The insulin meter was characterized metrologically (1) in laboratory, through comparison with reference impedance, (2) in vitro, on eggplants, (3) ex vivo, on pigs, and (4) preliminary in vivo, on a human subject, through insulin infiltration.

Laboratory tests

Experimental setup

In laboratory tests, the transducer performance was compared with the 4263B LCR Meter from Agilent Technologies as a reference. As equivalent circuit, a parallel between a capacitor [0.5 nF] and a variable resistor [42–2500 \(\Omega \)] was realized through a 1433-M Decade Resistor and a Standard Capacitor Type 509-F both of General Radio.

Calibration

32 measurements were carried out, for each resistor value, at the frequencies of [100, 120, 10,000, 10,000, 20,000] Hz, with a sine wave amplitude of 100 mV, at a temperature of \({23}^{\circ }\hbox {C}\) and humidity of 50%. Average and standard deviation of the impedance module of the RC loop were assessed, at varying the resistor value linearly within [42, 2500] \(\Omega \).

Results

Figure 3 shows the 1 kHz impedance variation measured by the Agilent and the InsulinMeter in comparison with the nominal values at 1 kHz for an RC loop. The instruments present a compatible trend with the nominal one.

Figure 3

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Impedance magnitude at 1 kHz at varying the resistor value of the RC loop: theoretical trend (continuous line), insulin meter (\(\times \)), and reference LCR Meter (+).

Figure 4

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Dried eggplant drift in 2-(\(\times \)) and 4-wire (\(+\)) configuration (average on 10 measurements).

In-vitro tests

Eggplants were selected for in-vitro tests owing to their recognized capability of emulating the electrical behavior of human skin15,16. In particular, drift, sensitivity, nonlinearity, repeatability, reproducibility and accuracy were assessed. For each metrological characteristic, experimental results of a generic and a personalized model, or 2 and 4-wire measurement are compared. Furthermore, for the parameters of greatest interest, the differences between the two abovementioned set-ups, are also pointed out. The generic model was identified off line on all the samples during the metrological qualification tests. The personalized model was identified on line on the specific subject tissue in the particular measurement conditions. The general model points out the performance of a system applicable to a generic individual independently from the condition of use and the tissue. The personalized model points out the performance of the proposed insulin meter with a personalized model identified in every condition of use.

Experimental setup

Tests were carried out on 29 peeled and dried eggplants to attenuate impedance intrinsic uncertainty arising from water evaporation during measurements (9 on a setup with inter-electrodic distance of 12 mm, and 20 on a setup with a distance of 5 mm). Drying was carried out under the same conditions: 2 h, temperature of 23 °C, and relative humidity of 50%. Each eggplant was cut as a specimen of \(10 \times 4 \times 4\) cm. 12 mm setup: The FIAB PG500 electrodes (\(28 \times 36\) mm) were placed on each specimen, cut lengthwise in half (to obtain four electrodes \(14 \times 36\) mm) and placed at a distance of 12 mm. Measurements were carried out by imposing a sinusoidal voltage amplitude of 20 mV, at a frequency of 1 kHz. Preliminary measurements were carried out for each sample before infiltration, in order to both leave aside the initial value and improve inter-species reproducibility. Lilly’s Humalog pen solution, containing fast-acting insulin (100 UI/ml, where each UI indicates 0.0347 mg of human insulin) was used. Insulin was injected by five consecutive steps of 0.05 ml (thus reaching a total volume of 0.25 ml), at a depth of 8 mm (PIC Insumed31G syringe with G31 \(\times \) 8 mm). 5 mm Setup: The instrument sensitivity was improved by optimizing the setup in order to enhance also as much as possible the usefulness in diagnostic-therapeutic applications. To this aim, the inter-electrode distance, the injection depth, and the amount of insulin were varied. Two electrodes FIAB PG500 (\(28 \times 36\) mm) were cut lengthwise to obtain four electrodes of \(7 \times 36\) mm. The inter-electrodic distance was set at 5 mm and an insulin injection was performed using a 100 U/ml Insulin Pen at a depth of 4 mm. 2 IU (i.e. 20 \(\upmu \)l of insulin solution) were administered for five consecutive injection, reaching a total 10 IU dosage (i.e. 100 μl of solution) in each individual experiment; this experimental setup was chosen to closely reproduce insulin injection technique and doses commonly used in diabetes care. After each injection (12 mm and 5 mm setup), impedance measurements were repeated to reduce uncertainty.

Drift

The four-wire configuration attenuates the impact of electrolytic gels on the measurement drift, a strong impact factor in previous studies10. In Fig. 4, the trends of the progressive penetration of the gel are pointed out for the two and four electrode configurations. In two-wires configuration, the gel progressive penetration into the tissue results in a decrease in contact impedance within 160 min. The four-wires configuration neutralized this effect: The drift is 2.9% (Fig. 4).

Sensitivity

The insulin meter sensitivity was assessed by the slope of the linear model. The average value is equal to 24.7 ml−1 in 12 mm and 497.3ml−1 in 5 mm setup. In particular, for a variation of 1 ml of insulin solution, a corresponding variation of 497.3% is appreciated in percentage impedance with respect to the initial value before the injection. The typical trend of results in eggplant in 5 mm Fig. 5 indicates the percentage change in impedance in relation to the drug quantity. A sensitivity improvement of 20% due to the 4-wire configuration is highlighted10.

Figure 5

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Percentage impedance magnitude variation versus amount of insulin solution in in-vitro experiments in 5 mm setup.

Non-linearity

The non-linearity was determined through one-way ANOVA (ANalysis of VAriance), as the standard deviation of the residuals of the linear model. The typical percentage value (expressed as the average ± 1-σ of the sample mean) for 5 mm is reported in Table 1 for personalized and the generic model. The personalized model exhibits a non-linearity always lower than the generic model.

Table 1 Transducer non-linearity 5 mm.

Repeatability

The 1-σ repeatability of the 12-mm and 5-mm setups was assessed as the percentage variation with respect to the initial impedance value at varying the amount of injected drug. Average percentage values of 0.31% and 1.3% were determined per the 12-mm and the 5 mm setup, respectively. The trend for the former setup is reported in Fig. 6(A).

Figure 6

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1-σ-repeatability versus amount of injected drug in in-vitro (A) and ex-vivo (B) experiments.

Reproducibility

A 1-σinter-individual reproducibility of 0.1% and 0.7% was assessed for the personalized and the generic solution, respectively, for the 12-mm setup. The reproducibility for the optimal setup are 2.4% and 2.7% for the personalized and generic solution, respectively.

Accuracy

In Fig. 7, the RMS of the deterministic error is reported at varying the injected insulin, for both the personalized (+) and the generic model (\(\times \)), in the (A) 12-mm and (B) 5-mm setup, respectively.

Figure 7

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Percentage accuracy of personalized (+) and generic (\(\times \)) model versus amount of insulin, in in-vitro experiments for (A) 12-mm and (B) 5-mm setup.

Ex-vivo tests

According to several studies, the pig has properties very similar to human skin. The permeability of the membrane17, as well as the epidermal thickness and the lipid part, are indicated to be very similar to those of humans18,19. For this reason, ex-vivo tests were carried out on 15 samples of abdominal non-perfused muscle of different pigs, under controlled conditions (\(25^{\circ }\)C, and relative humidity of 50%). All methods were carried out in accordance with relevant guidelines and regulations. All the samples were provided by a local abattoir in compliance with the regulations on products of animal origin intended for human consumption. The experiments were not the cause of the pain, suffering, or death of any animal. The parts have dimensions of of \(7 \times 7 \times 4\) cm, and the surface was treated before each test. The optimal setup was used, by carrying out five consecutive injections of 2 insulin units (IU), corresponding to 20 \(\upmu \)l of insulin solution, at a depth of 4 mm via insulin pen. The resulting metrological characteristics are represented analogously as in eggplant experiments. In Fig. 8, the trend of the percentage variation of the impedance module is reported at varying the injected insulin.

Figure 8

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Typical percentage magnitude variation versus insulin solution in ex-vivo experiments.

Figure 9

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Percentage accuracy of personalized (+) and generic (\(\times \)) model versus amount of drug in ex-vivo experiments.

In Table 2, the sensitivity, the non-linearity, the 1-sigma repeatability, the reproducibility, and the accuracy measured in the pig and in the eggplant tests are reported.

Table 2 Metrological pig abdominal non-perfused muscle characteristics.

For the sake of the comparison, the same setup with inter-electrode distance 5 mm was used. In Figs. 6(B) and 9, the 1-sigma repeatability and percentage accuracy, respectively, are indicated for both the generic and the customized model.

Preliminary in-vivo tests

Some in-vivo tests were carried out in order to validate the proposed transducer on a voluntary human subject affected by type 1 diabetes. The Ethical Review Board of the University of Naples Federico II approved the research. The volunteer is a patient already undergoing diabetic therapy, with fast insulin administered as bolus in suitable amounts 20 min before meals. A commercial injectable solution of insulin Lilly’s Humalog of 100 U/ml, of 3 ml, in a configuration of pre-filled pen, was used. The experiment was carried out by measuring through the Insulin Meter the impedance just during the bolus injection of the patient. The same setup with inter-electrode distance 5 mm and injection depth 4 mm was used. Insulin was administered at successive steps of 0.02 up to the final amount of the patient therapeutic value of 0.10 ml (Fig. 10). For each administration step, the impedance was measured, according to the protocol established in in-vitro and ex-vivo tests. In Fig. 11, the typical results of the experiment are reported. A monotonous increasing trend is inferred, and an instrument sensitivity capable of appreciating the insulin variations typical of clinical practice. The linear model is proved to be useful also on human subjects, as well as optimal to describe the trend of the phenomenon already identified in in-vitro and ex-vivo tests.

After the first measurement session (Table 3, first row), the instrument was upgraded by optimizing the following parameters: (1) applied voltage, increased up to the limits allowed by the safety thresholds, and (2) impedance of the cables connection and contacts.

Then, further tests were carried out on the same subject over 2 months, up to a total of 300 measurements (namely, 50 for each daily session). 1-sigma repeatability was decreased by an order of magnitude on average with respect to the first session of tests (Table 3, last column). Among other advantages, the increase in repeatability allowed to double the resolution of the steps of the measured quantity (from 2 to 1 IU per step). The experiments confirmed the well-known problem of reproducibility for bio-impedance measurements20, also at intra-individual level, mainly due to changes in the skin moisture21. During the six measurement sessions, the subject exhibited impedance values with an uncertainty band of 42 \(\Omega \) compared to an average of 157 \(\Omega \). This variability in the initial impedance does not arise from the different frequency values of the stimulus signal. Even with the same applied frequency, the differences between the test sessions are significant. In the different measurement sessions, also sensitivity exhibits poor reproducibility: average of 98 ml\(^{- 1} \) and uncertainty band of 80 ml\(^{- 1} \).

The proposed method proved to be relevant in managing the impact of inter- and intra–individual reproducibility. The method allows the insulin emergence model to be built at each administration. Thus, the uncertainty is reduced to the sole contribution of the measurement non-repeatability. The optimized version of the proposed micro-transducer guarantees an average percentage of 1-\( \ sigma \) repeatability lower than 0.5%. Even considering the worst-case sensitivity of 47 ml\(^{- 1} \), if a bolus is administered (typically with a value of 10 IU), a significant variation of to 4.7% of the initial impedance, or 10 times greater than the 1-sigma repeatability, can be appreciated.

Figure 10

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Insulin injection during in-vivo experiments.

Figure 11

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Typical percentage magnitude variation versus insulin solution in in-vivo experiment.

Table 3 In vivo experimental results.

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