Comparison of Subcutaneous Regular Insulin and Lispro Insulin in Diabetics Receiving Continuous Nutrition

Abstract

Background:

Optimal management of non–critically ill patients with diabetes maintained on continuous enteral feeding (CEN) is poorly defined. Subcutaneous (SQ) lispro and SQ regular insulin were compared in a simulated type 1 and type 2 diabetic patient receiving CEN.

Method:

A glucose-insulin feedback mathematical model was employed to simulate type 1 and type 2 diabetic patients on CEN. Each patient received 25 SQ injections of regular insulin or insulin lispro, ranging from 0-6 U. Primary endpoints were the change in mean glucose concentration (MGC) and change in glucose variability (GV); hypoglycemic episodes were also reported. The model was first validated against patient data.

Results:

Both SQ insulin preparations linearly decreased MGC, however, SQ regular insulin decreased GV whereas SQ lispro tended to increase GV. Hourly glucose concentration measurements were needed to capture the increase in GV. In the type 2 diabetic patient, “rebound hyperglycemia” occurred after SQ lispro was rapidly metabolized. Although neither SQ insulin preparation caused hypoglycemia, SQ lispro significantly lowered MGC compared to SQ regular insulin. Thus, it may be more likely to cause hypoglycemia. Analyses of the detailed glucose concentration versus time data suggest that the inferior performance of lispro resulted from its shorter duration of action. Finally, the effects of both insulin preparations persisted beyond their duration of actions in the type 2 diabetic patient.

Conclusions:

Subcutaneous regular insulin may be the short-acting insulin preparation of choice for this subset of diabetic patients. Clinical trial is required before a definitive recommendation can be made.

Treatment of non–critically ill patients with diabetes who receive continuous enteral feeding (CEN) remains a challenge despite advances in diabetes mellitus (DM) management.^1,2 In this patient population, only 2 clinical studies have compared different short-acting subcutaneous (SQ) insulin preparations.^3,4 These studies focused primarily on mean glucose concentration (MGC) and hypoglycemia; glucose variability (GV) was not measured.

The current gold standard of glycemic control is glycosylated hemoglobin, established by the Diabetes Complications and Control Trial.^5,6 It is an integrated measure of glycemic exposure and when elevated, is associated with vascular complications.⁷ Increased GV has emerged as another glycemic control metric that may also be linked to morbidity and mortality.^8,9

The insulin analog lispro was developed to improve MGC in patients with diabetes while minimizing postprandial hypoglycemia.^10,11 Diabetic patients maintained on CEN comprise a very different patient cohort. In these patients, hyperglycemia results from DM and CEN. Assuming a constant rate for CEN, it might be expected that the underlying ultradian oscillations in glucose concentrations are uniform in amplitude. We therefore postulated that the short-acting insulin preparation with the longer duration-of-action would have a better GV profile and a smaller risk of hypoglycemia. This hypothesis was tested by numerically simulating the glucose-insulin feedback system.

Materials and Methods

The model^12,13 used delay differential equations (DDEs) to incorporate the time delays required to simulate the finite response time of the pancreas and liver to secrete insulin and glucose. The DDEs were derived from the principle of mass conservation for glucose concentration, G(t), and insulin concentration, I(t), for any time t. The principle states that the rate of change in G(t) must equal glucose production, G_p(t), minus glucose utilization, G_u(t). Similarly, the rate of change of I(t) must equal insulin production, I_p(t), minus insulin clearance, I_c(t). In equation format, this reads as follows:

$$\begin{array}{l}\mathrm{d}/\mathrm{dt\; G}\left(\mathrm{t}\right)={\mathrm{G}}_{\mathrm{p}}\left(\mathrm{t}\right)-{\mathrm{G}}_{\mathrm{u}}\left(\mathrm{t}\right),\\ \mathrm{d}/\mathrm{dt\; I}\left(\mathrm{t}\right)={\mathrm{I}}_{\mathrm{p}}\left(\mathrm{t}\right)-{\mathrm{I}}_{\mathrm{c}}\left(\mathrm{t}\right),\end{array}$$ (2.1)

Where

$${\mathrm{G}}_{\mathrm{p}}\left(\mathrm{t}\right)={\mathrm{G}}_{\mathrm{in}}\left(\mathrm{t}\right)+{\mathrm{f}}_5(\mathrm{I}\left(\mathrm{t}-{\mathrm{t}}_2\right))\times {\mathrm{f}}_6(\mathrm{G}\left(\mathrm{t}\right)),$$ (2.2a)

$${\mathrm{G}}_{\mathrm{u}}\left(\mathrm{t}\right)={\mathrm{f}}_2(\mathrm{G}\left(\mathrm{t}\right))+\beta \times {\mathrm{f}}_3\left(\mathrm{G}\left(\mathrm{t}\right)\right)\times {\mathrm{f}}_4\left(\mathrm{I}\left(\mathrm{t}\right)\right)+{\mathrm{f}}_7\left(\mathrm{G}\left(\mathrm{t}\right)\right),$$ (2.2b)

$${\mathrm{I}}_{\mathrm{p}}\left(\mathrm{t}\right)={\mathrm{I}}_{\mathrm{in}}\left(\mathrm{t}\right)+\alpha \times {\mathrm{f}}_1\left(\mathrm{G}\left(\mathrm{t}-{\mathrm{t}}_1\right)\right),$$ (2.2c)

$${\mathrm{I}}_{\mathrm{c}}\left(\mathrm{t}\right)={\mathrm{d}}_{\mathrm{i}}\times \mathrm{I}\left(\mathrm{t}\right),$$ (2.2d)

and d/dt is the time derivative. The functions f₁ through f₇ are highly nonlinear and describe different aspects of the glucose-insulin axis. Each component is described in Table 1 with each function being determined from human physiologic data.¹⁴ The numerical value of the model’s 5 adjustable parameters, t₁, t₂, d_i, α, and β, determines the pathophysiology being simulated and their role is clarified in Table 2.

Table 1.

Purpose of Functions f₁ Through f₇, G_in(t), and I_in(t).

Function name	Description
f1(G(t-t1))	Insulin production and release by pancreas
f2(G(t))	Insulin-independent glucose utilization
f3(G(t)) × f4(I(t))	Insulin-dependent glucose utilization
f5(I(t-t2))	Hepatic glucose production
f6(G(t))	Inhibitor of hyperglycemia
f7(G(t))	Inhibitor of hyperglycemia
Gin(t)	Nutritional source
Iin(t)	Exogenous insulin

Table 2.

Summary of the 5 Parameters in the Model and Their Functions.

Parameter name	Description
t1	Time delay, endogenous insulin secretion
t2	Time delay, endogenous glucose secretion
β	Amplitude, insulin-dependent glucose utilization
α	Amplitude, endogenous insulin production
di	Amplitude, insulin clearance

The model was validated for normal physiology and DM by showing that the detailed glucose concentration measurements taken from several normal subjects and type 1 and type 2 diabetic patients could be reproduced when the parameter values were appropriately chosen.¹² It was also demonstrated that the model correctly captured the effects of insulin therapy and a nutritional source. The reverse process was also found to be valid as an unknown patient’s corresponding parameter values could be used to correctly diagnose the patient’s underlying DM pathophysiology.¹² Type 1 DM was modeled primarily by decreasing the term that describes insulin secretion by a constant, α, in equation 2.2c. Type 2 DM was modeled mainly by decreasing the term that describes insulin-dependent glucose utilization, β, in equation 2.2b. When α and β are appropriately chosen and less than 1, the virtual patient will either secrete a suboptimal amount of insulin or demonstrate insulin resistance; however, to completely capture the diabetes pathophysiology within each patient, the other parameters must also be defined.

The 3 remaining additional model parameters are the rate of insulin clearance d_i and the time delays t₁ and t₂. Their purpose is shown in Table 2. The time delays allow the model to reproduce the naturally occurring glucose-insulin ultradian oscillations.^15,16 Finally, experiments have demonstrated that the process of insulin degradation is proportional to its concentration¹⁷ and this proportionality constant is d_i (equation 2.2d).

The parameter values validated against a type 1 and a type 2 DM patient¹² were utilized in this study (Table 3). The measureable quantities after SQ insulin injection were the changes in MGC and GV versus the SQ insulin dose; hypoglycemia was also reported.

Table 3.

Model Parameter Values Used for Each DM Patient.

Parameter	Type 1	Type 2
t1	15 (min)	15 (min)
t2	36 (min)	15 (min)
β	0.898	0.531
α	0.477	0.900
di	0.27 (1/min)	0.18 (1/min)

For each virtual patient, 25 injections of SQ regular insulin and insulin lispro were given with doses that ranged from 0 to 6 U. The term “baseline” was used to reference data gathered from the virtual patient when 0 U of insulin was injected. Patients therefore served as their own control. The changes in MGC and GV were then calculated as follows: MGC/GV was measured after a SQ insulin injection from which the baseline MGC/GV was subtracted. Mean glucose concentration was calculated in the usual fashion. GV does not have a standard definition.¹⁸ We chose to define GV as the average distance between adjacent local maximum and local minimum values in the patient’s G(t) data. Finally, the local maximum and minimum of G(t) data were referred to as peaks and troughs, respectively.

SQ insulin injections, I_in(t) in equation 2.2c, were modeled with piece-wise functions.^13,19 The duration of action used for SQ insulin lispro was 240 minutes whereas 480 minutes was used for SQ regular insulin. The rate of continuous nutrition (or glucose absorption), G_in(t) in equation 2.2a, was 135 mg/min. This is equivalent, for example, to 82.2 ml/hour of Glucerna® 1.2 Cal which would provide 2367 calories and 194 g of net carbohydrates over 24 hours. Finally, equation 2.1 was solved as previously described.¹³

Results

Subsections group the results by insulin therapy and the type of diabetes. Graphs depicting the change in MGC show a decrease in MGC when a data point is below the y = 0 line. A value above y = 0 indicates an increase in MGC. The same is true for the change in GV graphs.

No Insulin Therapy and Normal Physiology

The ultradian oscillations produced when the model parameters are set to normal physiologic values are shown in Figure 1. The G(t) data (Figure 1A) show the ultradian oscillations that produce 92.5 mg/dl MGC within a 100-minute period. Similarly, I(t) was found to oscillate (Figure 1B) with peaks that lag behind the glucose concentration peaks by approximately 16 minutes, consistent with t₁. The units of G(t) and I(t) in the functions f₁ through f₇ are mg and μU, respectively. They are first converted to mg/dl and μU/ml before G(t) and I(t) are presented in figure form. This syntax is used in all G(t) graphs.

Figure 1.

Parameters for simulation: β = 1, α = 1, t₁ = 15 min, t₂ = 5 min, and d_i = 0.06/min; a normal subject. (A) G(t), glucose concentration versus time. (B) I(t), insulin concentration versus time. Note that I(t) lags behind G(t) by 16 min, consistent with t₁.

Type 1 Diabetic Patient Receiving CEN

Figure 2A shows that SQ insulin lispro increased GV in a linear manner as the dose increased. SQ regular insulin, however, decrease GV in a geometric, nonlinear fashion. The corresponding MGC data (Figure 2B) show that both SQ preparations lowered MGC in a linear fashion with similar slopes. These results indicate a linear dose-response curve for both insulin preparations.

Figure 2.

Type 1 DM patient data. (A) Change in GV versus number of SQ insulin units injected. (B) Change in MGC versus number of SQ insulin units injected.

To understand why SQ regular insulin and insulin lispro have opposite effects on GV, detailed G(t) data were examined. Figure 3A shows G(t) data after a 6 U SQ insulin lispro injection at time t = 0. For syntax, the first peak and first trough occurred just after insulin injection, a convention used below. Corresponding baseline G(t) data were also plotted for comparison. The first glucose concentration trough, nearly 70 mg/dl, was well below the corresponding baseline value of approximately 120 mg/dl. Then, the first glucose concentration peak nearly returns to its preinsulin baseline values. Such dynamics are consistent with the 240-minute duration of action of SQ insulin lispro. The response to SQ lispro lowered MGC but increased GV. The effect of 6 U of SQ regular insulin was quite different (Figure 3B). The first trough was only slightly below its baseline value at nearly 110 mg/dl. In addition, the first 2 glucose concentration peaks were decreased whereas the third glucose concentration peak nearly returned to its preinsulin baseline value at 500 minutes. This timeline is consistent with SQ regular insulin’s 480-minute duration of action. The net result was a decrease in both MGC and GV.

Figure 3.

Type 1 DM patient. G(t) data, glucose concentration versus time, after 6 U of (A) SQ insulin lispro and (B) SQ regular insulin. The time of injection was t = 0 and baseline G(t) was plotted for comparison.

No episodes of hypoglycemia occurred, and as mentioned, SQ insulin lispro decreased the first glucose concentration trough more than SQ regular insulin (by approximately 40 mg/dl).

Type 2 Diabetic Patient Receiving CEN

Figure 4A shows that SQ insulin lispro did not significantly affect the GV for doses up to 4.5 U because the corresponding change in GV curve is nearly flat and close to y = 0. As the dose increased above 4.5 U, the GV began to abruptly increase. SQ regular insulin, however, linearly lowered the GV as its dose increased. Similar to the type 1 diabetic patient, both SQ insulin types decreased MGC in a linear fashion with similar slopes (Figure 4B). This again indicated a linear dose-response curve for both insulin preparations.

Figure 4.

Type 2 DM patient data. (A) Change in GV versus number of SQ insulin units injected. (B) Change in MGC versus number of SQ insulin units injected.

Figure 5 shows the effect of 6 U of SQ insulin lispro and SQ regular insulin after an injection at time t = 0. After the SQ lispro, the first glucose concentration trough was nearly 112 mg/dl, or approximately 15 mg/dl below its baseline value of 127 mg/dl. The first glucose concentration peak, however, “overshot” its preinsulin baseline values causing what we termed “rebound hyperglycemia.” This dynamic first occurred near the 4.5 U insulin lispro dose mark. Furthermore, the glucose concentration peaks and troughs did not return to their baseline values until approximately 350 minutes, or approximately 100 minutes longer than the duration of action of SQ insulin lispro. These responses to SQ lispro explain why the GV first slightly decreased, but subsequently increased, for doses above 4.5 U.

Figure 5.

Type 2 DM patient G(t) data, glucose concentration versus time, after 6 U of (A) SQ insulin lispro and (B) SQ regular insulin. The time of injection was t = 0 and baseline G(t) was plotted for comparison.

The effect of SQ regular insulin on G(t) differed (Figure 5B). In this case, the first 6 glucose concentration peaks were less than their baseline values. In addition, 700 minutes were required for the effects of SQ regular insulin to completely dissipate, which is nearly 200 minutes beyond its duration of action. The net result is a decrease in both the MGC and GV.

Finally, there were no episodes of hypoglycemia. SQ insulin lispro again decreased the first glucose concentration trough more than SQ regular insulin (by approximately 10 mg/dl).

These numerical experiments were repeated with 3 additional type 1 patients and 3 additional type 2 patients whose model parameters were known.¹² Compared to the patient graphs presented above, there were no significant qualitative differences between their changes in MGC and changes in GV graphs (data not shown).

Discussion

To the best of our knowledge, there have been no clinical comparisons of SQ insulin lispro and SQ regular insulin in patients with diabetes receiving continuous nutrition that examined GV. The 3 main findings of this study are that (1) SQ insulin lispro tended to increase GV, (2) SQ regular insulin consistently decreased both MGC and GV, and (3) SQ lispro is more likely to cause hypoglycemia.

GV was chosen as a primary end point because it is associated with negative clinical outcomes.^8,9 Repetitive fluctuations in glucose concentrations produce changes in plasma osmolality that can lead to cellular and organ dysfunction.²⁰ Oxidative stress, produced at higher levels during glucose fluctuations than by sustained hyperglycemia,²¹ may be 1 of the unifying mechanisms underpinning the vasoconstriction, microvascular thrombosis, and inflammation associated with elevated GV.²² Such studies have led some to argue that glucose management protocols should focus on both MGC and GV as treatment targets.^23,24 However, other studies do not agree.²⁵

The insulin analog lispro was developed to out perform SQ regular insulin and improve MGC in DM while also minimizing postprandial hypoglycemia.^10,11 When an otherwise healthy diabetic patient eats a meal, endogenous insulin concentrations spike and follow a narrow bell-shaped curve.²⁶ Clinical²⁷ and computational studies¹⁹ confirm that SQ insulin lispro tends to outperform SQ regular insulin in this clinical setting because of its shorter duration of action. It more closely mimics the body’s response to a food bolus. Diabetic patients who are receiving CEN may have a very different response to short-acting insulin preparations because they are continually postprandial. In these patients, hyperglycemia results from a uniformly amplified glucose ultradian cycle. Therefore, we postulated that the short-acting SQ insulin preparation with the longer duration of action would have a better GV profile and smaller risk of hypoglycemia. Our simulations have confirmed this hypothesis. The frequency of glucose measurements needed to detect an increase in GV is 1 measurement/hour (Figures 3 and 5). Typically, sliding scale SQ insulin therapies sample glucose values every 3-6 hours, which limits their ability to capture these effects. Finally, we noted that “rebound hyperglycemia” occurred only in the type 2 DM patient, suggesting that the glucose-insulin axis in these patients is more prone to increases in GV from changes in exogenous insulin concentrations. It is interesting to note that related numerical studies of critically ill patients with elevated insulin resistance have demonstrated similar results.^28,29

We questioned how short the insulin preparation’s duration of action should be before GV is increased. Two length scales that were present in each simulation were compared: the period of the patient’s ultradian glucose oscillations and the duration of action of the insulin preparation. The period of the ultradian oscillations in glucose represented the time needed by the glucose-insulin feedback system to maintain glucose concentrations within a particular range and variability. When the change in exogenous insulin concentration within this time frame was large, the glucose concentrations fluctuated, and GV increased. In this case, the SQ lispro absorption/concentration profile increased in the first 120 minutes, which was nearly the period of the patient’s ultradian oscillations in glucose concentration. The SQ lispro concentration then decreased to zero over the next 120 minutes, nearly matching the same period. In comparison, SQ regular insulin reaches its maximum over nearly 2 ultradian periods, and almost 3 ultradian periods are required for its concentration to reach zero.^13,19 A similar argument can be made as to why SQ lispro seems more prone to cause hypoglycemia as compared to SQ regular insulin.

Neither SQ lispro nor SQ regular insulin was found to cause hypoglycemia. However, review of the G(t) data for both diabetic patients (Figures 3 and 5) demonstrated that the absolute lowest glucose concentration occurred after SQ insulin lispro, particularly for the type 1 DM patient. In general, SQ regular insulin lowered the glucose concentration peaks more than the glucose concentration troughs. Therefore, it can be expected that hypoglycemia would be more likely to occur after SQ insulin lispro, which is consistent with data from a recent clinical trial.³ Hypoglycemia can also be caused from insulin stacking.³⁰ For the type 1 DM patient, the effects of both insulin preparations were observed to dissipate after a time frame consistent with their duration of actions (Figure 3). In the type 2 diabetic patient, the effects of both insulin preparations persisted slightly beyond their respective duration of actions (Figure 5). This result suggests that type 2 diabetic patients are more likely to develop insulin stacking.

These findings suggest that SQ regular insulin may be the short-acting SQ preparation of choice when used in DM patients who are restricted to CEN, provided that insulin stacking in type 2 diabetics can be avoided. The primary limitation of this study is that it is a validated numerical study of only 8 diabetic patients. Our data should be confirmed by a randomized control study that directly compares SQ insulin lispro and regular insulin in patients with DM receiving CEN before any definitive clinical recommendation can be made. GV should remain a primary end point, which would require continuous glucose monitoring or glucose checks at least every hour for evaluation.³¹

Conclusion

Diabetes and different SQ insulin therapies can be studied using a mathematical model of the glucose-insulin feedback system. This type of study allows for examination of MGC, GV, and hypoglycemia following SQ injections of insulin lispro and regular insulin in patients restricted to CEN.

For the 8 diabetic patients simulated, SQ regular insulin consistently lowered MGC and GV. The inferior performance of SQ insulin lispro in terms of GV and hypoglycemia in patients with both type 1 and type 2 diabetes results from its shorter duration of action. Type 2 diabetic patients appeared more likely to develop insulin stacking due to the lingering effects of both insulin preparations.

Clinical trials are needed to examine whether these numerical results represent the glucose-insulin dynamics that occur in diabetic patients receiving CEN who are treated with short-acting SQ insulin therapies. If such dynamics are present, their effects should be evaluated before a definitive clinical recommendation can be presented.