Transplant Estimated Function: A simple index to evaluate β-cell secretion after islet transplantation

The β-score was calculated from the DIR, A1C, fasting plasma glucose concentration, and stimulated/fasting C-peptide levels according to the method described by Ryan et al. (6). Briefly, each metabolic component is subjected to a staircase function that maps its value into a discrete score (0, 1, or 2 points). The cutoff values of the staircase functions and the scoring system are empirical and are founded on clinical judgment. The β-score ranges from 0 (no graft function) to 8 (interpreted as an index of excellent graft function). A stepwise multiple regression carried out on β-scores measured in the islet transplant recipients from our transplant center selected DIR, A1C, and fasting plasma glucose concentration as the best set of predictors of the β-score, with C-peptide playing a marginal role.

TEF selects the two pivotal components of the β-score (DIR and A1C) and links them together through a simple description of how insulin supply influences the patient's glycemic control. To describe such a causal relationship between DIR and A1C, we refer to the pretransplant condition of a type 1 diabetic patient who has negligible endogenous insulin secretion and relies on exogenous insulin therapy. The patient can be described as having a metabolic system whose input is insulin supply (quantified by DIR) and whose output is glycemic control (quantified by A1C). A change (Δ) in insulin therapy will produce a change in glycemic control:

where parameter K measures the sensitivity of the glycemic control to the insulin supply (K is a negative number because an increment in insulin availability determines a reduction in A1C). The same reasoning can be applied to posttransplant conditions when the islet transplant recipient has two sources of insulin supply. One source is exogenous insulin administration and the other is endogenous β-cell secretion. Restoration of endogenous β-cell secretion is followed by an adjustment in DIR and a change in A1C. Such changes will be linked together through an expression analogous to Eq. 1,

where ΔA1C and ΔDIR are the changes in glycemic control and insulin requirement that follow transplantation and TEF represents the daily amount of insulin secreted by the β-cells. TEF can be derived from Eq. 2 as a linear combination of DIR and A1C,

where a = −1, b = 1/K, and c is a constant depending on the pretransplant DIR and A1C of the patient:

Calculation of TEF requires knowledge of parameter K. Because individual estimates of K are not available for transplant recipients, a population value of K was estimated from the ΔDIR and ΔA1C data recorded in a group of type 1 diabetic patients (see statistical analysis). A value of −5.43 was found for K. By definition, TEF estimates the daily amount of endogenously secreted insulin by transplanted islets. It is null before the first engraftment and can be computed at any time during the posttransplant period. Occasionally, TEF can take on slightly negative values. This happens when the patient's metabolism deteriorates to the point that the balance between A1C and DIR becomes worse than before the first engraftment.

A gain in TEF is experienced when the effect of the engraftment has stabilized. If such a gain is normalized to the number of infused islets, one obtains an index reflecting the average contribution of the single islet. This index was denoted islet estimated function (IEF):

IEF allows the clinician to evaluate the benefit-to-cost ratio of each single engraftment. In fact, it estimates how much each infusion adds to the patient's endogenous secretion against how “expensive” it is (in terms of number of islets). IEF can also be used to obtain a score of the cost-effectiveness of the overall transplant procedure for each patient. In this case, given that the pretransplant TEF is 0, the gain in TEF will coincide with the maximum value of TEF achieved after the last engraftment. This value is normalized to the total number of islets received by the patient.

TEF estimates the amount of endogenously secreted insulin over 24 h. To validate TEF, we examined its association with the area under the 24-h C-peptide concentration profile, denoted as 24-h area under the curve for C-peptide [AUC(C-pep)]. Blood samples were collected for the measurement of C-peptide concentration at 0300, 0500, 0800, 0900, 1100, 1300, 1400, 1600, 1700, 2000, 2100, and 2400 h. Meal times were 0800 h for breakfast, 1300 h for lunch, and 1900 h for dinner. Sixteen type 1 diabetic subjects (mean age 40 ± 3.5 years and mean duration of diabetes 26 ± 7 years) who received an islet after kidney transplant (IAK) (with anti-thymocyte globulin, calcineurin inhibitors, and mycophenolate mofetil as immunosuppression) and five type 1 diabetic subjects (mean age 33 ± 10 years and mean duration of diabetes 24 ± 9 years) who received islet transplant (ITA) (with the Edmonton protocol as immunosuppression) were included in this analysis.

The associations between TEF and the insulin response to tolerance tests entailing either glucose or arginine administration (1,7) were also examined. Both tolerance tests were performed under fasting conditions and after overnight withdrawal of insulin administration. An intravenous glucose tolerance test (IVGTT) (0.5 g of glucose/kg body weight) was performed in IAK patients only (n = 24). Blood samples were collected for the measurement of insulin and glucose concentrations at baseline, 1, 3, 5, 10, 15, 20, 30, 40, 50, and 60 min. The acute insulin response to glucose (AIR_glu) was calculated as the incremental (above basal) area under the insulin curve in the interval 0–10 min. The arginine test (30 g of arginine hydrochloride administered in 30 min) was performed in both IAK (n = 34) and ITA (n = 21) patients. Blood samples were collected for the measurement of insulin, glucose, and C-peptide concentrations at baseline and at 5, 10, 20, 30, 40, 50, and 60 min. Indexes of the first-phase (acute insulin response to arginine [AIR_arg]) and second-phase insulin responses were calculated as the incremental area under the insulin curve in the intervals 0–10 min and 10–30 min, respectively.

Serum insulin levels were assayed with a microparticle enzyme immunoassay (IMx; Abbott Laboratories, North Chicago, IL) in which the lowest insulin sensitivity was 1 μU/ml. Serum C-peptide levels (intra-assay coefficient of variation 3.0% and interassay coefficient of variation 3.0%) were assayed by radioimmunoassay using commercial kits (Dako, Cambridgeshire, U.K.). The plasma glucose concentration was determined by the glucose oxidase method on a glucose analyzer (Beckman Coulter, Fullerton, CA). A1C was measured by the Variant II Hemoglobin A1C program (Bio-Rad, Hercules, CA), which uses the principle of ion (cation)-exchange high-performance liquid chromatography.

Sensitivity analysis is the process of varying a parameter over a reasonable range to observe changes in the results. TEF requires the use of the population parameter K measuring how much A1C changes in response to a unit change in daily insulin supply. Any sizable change in K will adjust the weight (and thus the importance) of A1C with respect to that of DIR in the calculation of TEF. To ascertain whether a change in K will have an impact on TEF validation, we recalculated the correlations of TEF versus 24-h AUC(C-pep) and TEF versus AIR_arg for a ±50% change of K.

Stepwise multiple regression was used to determine the relative importance of the components of the β-score. Simple linear regression was used to determine a population value for K from the changes (Δ) in DIR and A1C recorded for a group of n = 100 type 1 diabetic patients (age 40 ± 7 years, duration of diabetes 16 ± 10 years, A1C 7.5 ± 1.2%, and insulin 43.4 ± 17 units/day). The constant term of the linear regression equation was constrained to be zero (i.e., no change in insulin therapy and no change in A1C). In addition, before the analysis, a power transformation (cubic root) was applied to ΔDIR and ΔA1C data to even out their distribution and increase linearity. Validation of TEF against reference indexes of β-cell secretion and comparison of TEF against the β-score were examined by simple regression. Descriptive statistics are given in the text and tables as means ± SD. All statistical analyses were performed using the Statistical Package for the Social Sciences (SPSS 11.0; SPSS, Chicago, IL).

Daily insulin requirement, A1C, and fasting glucose concentration were selected as the best set of β-score predictors (P < 0.0001 for each), with C-peptide playing a nonsignificant role (P = 0.07). The daily insulin requirement was the most important correlate of the β-score (r = 0.76), A1C yielded an additional contribution (r became 0.85), and fasting glucose provided only a minor contribution (r became 0.88). Inclusion of C-peptide did not improve the correlation coefficient further.

Figure 1 shows the results of the TEF validation study against the 24-h C-peptide profile. Table 1 compares the correlation results obtained by TEF and β-score against 24-h AUC(C-pep) and the indexes of β-cell function obtained from the IVGTT and the arginine test. The arginine tests results are shown for all patients and for the IAK (n = 34) and ITA (n = 21) subgroups.

Figure 2 depicts the relationship between TEF and β-score. The left panel shows that TEF and β-score were correlated well (r = 0.69, P < 0.0001). The correlation coefficient remained virtually the same when ITA and IAK patients were analyzed separately. The right panel shows a comparison of posttransplant time courses of TEF and β-score in a representative patient. The two profiles change in parallel, confirming that TEF embodies the essential features of the β-score. The figure inset shows the average time courses of TEF and β-score in a group of transplant recipients who were followed for >2 years after the first engraftment (n = 36). Figure 3 exemplifies the different roles of TEF and IEF. Two patients having more or less the same TEF but very different IEF values are shown.

TEF remained robust with respect to a ±50% change in K (K upper and lower bounds were −2.7 and −8.1, respectively). The relationship of TEF versus 24-h AUC(C-pep) remained unaltered (r = 0.73 and r = 0.72 for K = −2.7 and K = −8.1, respectively). Likewise, the relationship of TEF versus AIR_arg did not appreciably change (r = 0.32 and r = 0.31 for K = −2.7 and K = −8.1, respectively).

Assessment of β-cell function in the islet transplant setting is important and challenging. Recently, the β-score has reshaped the way islet transplantation is assessed thanks to its simplicity and soundness (6). Therefore, it is mandatory to provide reasons why additional methodology for β-cell function assessment might be useful and to clarify how the β-score and TEF are related. The need for TEF arises from the observation that the β-score has a broader scope than just the assessment of β-cell secretion. The β-score measures transplant success in terms of an individual's overall homeostatic ability, and its scoring system hinges on metabolic variables related to both β-cell secretion and insulin sensitivity. The decision of Ryan et al. (6) to validate the β-score against the 90-min postprandial glucose concentration is congruent with this idea. In fact, glucose excursion during a meal is a well-recognized indicator of glucose tolerance and reflects the interplay of β-cell secretion and insulin sensitivity. The ability of the β-score to yield a comprehensive picture of transplant success is one of its major strengths. Even so, it would be useful to have a simple way of distinguishing the individual contribution of β-cell secretion. TEF can help to meet this need. Another aspect that motivated us to develop TEF is the fact that β-score requires the execution of a test eliciting a C-peptide response, which may be time-consuming. TEF quantitates β-cell secretion in a simple way that does not require a stimulus-response test. TEF is a combination of DIR and A1C (i.e., the pivotal components of the β-score), the respective weights of which originate from a simple description of how endogenous and exogenously administered insulin work together to determine glucose control. Because TEF hinges on the two most important components of the β-score, it is not surprising that TEF and β-score are well correlated (r = 0.69, P < 0.0001) and exhibit similar time profiles (Fig. 2).

The overall performance of TEF against reference indexes of β-cell secretion was in line with that exhibited by the β-score. TEF estimates the amount of endogenously secreted insulin over 24 h, and its correlation coefficient with 24-h AUC(C-pep) was 0.73 (P < 0.005), whereas the β-score attained r = 0.33 (NS). This means that changes in β-cell function, represented by the 24-h AUC(C-pep), only explain ∼50% (r² = 0.53) of the variability in TEF and, consequently, changes in TEF may not always be due to changes in β-cell function. Nonetheless, in this regard TEF appears to be superior to the β-score, which has an r² value of only 0.11. Interestingly, in those patients who achieved insulin independence, the TEF median value (1.0 unit · kg⁻¹ · 24 h⁻¹) was close to the 24-h insulin secreted value in kidney-alone transplant recipients, as derived by Polonsky et al. (8,9). They reported a value of 221 nmol/m² per 24 h in six patients having BMI of 30 kg/m². Assuming that body surface area and body weight were 2.0 m² and 85 kg, respectively, 221 nmol · m⁻² · 24 h⁻¹ correspond to 0.87 units · kg⁻¹ · 24 h⁻¹. As for the IVGTT results, the TEF correlation with AIR_glu in IAK patients was r = 0.59 (P < 0.001) and close to that by the β-score (r = 0.65, P < 0.001). As for the arginine test results, when the IKA and ITA subjects were considered together, the correlation coefficients found for TEF were the same size as those found for the β-score (Table 1). This is noteworthy because the β-score includes results of the arginine test among its components, whereas TEF relies simply on DIR and A1C. All in all, TEF provides an assessment of β-cell secretion that, at a fraction of the cost, does not seem inferior to that provided by the β-score.

A by-product of TEF that can have practical relevance is the calculation of IEF, an index quantifying the average contribution of the single transplanted islet. IEF can be interpreted as a benefit-to-cost ratio applicable to either the single infusion or the overall transplant procedure. The benchmarking ability of IEF is illustrated in Fig. 3 in which the values of IEF corresponding to each single engraftment are shown in two representative subjects. Benefits expected from use of IEF include an enhanced ability to evaluate the cost-effectiveness of the transplant and consistency in accounting for the benefits of the transplant across transplant centers.

As for all indexes, TEF also has limitations. Its major limitation is that, by using a population value of parameter K, TEF implicitly assumes the same degree of insulin sensitivity in all patients. We have documented the fact that the choice of K is not critical at the group level because the TEF validation results are unaffected by a ±50% change in K. Nevertheless, development of a feasible approach to individualize K in each transplant recipient would be a worthwhile goal that might enhance TEF accuracy.

In summary, TEF is a practical index of β-cell function that can be obtained without the need for an insulin stimulus-response test. It has a clear-cut physiological interpretation, and its performance against reference indexes of β-cell secretion is in line with that exhibited by the β-score. In addition, TEF can be normalized to the number of transplanted islets and thereby provide a benchmarking tool to evaluate the cost-effectiveness of the transplant.