) with between-day coefficient of variation of 2.30% and a recovery of 102% and 98%, respectively, when added to urine and plasma. Interference from drugs and other urinary compounds is eliminated with this method. Collectively, this study has shown that CE is a cost-effective alternative to the current methodology for measuring GFR.

Measurement of serum iohexol by determination of iodine with inductively coupled plasma–atomic emission spectroscopy

We used inductively coupled plasma–atomic emission spectroscopy to measure serum iodine to determine plasma clearance of iohexol, an iodinated radiographic contrast agent. We determined I at 178.276 nm on the phosphorus 178.287 nm channel of the polychromator by utilization of spectrum shifter offset software, while correcting for P with the sequential P 214.914 nm emission line. Determination of I on the polychromator provided excellent precision in the measurement of serum I, even though the interelement correction of P was done with a sequential P line. Total imprecision (CV) (n = 13) was 16% (at 13.7 mg/L I), 8.6% (28.7 mg/L), 3.6% (59.0 mg/L), 2.6% (120.5 mg/L), 1.7% (237.8 mg/L), 1.2% (478.7 mg/L), and 1.8% (597 mg/L). The linear range was 15 to 600 mg/L. Iohexol added to serum (mg/L I) and recoveries (%) were 15 (91.3%), 30 (95.7%), 60 (98.3%), 120 (100.4%), 240 (99.1%), 480 (99.7%), and 600 (99.5%). Studies on dogs and cats administered a single intravenous injection of iohexol indicated that a dose of 300 mg I/kg body weight was sufficient for measurement of glomerular filtration rate by using a single compartment model for plasma clearance with three samples drawn 3 to 7 h after treatment. With this protocol, correlation coefficients were &gt;0.99 on the β phase of the plasma disappearance curve.