Method and device for monitoring analyte concentration by determining its progression in the living body of a human or animal
View Patent ↗The present invention generally relates to a method and a device for monitoring an analyte concentration in the living body of a human or animal. In particular to a method and device for determining analyte values y(t n ) correlating with the concentration to be determined are determined for consecutive points in time t n . The analyte values y(t n ) is used to predict a prediction value for an analyte y(t n0 +Δt) over a prediction period Δt.
1. A device for continuous monitoring of an analyte concentration by determining its progression in the living body of a human or animal, comprising:
a measuring unit configured to produce a measurement signal that is indicative of a concentration of the analyte, and
an analytical unit configured to correlate analyte values y(t n ) with the concentration of the analyte for consecutive points in time t n based on the measurement signal, the analytical unit further configured to determine a function F(t k , t k-Δn , t k-2Δn , . . . , t k-(m-2) Δn , t k-(m-1) Δn ), which depends on corresponding analyte values y(t k ), y(t k-Δn ), y(t k-2 Δn ), . . . , y(t k-(m-2) Δn ), y(t k-(m-1) Δn ), and which approximates the progression of the analyte values y(t n ) at time t n0 in a vicinity U of an analyte value y(t n0 ) with a pre-determined accuracy σ, such that
σ
2
≥
∑
t
k
∈
U
[
y
(
t
k
)
-
F
(
t
k
-
Δ
t
,
t
k
-
Δ
n
-
Δ
t
,
t
k
-
2
Δ
n
-
Δ
t
,
…
t
(
k
-
(
m
-
2
)
Δ
n
)
-
Δ
t
,
t
(
k
-
(
m
-
1
)
Δ
n
)
-
Δ
t
)
]
wherein Δn is an integer, and to calculate a prediction value y(t n0 +Δt) for an analyte value over a prediction period Δt using the following equation:
y ( t n0 +Δt )= F ( t n0 , t n0-Δn , . . . , t( n0-(m-2)Δn) , t (n0-(m-1)Δn) ).
2. The device according to claim 1 , wherein the analytical unit is configured to determine the function F in a manner that depends not only on the analyte values y(t k ), y(t k-Δn ), y(t k-2Δn ), . . . , y(t k-(m-2) Δn ), y(t k-(m-1) Δn ), but in addition on their first time derivatives.
3. The device according to claim 1 , wherein the analytical unit is configured to determine the function F in a manner that depends not only on the analyte values y(t k ), y(t k-Δn ), y(t k-2Δn ), . . . , y(t k-(m-2) Δn ), y(t k-(m-1) Δn ), but in addition on their first and second time derivatives.
4. The device according to claim 1 , wherein the analytical unit is configured to include linear or square terms in the function F.
5. The device according to claim 1 , wherein the analytical unit is configured to determine the function F as a linear function.
6. The device according to claim 1 , wherein the analytical unit is configured to represent the function F by coefficients a 0 to a m as follows:
F
=
a
0
+
∑
j
=
1
m
y
(
t
(
k
-
(
m
-
j
)
Δ
n
)
)
a
j
.
7. The device according to claim 6 , wherein the analytical unit is configured to determine the coefficients, a 0 to a m , by minimizing the sum
∑
t
k
∈
U
[
y
(
t
k
)
-
a
0
-
∑
i
=
1
m
y
(
t
(
k
-
(
m
-
1
)
Δ
n
)
-
Δ
t
)
a
i
]
.
8. The device according to claim 6 , wherein the analytical unit is configured to determine the coefficients, a 0 to a m , by solving a system of linear equations which contains one equation each of the type
y
(
t
k
)
=
a
0
+
∑
j
=
1
m
y
(
t
(
k
-
(
m
-
j
)
Δ
n
)
-
Δ
t
)
a
j
for at least m+1 different analyte values y(t k ) from the vicinity U of the point in time t n0 .
9. The device according to claim 8 , wherein the analytical unit is configured to determine the coefficients a 0 to a m by numerically solving the system of linear equations,
and wherein the system of linear equations contains more than m+1 equations.
10. The device according to claim 6 , wherein the analytical unit is configured to determine the function F with the coefficients a 0 to a m ranging in number between 4 and 11.
11. The device according to claim 10 , wherein the analytical unit is configured to determine the function F with the coefficients a 0 to a m ranging in number between 6 and 9.
12. The device according to claim 1 , wherein the analytical unit is configured to obtain the analyte values y(t n ) used to determine the function F by numerical processing of measured values.
13. The device according to claim 12 wherein the analytical unit is configured to filter the measured values in the numerical processing of the measured values.
14. The device according to claim 1 wherein the analytical unit is further configured to define the function F(t k , t k-Δn , t k-2Δn , . . . , t k-(m-2) Δn , t k-(m-1)Δn ) in a vicinity U of an analyte value y(t n0 +Δt) at a point in time t n =t n0 +Δt for a calculated prediction value y(t n0 +Δt), such that the defined function F approximates the progression of analyte values y(t n ) in the vicinity U with a predetermined accuracy and an additional prediction value y(t n0 +2Δt) is calculated therefrom.
15. The device according to claim 1 , wherein the analytical unit is configured to determine the analyte values y(t n ), that are used calculate the prediction value, from consecutive points in time t n which are separated by predefined time intervals.
16. The device according to claim 15 , wherein the analytical unit is configured to determine the analytical values y(t n ) from consecutive points in time t n that are separated by predefined time intervals within the range of 30 seconds to 5 minutes.
17. The device according to claim 16 , wherein the analytical unit is configured to determine the analytical values y(t n ) from consecutive points in time t n that are separated by predefined time intervals within the range of 1 to 3 minutes.
18. The device according to claim 1 , wherein the analytical unit is configured to determine the analyte values y(t n ), that are used to calculate the prediction value or one of the prediction values, for times t n which are separated by an interval corresponding to the prediction period Δt.
19. The device according to claim 1 , wherein the analytical unit is further configured to determine the function F as a function of transformed coordinate values Ty(t k ), Ty(t k-Δn ), Ty(t k-2Δn ), . . . , Ty(t k-(m-2)Δn ), Ty(t k-(m-1)Δn ), which transformed coordinate values are determined by a transformation from analyte values y(t k ), y(t k-Δn ), y(t k-2Δn ), . . . , y(t k-(m-2) Δn ), y(t k-(m-1) Δn ) in which at least one of the values Ty(t k ), Ty(t k-Δn ), Ty(t k-2Δn ), . . . , Ty(t k-(m-2) Δn ), Ty(t k-(m-1) Δn ) has a negligible influence on the function F at the predetermined accuracy σ.
20. The device according to claim 19 , wherein the analytical unit is configured to determine the transformed coordinate values using a linear transformation.
21. A method for continuous monitoring of an analyte concentration by determining its progression in the living body of a human or animal, comprising:
receiving a measurement signal produced by a measuring unit that is indicative of a concentration of the analyte,
determining analyte values y(t n ) correlating with the concentration of the analyte for consecutive points in time t n based on the measurement signal,
determining a function F(t k , t k-Δn , t k-2Δn , . . . , t k-(m-2) Δn , t k-(m-1) Δn ), which depends on corresponding analyte values y(t k ), y(t k-Δn ), y(t k-2Δn ), . . . , y(t k-(m-2) Δn ), y(t k-(m-1) Δn ), and which approximates the progression of the analyte values y(t n ) at time t n0 in a vicinity U of an analyte value y(t n0 ) with a pre-determined accuracy σ, such that
σ
2
≥
∑
t
k
∈
U
[
y
(
t
k
)
-
F
(
t
k
-
Δ
t
,
t
k
-
Δ
n
-
Δ
t
,
t
k
-
2
Δ
n
-
Δ
t
,
…
t
(
k
-
(
m
-
2
)
Δ
n
)
-
Δ
t
,
t
(
k
-
(
m
-
1
)
Δ
n
)
-
Δ
t
)
]
2
whereby Δn is an integer, and
calculating a prediction value y(t n0 +Δt) for an analyte value over a prediction period Δt using the following equation:
y ( t n0 +Δt )= F ( t n0 , t n0-Δn , . . . , t (n0-(m-2)Δn) , t (n0-(m-1)Δn) ).
22. The method according to claim 21 , wherein the function F depends not only on analyte values y(t k ), y(t k-Δn ), y(t k-2Δn ), . . . , y(t k-(m-2)Δn ), y(t k-(m-1) Δn ), but in addition on their first time derivatives.
23. The method according to claim 21 , wherein the function F depends not only on analyte values y(t k ), y(t k-Δn ), y(t k-2Δn ), . . . , y(t k-(m-2)Δn ), y(t k-(m-1) Δn ), but in addition on their first and second time derivatives.
24. The method according to claim 21 , wherein the function F contains linear or square terms.
25. The method according to claim 21 , wherein the function F is a linear function.
26. The method according to claim 21 , wherein the function F is represented by coefficients a 0 to a m as follows:
F
=
a
0
+
∑
j
=
1
m
y
(
t
(
k
-
(
m
-
j
)
Δ
n
)
)
a
j
.
27. The method according to claim 26 , wherein the coefficients, a 0 to a m , are determined by minimizing the sum
∑
t
k
∈
U
[
y
(
t
k
)
-
a
0
-
∑
i
=
1
m
y
(
t
(
k
-
(
m
-
i
)
Δ
n
)
-
Δ
t
)
a
i
]
.
28. The method according to claim 26 , wherein the coefficients, a 0 to a m , are determined by solving a system of linear equations which contains one equation each of the type
y
(
t
k
)
=
a
0
+
∑
j
=
1
m
y
(
t
(
k
-
(
m
-
j
)
Δ
n
)
-
Δ
t
)
a
j
for at least m+1 different analyte values y(t k ) from the vicinity U of the point in time t n0 .
29. The method according to claim 28 , wherein the system of equations contains more than m+1 equations and is solved numerically by approximation to determine the coefficients a 0 to a m .
30. The method according to claim 21 , wherein the analyte values y(t n ) used to determine the function F are obtained by numerical processing of measured values.
31. The method according to claim 30 wherein the numerical processing of measured values includes filtering the measured values.
32. The method according to claim 21 further comprising configuring the function F(t k , t k-Δn , t k-2Δn , . . . , t k-(m-2) Δn , t k-(m-1) Δn ) in a vicinity U of an analyte value y(t n0 +Δt) at a point in time t n =t n0 +Δt for a calculated prediction value y(t n0 +Δt), such that the configured function F approximates the progression of analyte values y(t n ) in the vicinity U with a predetermined accuracy and an additional prediction value y(t n0 +2Δt) is calculated therefrom.
33. The method according to claim 21 , wherein the analyte values y(t n ) used to calculate the prediction value are determined from consecutive points in time t n which are separated by predefined time intervals.
34. The method according to claim 33 , wherein the predefined time intervals are within the range of 30 seconds to 5 minutes.
35. The method according to claim 34 , wherein the predefined time intervals are within the range of 1 to 3 minutes.
36. The method according to claim 21 , wherein the analyte values y(t n ) used to calculate the prediction value or one of the prediction values are determined for times t n which are separated by an interval corresponding to the prediction period Δt.
37. The method according to claim 21 , wherein the number of the coefficients a 0 to a m is within the range of 4 to 11.
38. The method according to claim 37 , wherein the number of the coefficients a 0 to a m is within the range of 6 to 9.
39. The method according to claim 21 , wherein the function F is determined as a function of transformed coordinate values Ty(t k ), Ty(t k-Δn ), Ty(t k-2Δn ), . . . , Ty(t k-(m-2)Δn ), Ty(t k-(m-1)Δn ), which transformed coordinate values are determined by a transformation from analyte values y(t k ), y(t k-Δn ), y(t k-2Δn ), . . . , y(t k-(m-2) Δn ), y(t k-(m-1)Δn ) in which at least one of the values Ty(t k ), Ty(t k-Δn ), Ty(t k-2Δn ), . . . , Ty(t k-(m-2) Δn ), Ty(t k-(m-1)Δn ) has a negligible influence on the function F at the predetermined accuracy σ.
40. The method according to claim 39 , wherein the transformation is a linear transformation.
41. The method according to claim 21 , wherein the prediction value is produced as an output.