Real time modeling of analyte transport in a medium surrounding an implanted sensor to calculate a corresponding concentration of analyte in a distant medium
An analyte monitoring system and method. The analyte monitoring system may include an analyte sensor and a transceiver. The analyte sensor may include an indicator element that exhibits one or more detectable properties based on a concentration of an analyte in proximity to the indicator element. The transceiver may be configured to (i) receive measurement information from the analyte sensor, (ii) calculate the concentration of the analyte in proximity to the indicator element based on at least the received measurement information, and (iii) calculate a blood analyte concentration based on the calculated concentration of the analyte in proximity to the indicator element by (1) incorporating the calculated concentration of the analyte in proximity to the indicator element into a governing equation that models analyte transport over an interval, and (2) solving the governing equation. In some embodiments, the governing equation includes no more than two discrete boundary conditions.
1. An analyte monitoring system comprising:
an analyte sensor including an indicator element that exhibits one or more detectable properties based on a concentration of an analyte in proximity to the indicator element; and
a transceiver configured to (i) receive measurement information from the analyte sensor, (ii) calculate the concentration of the analyte in proximity to the indicator element based on at least the received measurement information, and (iii) calculate a blood analyte concentration based on the calculated concentration of the analyte in proximity to the indicator element by (1) incorporating the calculated concentration of the analyte in proximity to the indicator element into a governing equation that models analyte transport over an interval, and (2) solving the governing equation;
wherein the governing equation includes no more than two discrete boundary conditions, and the interval has a first endpoint at an interface between a bloodstream and surrounding tissue and a second endpoint at the sensor.
2. The analyte monitoring system of claim 1 , wherein the two discrete boundary conditions include (1) a concentration of the analyte at the second endpoint being equal to the calculated concentration of the analyte in proximity to the indicator element, and (2) constant flux of the analyte at the second endpoint.
3. The analyte monitoring system of claim 1 , wherein the governing equation includes a parameter for a maximum attainable diffusivity of the analyte and a diffusivity controlling parameter.
4. The analyte monitoring system of claim 1 , wherein the governing equation relates a rate of change of the concentration of the analyte over time to a diffusivity of the analyte at a given location within the interval.
5. The analyte monitoring system of claim 1 , wherein the transceiver is configured to calculate the blood analyte concentration in real time, based on at least the calculated analyte concentration in proximity to the sensor.
6. The analyte monitoring system of claim 1 , wherein the medium surrounding the sensor is a fibrous capsule.
7. An analyte monitoring system comprising:
an analyte sensor including an indicator element that exhibits one or more detectable properties based on a concentration of an analyte in proximity to the indicator element; and
a transceiver configured to (i) receive measurement information from the analyte sensor, (ii) calculate the concentration of the analyte in proximity to the indicator element based on at least the received measurement information, and (iii) calculate a blood analyte concentration based on the calculated concentration of the analyte in proximity to the indicator element by (1) incorporating the calculated concentration of the analyte in proximity to the indicator element into a governing equation that models analyte transport over an interval, and (2) solving the governing equation;
wherein the governing equation includes no more than two discrete boundary conditions, and the governing equation and the boundary conditions are defined in the Cartesian coordinate system.
8. An analyte monitoring system comprising:
an analyte sensor including an indicator element that exhibits one or more detectable properties based on a concentration of an analyte in proximity to the indicator element and
a transceiver configured to (i) receive measurement information from the analyte sensor, (ii) calculate the concentration of the analyte in proximity to the indicator element based on at least the received measurement information, and (iii) calculate a blood analyte concentration based on the calculated concentration of the analyte in proximity to the indicator element by (1) incorporating the calculated concentration of the analyte in proximity to the indicator element into a governing equation that models analyte transport over an interval, and (2) solving the governing equation;
wherein the governing equation includes no more than two discrete boundary conditions, the governing equation accounts for consumption of the analyte, and the governing equation includes a maximum rate of consumption parameter.
9. The analyte monitoring system of claim 8 , wherein the interval has a first endpoint at an interface between a bloodstream and surrounding tissue and a second endpoint at the sensor.
10. The analyte monitoring system of claim 8 , wherein the governing equation includes a consumption rate controlling parameter.
11. The analyte monitoring system of claim 8 , wherein the governing equation accounts for consumption of the analyte using a Michaelis-Menten equation, and the consumption is defined in the Cartesian coordinate system.
12. An analyte monitoring system comprising:
an analyte sensor including an indicator element that exhibits one or more detectable properties based on a concentration of an analyte in proximity to the indicator element and
a transceiver configured to (i) receive measurement information from the analyte sensor, (ii) calculate the concentration of the analyte in proximity to the indicator element based on at least the received measurement information, and (iii) calculate a blood analyte concentration based on the calculated concentration of the analyte in proximity to the indicator element by (1) incorporating the calculated concentration of the analyte in proximity to the indicator element into a governing equation that models analyte transport over an interval, and (2) solving the governing equation;
wherein the governing equation includes no more than two discrete boundary conditions, and the transceiver is further configured to solve the governing equation numerically using a discretization process followed by a linear algebra process.
13. The analyte monitoring system of claim 12 , wherein the transceiver is configured to perform the discretization process using a finite difference method.