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The desire to deliver measured amount of insulin continuously to patients with type I diabetes, for glycemic control, has attracted a lot of attention. Continuous subcutaneous insulin infusion has seen some success in recent years. However, occlusion of insulin delivery may prevent the patient from receiving the prescribed dosage, with adverse consequence. An <i>in vitro</i> study of insulin delivery is performed, using different insulin pumps, insulin analogs and operating conditions. The aim is to identify incidences of occlusion due to bubble formation in the infusion line. A detailed statistical analysis was performed on the data collected to determine any significant differences and deviations in insulin delivery rates that might be due to factors such as: pump type, the set basal flow rate, insulin type, vibration, and possible insulin occlusion due to air bubble formation within the infusion line. Our findings from the Graeco-Latin Square design model show that there are statistical differences due to the devices, and statistical identifiable clusters are used to distinguish the devices. Such hierarchical models used to describe the analyses, include the flow rate, the pump types, and the activity level.

Type 1 diabetes affects about 1 in 400 children under the age of 18 years. Continuous subcutaneous insulin infusion (CSII), also known as insulin pump therapy, is now commonplace [

The present paper reports on a parametric in vitro study, performed to simulate CSII under varying conditions of pump type, basal dosage rate, activity level, etc. Although this controlled laboratory study does not use real test subjects and therefore cannot address effects of possible insulin occlusion due to physiological interactions between insulin, infusion set and the patient, other more basic factors are investigated. The paper is organized as follows. In Section 2, the nature of the data is discussed, and a need for data model characterization is presented. Section 3 specifies the model for Graeco-Latin Square and its use for statistical inference. Our proposed approach is based on practicality and is pragmatic, seeking to identify differences based on the devices. The effects of the selected factors are studied. In Section 4, the results are presented. Section 5 contains a brief summary.

The experimental setup is designed to reproduce typical operating conditions for CSII.

Since the pump is usually close to the patient’s body, the model can assume that temperature is fixed. So a single temperature setting will be used to obtain information, and data will be used in conjunction with this to determine significant difference between the values of the dependent variables.

Given a fixed time periods, the parameters can be estimated by the maximum likelihood method. The issue is that in most applications, the Gaussian mixtures formalize the shape of the flow distribution. However, the significant difference between the insulin types, the types of pumps, the activity levels are not known, and little to no data on them has been recorded.

The desired basal rate is set and each experiment is run for 5 day duration (hereafter denoted as week), as is commonly used in CSII therapy. Volume flow rates of insulin through the CSII infusion sets are measured with Sensirion SLG1430-480 flow meters and recorded on a computer every 0.64 second, along with pump temperatures and total mass of insulin deposited in bottles placed on analytical balances (Sartorius TE-64) with sensitivity of 0.0001 g. The overall total volume of insulin, which has been pumped over a particular period, is obtained by integrating the recorded flow meter readings. This can then be compared, after multiplying with insulin density, to the recorded analytical balance reading. Thus, the flow meters indicate instantaneous flow rate, whereas the scales record cumulative flow. There is considerable lag in the times both instruments record the flow, since at the very low flow rates it may take several hours for insulin to traverse the length of the infusion line, from the Sensiron flow meter to the collection bottle on the scale. However, as shown in

than operate continuously, insulin pumps move the fluid pulsatingly. Demuren and Doane (2007) [

Four different models of insulin pumps are investigated, namely, the Paradigm M511, Paradigm M712, and Animas IR-1200. By design, the pumps operate intermittently at a frequency, which depends on the set basal rate. For example, the Paradigm M511 delivers 0.1 U per actuation in the basal dosage mode. At a basal rate of 0.1 U/hr, the pump would be actuated once per hour, at 0.3 U/hr three times per hour, at 1.0 U/hr ten times per hour, and so on. The pumps are connected to the flow meters and collection bottles, placed on the analytical balances, via two types of infusion sets, namely, the Sof-Set (0.48 mm i.d.) and the Quick Set (0.36 mm i.d.). These are standard infusion sets used in practice, and have lengths of between 20 and 40 cm. The catheter, at the end of the infusion set, is sealed to the collection bottle to prevent any evaporation over the five day period of the experiments. The three types of insulin used in this study: Apidra (glulisine), Humalog (lispro), and Novolog (aspart), are rapid acting insulin analogs in common use [

The Sensirion flow meter can measure a maximum flow rate of 40,000 nl/min (240 U/hr) with a resolution of 7 nl/min (0.042 U/hr) and a repeatability of 0.6% of the measured value. The flow meter is very sensitive to environmental conditions and must be recalibrated frequently. For this purpose, the Harvard PHD 2000 Programmable calibration apparatus was utilized. The calibration is performed to ensure that the Sensiron flow meter can accurately record flow rates in the range between 1 U/hr and 120 U/hr.

The objective of this study is to assess and compare the performance of the insulin delivery based on the type of pumps, the level of activity characterized by the intensity of vibration, the insulin type, and the flow rate level. The study of interaction will assess the understanding of the structure and modeled insulin delivery. The simulations are carried out to illustrate the behavior of the process. Since each of the experiments takes five days to run, the number of replicates is typically small, and would lead to low statistical power and large variance estimates [

In so doing, we aim for simulation, optimization and prediction under a sound experimental design. We propose a four-way Graeco-Latin squares design. The analysis provides a theoretical basis for the comparison of flow rates, insulin types (Humolog, Apidra, Novolog), pump types (M511-#1, M511-#2, M511-#3, M712, Animas), vibrations, and flow meters (line 1, 2 or 3) without ignoring noise dependence. The flow rates are set on low to 0.1 U/hr, medium to 0.3 U/hr, and high to 1.0 U/hr. The vibration levels are set on low to 0, medium to 100 and high to 200 RPM. The design is chosen in such a way that test of the difference between factors can be made without having to run each of the 34 = 81 cases individually [

To formulate the problem, the standard linear equation model for a Graeco-Latin Square design without interaction effects is as follows:

Line 1 | Line 2 | Line 3 | ||
---|---|---|---|---|

Week 1 | Flow rate | 0.1 U/hr | 0.3 U/hr | 1.0 U/hr |

2 runs | Insulin | Humalog | Apidra | Apidra |

Pump | M511-#1 | M511-#2 | Animas | |

Vibration | Vib1 (0 RPM) | Vib1 (0 RPM) | Vib1 (0 RPM) | |

Week 2 | Flow rate | 0.1 U/hr | 0.3 U/hr | 1.0 U/hr |

2 runs | Insulin | Novolog | Apidra | Novolog |

Pump | Animas | M511-#1 | M511-#3 | |

Vibration | Vib2 (100 RPM) | Vib2 (100 RPM) | Vib2 (100 RPM) | |

Week 3 | Flow rate | 0.3 U/hr | 0.3 U/hr | 1.0 U/hr |

2 runs | Insulin | Humalog | Humalog | Novolog |

Pump | M511-#3 | Animas | M511-#1 | |

Vibration | Vib3 (200 RPM) | Vib3 (200 RPM) | Vib3 (200 RPM) | |

Week 4 | Flow rate | 0.3 U/hr | 0.1 U/hr | 0.3 U/hr |

2 runs | Insulin | Apidra | Apidra | Novolog |

Pump | M511-#2 | M511-#3 | M712 | |

Vibration | Vib1 (0 RPM) | Vib1 (0 RPM) | Vib1 (0 RPM) | |

Week 5 | Flow rate | 0.1 U/hr | 0.3 U/hr | 1.0 U/hr |

2 runs | Insulin | Apidra | Novolog | Humalog |

Pump | M712 | M511-#3 | M712 | |

Vibration | Vib3 (200 RPM) | Vib2 (100 RPM) | Vib2 (100 RPM) |

where ^{th} flow rate, the j^{th} insulin type, the k^{th} pump type, and the l^{th} vibration level, μ is the overall mean,

As usual, the effects are subject to the restriction that:,

rors are independent

Flow data of the insulin delivery can provide important information about the differences in the insulin types, pump types, and dynamic circuitries. These counts are correlated and over disperse. There is no straightforward method of collecting such data than setting up the calibration before each experiment. In fact, the Graeco-Latin square design turns out to be the most suitable for this experiment with three levels of the flow rate, pump types, vibration level. It is at the cornerstone for evaluating new interventions and will allow us to solve challenging clinical trial set up [

The data represent thousands of values of time and flow quantities recorded over a period of five days. Experimentations are one way of obtaining and analyzing data for such issues. Typical experimental data, collected for one of the runs, are shown in

All model analyses under Equation (1) are performed several times due to the weekly data collected, and compressed using SAS® 9.2 on the 10 week experiments. Under the general linear model framework, the general class described in (1) was fitted. The analysis investigates first the effects of measurement errors on the estimations of the parameters of interest such as mean and variance. Ignoring measurement error can lead to inconsistent estimators. In that sense, we proposed a bias reduction by calibrating the instruments. A check of the normality of the data is not in our cases valid option. The insulin is delivered by influx in selected time periods. The data does not follow normal assumption settings. Nevertheless, it must be decreasing before another influx of insulin is delivered. Our first analysis showed that the delivery was not equally spread and consistent, and this causes attenuation in the estimators. This behavior is typical in all the instruments, and called attention for calibration. When a “gold” standard is available, a validation study can then be performed, and design of analysis can be used to test assumptions of data and significant difference among the factors.

The estimates of the parameters of the model of Equation (1) based on a sample of 1609 observation values are reported in

The overall analysis of the model Equation (1) shows that all the effects are significant and must be entered in the model. So, the full model is significant. From

Experiments were performed at three chosen levels of flow rate: 0.1, 0.3 and at 1.0 (U/hr). It was expected that

Overall mean | Flow rate | Insulin types | Pump Types | Vibration level |
---|---|---|---|---|

Source | Degree of Freedom | Type I Sum of Squares | Mean Sum of Squares | F Value | P-values |
---|---|---|---|---|---|

Insulin | 2 | 21.356 | 10.678 | 191.87 | <0.01 |

Flow rate | 2 | 120.986 | 60.493 | 1086.96 | <0.01 |

Pump type | 2 | 5.014 | 2.507 | 45.05 | <0.01 |

Vibration | 2 | 4.185 | 2.092 | 37.60 | <0.01 |

lower flow rates will lead to lower insulin delivery, and that is exactly what was observed in the data as summarized in

The panel plot of the flow rates 0.1, 0.3 and 1.0 for the insulin types is shown in

Design Flow rate (U/hr) | Insulin Type | Measured Flow rate (U/hr) | Standard Deviation (U/hr) |
---|---|---|---|

0.1 | Apidra | 0.155 | 0.026 |

Humalog | 0.115 | 0.030 | |

Novolog | 0.133 | 0.014 | |

0.3 | Apidra | 0.274 | 0.348 |

Humalog | 0.278 | 0.324 | |

Novolog | 0.374 | 0.018 | |

1.0 | Apidra | 0.553 | 0.085 |

Humalog | 0.100 | 0.028 | |

Novolog | 0.915 | 0.248 |

Three insulin types that were utilized; namely Humalog, Novolog and Apidra. The results of the measured flow rates for each of the insulin types are summarized in

There were three types of pumps: M511, M712, and Animas. Three pumps of type M511 were utilized, we call them M511-#1, M511-#2, and M511-#3. Each pump was used three times or more except for M511-#2 (2 times).

Animas has been used three times on week 1 through week 3. It has been very consistent in its measured flow rates and means except on week 3, where the vibration level used was 200 RPM.

Pump type | Mean | Standard deviation |
---|---|---|

M712 | 0.701 | 0.314 |

Animas | 0.318 | 0.306 |

M511 | 0.409 | 0.401 |

Pump type M712 has been used at all levels of flow rate, and at different vibration levels. It has shown consistency in its results. The standard deviations recorded were quite reasonable. One thing to notice is that the high vibration was set at lower flow rate. This is a suggestive idea as to minimize variation in the flow for pump type M712, making it fit more accurately to the patient’s need.

The effects of the vibration level on measured flow rates are shown in

The analysis of insulin delivery in CSII has been shown to be a very challenging task. Many factors have to be taken into account.

Firstly, the analysis cannot be performed on just one variable, whilst ignoring the others. The flow rate behaves differently depending on the insulin type, and vice-versa. The flow rate of 0.1 U/hr were found to be the most consistent in terms of the corresponding standard deviations. In fact, the experiments in week 2, which are

Vibration | Mean measured flow rate | Standard deviation |
---|---|---|

0 | 0.280 | 0.297 |

100 | 0.564 | 0.392 |

200 | 0.516 | 0.430 |

at low flow rate with medium vibration, yielded the smallest standard deviation. So pump type M511 operates as expected with low flow rate and no vibration. It also appears that the pump types M511 and M712 perform better with Humalog. The vibration could be another factor to be considered with Humalog, as Humalog with vibration at level 3 yielded the most variation in insulin delivery.

Secondly, the insulin type used is an important factor as Apidra usage in weeks 4, and 5 gave higher mean value of insulin, whereas Novolog appeared to be the most stable, with the smallest associated variation. Another potential bias is the selection of pump type: pump type M712 has higher return of insulin than Animas and M511: further experiments are need for the comparison between Animas and M511.

Comparing the data from week 1 flow 1, and week 2 flow 1, we find that there is significant difference in insulin delivery due to insulin type, or pump type, or vibration or any combinations of those 3. Apridra yields higher flow than Novolog, and finally Humalog.

We assumed that there is no significant difference in the pumps types M511. However, comparing the data obtained from week 4 in their first two experiments, a test of trend with respect to flow rate should be performed. If the assumption of no trend with flow rate is to be rejected, one should consider the parameters in analyzing the pumps of type M-511. Moreover, instead of flow rate, a further study could be done to check that assumption, taking into account the insulin types: Humalog, Apidra or Novolog. The higher vibration level with the use of M712 leads to higher volume of insulin than the lower vibration level and the use of M511.

In summary, the higher the preset flow rate, the higher the delivered insulin volume. At low flow rate and low variation level, Humalog is recommended. Similarly, at low flow rate and high vibration level, Apidra is recommended. Novolog works significantly well at low vibration level, but for high flow rate or medium/high vibration, it is not recommended.

Insulin delivery via CSII is a complex task in which the quality and reliability of the system must be tested with a model including different parameters, such as pump type, insulin type, activity level, etc. Because of that, the simple regression model will not be adequate. In this study, we were interested in the discriminations between components of the insulin delivery hypothesis using a linear response function, after careful selection of the experimental design and characteristic components. The design has allowed us to minimize the total variation and the number of experimental simulation runs to consider while keeping all significant factors. Several model combinations of factors have been studied. Our research has shown that the insulin delivery in infants is subjected to several factors such as pump types, flow rate, insulin types. It is apparent that either frequent recalibration of the flow meters is necessary or a process for correcting “off-calibration” Sensirion flow rate data needs to be developed. All flow meters showed signs of calibration shifts to occur to some degree. The most relevant elements of our simulated study are the following:

1) If one aims to control the insulin delivery at low levels of flow rate and vibration, then the insulin types Apidra and Novolog should be used. High vibration level may be detrimental in the CSII delivery regardless of the insulin types. At low levels of flow rates and vibration, the pump type Animas gives a better control of the insulin delivery.

2) At high vibration level, Novolog and Humologare are preferred to Apidra.

Other factors such as bubble formation should also be considered in more details in future studies. The number of replicates could be an issue in this report as the power analysis would lead to better predictions. The statistical computations show that the process is affected by insulin and pump types, vibration level and flow rates.

The authors are very grateful for support from the Department of Pediatrics at East Virginia Medical School and the Office of Research at Old Dominion University.

Norou Diawara,Ayodeji Demuren,Eric Gyuricsko, (2016) Impairment of Continuous Insulin Delivery Therapy and Analysis from Graeco-Latin Square Design Model. Journal of Biosciences and Medicines,04,40-51. doi: 10.4236/jbm.2016.48006