# Glucose Single- and Multi-point calibrations

Calibration itself is always implemented at a single point in time. If it is a multipoint calibration, then a slope and intercept are determined. If it is a single point, then the intercept is held constant and only the slope is recalculated. Between every point in time where there is a calibration in use the slope and intercept are interpolated as a function of time.

In Review interpolation affects data forwards and backwards in time. During Acquisition it only affects future Data.

Below are 4 examples:

**Multipoint to Single Point**

- Multipoint establishes a slope and intercept. (y = m1*nA + b1)
- Single point establishes a new slope for a constant intercept. (y = m2*nA + b1)
- Between these two points m1 is interpolated to m2 as a function of time. (Same for b1 but since it is constant no change occurs)

**Single Point to Single Point**

- First single point has a slope and intercept calculated based upon rules such that y = m2*nA + b1
- Second single point has a slope and intercept calculated based upon rules such that y= m3*nA + b1
- Between these two points m2 is interpolated to m3 as a function of time. (Same for b1 but since it is constant no change occurs)

**Single Point to Multipoint**

- If no slope and intercept have been previously established then this is the classic example of interpolating backwards.
- Multipoint establishes a slope and intercept. (y = m1*nA + b1)
- PRIOR Single point establishes a new slope for a constant intercept. (y = m0*nA + b1)
- Between these two points m1 is interpolated to m0 as a function of time. (Same for b1 but since it is constant no change occurs)

- If a slope and intercept have been established previously… then
- Single point establishes a new slope for a constant intercept (y = m6*nA + b1) based upon prior calibrations in use
- Multipoint establishes a slope and intercept. (y = m7*nA + b7)
- Between these two points m6 and b1 are interpolated to m7 and b7 as a function of time.

**Multipoint to Multipoint**

- First Multipoint establishes a slope and intercept. (y = m1*nA + b1)
- Second Multipoint establishes a slope and intercept. (y = m2*nA + b2)
- m1 and b1 are interpolated to m2 and b2 as a function of time.

# Examples of interpolation

1. Multipoint to Single - only the slope

2. Single to Single - only the slope

3. Single to Multipoint - slope and intercept

4. Multipoint to Multipoint - slope and intercept

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