Reliability of Automated Insulin Reliability of Automated Insulin PumpsPumps

Medtronic Mini-Med Medtronic Mini-Med Paradigm®Paradigm®

DSES-6070 HV7DSES-6070 HV7Statistical Methods for Reliability EngineeringStatistical Methods for Reliability Engineering

Professor Ernesto Gutierrez-MiraveteProfessor Ernesto Gutierrez-MiraveteRensselaer Polytechnic InstituteRensselaer Polytechnic Institute

Monique ParisiMonique ParisiDecember 4, 2008December 4, 2008

BackgroundBackground• Type I diabetics have an autoimmune disease in which the immune system attacks the beta cells in the pancreas that produces insulin.

• The result of the body not being able to produce its own insulin disables the body to break down the sugar in the blood which the body produces over the course of the day. Therefore, a Type I diabetic becomes insulin dependent for the rest of their lives.

• It is critical for individuals with this condition to monitor and treat the lack of pancreatic behavior in order to decrease the probability of future health problems (kidney failure, blindness, circulation issues and heart disease).

• The objective of this term project is to investigate the reliability of automated insulin pump systems and determine what the critical failure mode is through using quantitative and computer based reliability functions.

ObjectiveObjective

System System • There are 3 main steps in the process:

1. The ability to accurately measure the body’s glucose level

2. The ability to compute the amount of insulin required to bring the blood sugar level within a target range (in this case study that is 100mg/dL)

• 1 unit of insulin / 4 carbohydrates consumed

3. The actual mechanical transfer of insulin from the pump to the blood stream.

Test blood sugar level

Stable

Falling

Unsafe

Do not inject

insulin

Warn the user

Input into Pump Controller

Retrieve insulin from

reservoir

Deliver insulin via catheter

Re-measure sugar level

Calculate dosage

(As applicable)

•The diagram above illustrates the behavior one would expect to occur during a diabetic’s day (tests 8-10 x daily).

Pump Functionality

Methodology Methodology • Minitab & Excel were used simultaneously to analyze the quantitative data as well as determine the distribution of the data.

• Maple was used to illustrate the mathematical reliability expressions, Cumulative Failure Probability Distribution Function –F, Reliability/Survival Function –R, Failure Probability Density Function –f, Hazard / Failure Rate Function –z and the Mean Time To Failure Function –MTTF.

• A Monte Carlo simulation was run to substantiate the reliability of the insulin pump and compared against the outputs from both Minitab and Maple.

Results/Discussion Results/Discussion Gathered 1 months worth of data from a Type I diabetic (Feb 23, 2008 – March 24,2008)

• Averaged the total day’s Glucose Level (140 mg/dL)& Carbohydrate intake (44 g)• Counted the # of times in a day an “Expected” shot & a “Correction” shot was taken.

6420

12

10

8

6

4

2

0

Total No of Correction Shots

Frequency

Mean 2.839StDev 1.675N 31

Total # of Daily Correction BolusNormal

A histogram of the Total # of Correction Bolus’s taken by the diabetic in a 1 month timeframe revealed:

• Mean = 2.8 corrections/day

Insulin shoot brings your level down

Food intake brings your level up

Results/DiscussionResults/Discussion• Established Start & End times based on the number of hours in a day for 31 days.

• 31 days = 744 hours

• The calculated MTTF = 396.273• Compare to Minitab =394.897

Results/DiscussionResults/DiscussionTo determine the distribution of the data, the Anderson Darling statistic was used:

• Distribution ID Plot• Weibull distribution is the best fit with an AD Statistic = 0.914

The probability plot of the Weibull distribution of the Total # of Correction Bolus’s taken daily results in:

• Shape = 1.923• Scale = 445.185• Mean = 394.897

1000100

90

50

10

1

Start

Perc

ent

1000100

99

90

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Perc

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100010010

90

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Start

Perc

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1000100

99

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Perc

ent

Weibull0.914

Lognormal1.273

Exponential2.852

Loglogistic0.961

Anderson-Darling (adj)

Probability Plot for StartML Estimates-Arbitrary Censoring

Weibull Lognormal

Exponential Loglogistic

100010010

99

90

8070605040

30

20

10

5

3

2

1

Start

Perc

ent

Shape 1.92297Scale 445.185Mean 394.897StDev 213.856Median 367.930IQR 294.711AD* 0.914

Table of Statistics

Probability Plot for Start

Arbitrary Censoring - ML EstimatesWeibull - 95% CI

10005000

0.0015

0.0010

0.0005

0.0000

Start

PD

F

1000100

90

50

10

1

StartP

erc

ent

10005000

100

50

0

Start

Perc

ent

10005000

0.0075

0.0050

0.0025

0.0000

Start

Rate

Shape 1.92297Scale 445.185Mean 394.897StDev 213.856Median 367.930IQR 294.711AD* 0.914

Table of StatisticsProbability Density Function

Survival Function Hazard Function

Distribution Overview Plot for StartML Estimates-Arbitrary Censoring

Weibull

Reliability FunctionsReliability FunctionsCumulative Failure Probability Distribution FunctionF = 1 - exp [ - (t / a)^b]

• a = scale parameter• b = shape parameter

Reliability Function (Survival)

Failure Probability Density Function Hazard / Failure Rate Function

Monte Carlo Simulation Monte Carlo Simulation The Monte Carlo Simulation validates the system analysis in Minitab and Maple.

The Weibull distribution generated a Mean Failure of 442.96 hours.

Conclusion Conclusion • Determined the critical failure mode of the automated insulin pump system is based on the number of correction bolus’s a patient needs to administer in a given day.

• Example:• Measure glucose level @ 280 mg/dL• Target level is 100 mg/dL

• 280 – 100 = 180 mg/dL over target•Correction: 1 unit of insulin / 30 mg/dL over 6 units

• This would be counted as a Failure to the system

• Found that a Weibull distribution fit the data set best.

• MTTF of the automated insulin pump for this individual is 395 hours.

• Overall, the system is as reliable as the individual is administering it. • As long as the user enters in the correct # of carbohydrates, the pump will calculated the # of units required. • The pump will measure the glucose level accurately, however, if there was a mistake in the initial input of carbohydrates, than the outcome of the newly measured level will more than likely deviate from the set target.

Back-upBack-up

SystemSystem

Needle Assembly

Pump Clock

Sensor Controller Alarm

Visual Display

Insulin Reservoir

• The flow chart below is the typical components of an automated insulin pump.

• Reservoir = Holds/stores insulin (3 mL) – New one every time user sets up the pump system.• Vile of insulin = Holds/stores insulin (10 mL) – able to use for 3 refills 300 units of insulin = 3 mL• During the refill process, user makes sure there is no air bubbles in the reservoir.• Paradigm Quick Set = In which the reservoir attaches to.• User “Rewinds” Pump setting.• Take the Reservoir and the Paradigm Quick Set and insert it into the insulin pump. (pump has life span of ~ 2 years)• Prime the tube with the insulin stored inside the reservoir – usually takes 12 units of insulin to prime and remove air bubbles within the tubing.• Quick Serter = Attach the other end of Paradigm Quick Set into serter. Remove paper seal. Set springs by pulling serter end down. To inject, press both side tabs on serter.• The needle is inserted & user pulls the Paradigm Quick Set needle out, leaving only the cannula.• Once cannula is in the body, user “Fix Prime” the pump which will automatically send 0.5 units of Insulin into the body to ensure the assembly is attached correctly and the user is receiving the units.

Novolg Insulin lasts in system

for ~3 hours

&

Peaks at ~2 hours