Method and system for model-based tracking of changes in average glycemia in diabetes
A method, system and computer readable medium for tracking changes in average glycemia in diabetes is based on a conceptually new approach to the retrieval of SMBG data. Using the understanding of HbA1c fluctuation as the measurable effect of the action of an underlying dynamical system, SMBG provides occasional glimpses at the state of this system and, using these measurements, the hidden underlying system trajectory can be reconstructed for individual diabetes patients. Using compartmental modeling a new two-step algorithm is provided that includes: (i) real-time estimate of HbA1c from fasting glucose readings, updated with any new incoming fasting SMBG data point(s), and (ii) initialization and calibration of the estimated HbA1c trace with daily SMBG profiles obtained periodically. The estimation of these profiles includes a factorial model capturing daily BG variability within two latent factors.
1. A computer-implemented method for providing a real-time estimate of glycosylated hemoglobin (HbA1c) of a patient from a self-monitoring blood glucose (SMBG) measurement, and tracking changes in average glycemia of said patient over time, said method comprising:
receiving, by a processor, a fasting SMBG measurement from said patient;
computing, by a processor, a glycation value using said fasting SMBG measurement in a predetermined glycation equation;
outputting, by a processor, said glycation value as an initial estimate of HbA1c upon initialization of tracking of said patient's average glycemia;
updating, by a processor, said glycation value by using an updated SMBG value in said predetermined glycation equation, said updated SMBG value being based on a subsequent fasting SMBG measurement from said patient;
computing, by a processor, an updated estimate of HbA1c using said initial estimate of HbA1c and said updated glycation value in a predetermined HbA1c estimation equation; and
outputting, by a processor, said updated estimate of HbA1c to a user.
2. The computer-implemented method of claim 1 , further comprising:
updating, by a processor, said updated estimate of HbA1c by:
using a subsequent updated SMBG value in said predetermined glycation equation based on a further subsequent fasting SMBG measurement from said patient to compute a further updated glycation value; and
computing, by a processor, a further updated estimate of HbA1c using a last updated estimate of HbA1c and said further updated glycation value in a predetermined HbA1c estimation equation; and
outputting, by a processor, said further updated estimate of HbA1c to a user.
3. The computer-implemented method of claim 2 , wherein said predetermined glycation equation is given by:
f
(
SMBG
t
)
=
MAX
(
γ
*
(
4.7561
+
4.854
1000
*
mP
0
(
t
)
+
CalA
1
c
)
,
5
)
where
mP 0 (t) is the average fasting glucose over a predetermined period of time and is updated every time a new fasting glucose measurement is obtained from said patient,
CalA1c is a calibration offset, and
γ is a glycation efficacy parameter;
the initial estimate of HbA1c is given by
eA 1 c ( t 0 )=ƒ(SMBG t 0 ); and
the updated estimate of HbA1c is given by
eA 1 c ( t )=0.95* eA 1 c ( t −1 day)+0.05*ƒ(SMBG t ).
4. The computer-implemented method of claim 3 , wherein γ is set so that the last updated estimate of HbA1c, eA1c(t), is set to correspond to a reference HbA1c measurement obtained from said patient.
5. The computer-implemented method of claim 3 , wherein
CalA
1
c
=
6.507
1000
*
θ
1
+
4.353
1000
*
θ
2
,
θ 1 and θ 2 are predefined factors in a SMBG profile of said patient.
6. The computer-implemented method of claim 5 , wherein said SMBG profile is a multipoint peri-prandial profile.
7. The computer-implemented method of claim 6 , wherein said multipoint peri-prandial profile is a seven point profile including the following SMBG measurements:
PG2: first meal preprandial
PG3: first meal postprandial
PG4: second meal preprandial
PG5: second meal postprandial
PG6: third meal preprandial
PG7: third meal postprandial
PG8: before bedtime.
8. The computer-implemented method of claim 7 , wherein
θ 1 =0.4006*PG2+0.4645*PG3+0.3753*PG4+0.2411*PG5−0.1805*PG6−0.2528*PG7+0.0481*PG8, and
θ 2 =−0.1557*PG2−0.2077*PG3.1177*PG4+0.0341*PG5+0.5255*PG6+0.6014*PG7+0.2543*PG8.
9. The computer-implemented method of claim 1 , wherein said predetermined glycation equation is given by:
f
(
SMBG
t
)
=
MAX
(
γ
*
(
4.7561
+
4.854
1000
*
mP
0
(
t
)
+
CalA
1
c
)
,
5
)
where
mP 0 (t) is the average fasting glucose over a predetermined period of time and is updated every time a new fasting glucose measurement is obtained from said patient,
CalA1c is a calibration offset, and
γ is a glycation efficacy parameter;
the initial estimate of HbA1c is given by
eA 1 c ( t 0 )=ƒ(SMBG t 0 ); and
the updated estimate of HbA1c is given by
eA 1 c ( t )=0.95* eA 1 c ( t −1 day)+0.05*ƒ(SMBG t ).
10. A system for providing a real-time estimate of glycosylated hemoglobin (HbA1c) of a patient from a self-monitoring blood glucose (SMBG) measurement, and tracking changes in average glycemia of said patient over time, comprising:
a processor; and
a processor-readable memory including processor-executable instructions for:
receiving a fasting SMBG measurement from said patient;
computing a glycation value using said fasting SMBG measurement in a predetermined glycation equation;
outputting said glycation value as an initial estimate of HbA1c upon initialization of tracking of said patient's average glycemia;
updating said glycation value by using an updated SMBG value in said predetermined glycation equation, said updated SMBG value being based on a subsequent fasting SMBG measurement from said patient;
computing an updated estimate of HbA1c using said initial estimate of HbA1c and said updated glycation value in a predetermined HbA1c estimation equation; and
outputting said updated estimate of HbA1c to a user.
11. The system of claim 10 , wherein said memory further includes processor-executable instructions for:
updating said updated estimate of HbA1c by:
using a subsequent updated SMBG value in said predetermined glycation equation based on a further subsequent fasting SMBG measurement from said patient to compute a further updated glycation value; and
computing a further updated estimate of HbA1c using a last updated estimate of HbA1c and said further updated glycation value in a predetermined HbA1c estimation equation; and
outputting said further updated estimate of HbA1c to a user.
12. The system of claim 11 , wherein said predetermined glycation equation is given by:
f
(
SMBG
t
)
=
MAX
(
γ
*
(
4.7561
+
4.854
1000
*
mP
0
(
t
)
+
CalA
1
c
)
,
5
)
where
mP 0 (t) is the average fasting glucose over a predetermined period of time and is updated every time a new fasting glucose measurement is obtained from said patient,
CalA1c is a calibration offset, and
γ is a glycation efficacy parameter;
the initial estimate of HbA1c is given by
eA 1 c ( t 0 )=ƒ(SMBG t 0 ); and
the updated estimate of HbA1c is given by
eA 1 c ( t )=0.95* eA 1 c ( t −1 day)+0.05*ƒ(SMBG t ).
13. The system of claim 12 , wherein γ is set so that the last updated estimate of HbA1c, eA1c(t), is set to correspond to a reference HbA1c measurement obtained from said patient.
14. The system of claim 12 , wherein
CalA
1
c
=
6.507
1000
*
θ
1
+
4.353
1000
*
θ
2
,
θ 1 and θ 2 are predefined factors in a SMBG profile of said patient.
15. The system of claim 14 , wherein said SMBG profile is a multipoint peri-prandial profile.
16. The system of claim 15 , wherein said multipoint peri-prandial profile is a seven point profile including the following SMBG measurements:
PG2: first meal preprandial
PG3: first meal postprandial
PG4: second meal preprandial
PG5: second meal postprandial
PG6: third meal preprandial
PG7: third meal postprandial
PG8: before bedtime.
17. The system of claim 16 , wherein
θ 1 =0.4006*PG2+0.4645*PG3+0.3753*PG4+0.2411*PG5−0.1805*PG6−0.2528*PG7+0.0481*PG8, and
θ 2 =−0.1557*PG2−0.2077*PG3.1177*PG4+0.0341*PG5+0.5255*PG6+0.6014*PG7+0.2543*PG8.
18. The system of claim 10 , wherein said predetermined glycation equation is given by:
f
(
SMBG
t
)
=
MAX
(
γ
*
(
4.7561
+
4.854
1000
*
mP
0
(
t
)
+
CalA
1
c
)
,
5
)
where
mP 0 (t) is the average fasting glucose over a predetermined period of time and is updated every time a new fasting glucose measurement is obtained from said patient,
CalA1c is a calibration offset, and
γ is a glycation efficacy parameter;
the initial estimate of HbA1c is given by
eA 1 c ( t 0 )=ƒ(SMBG t 0 ); and
the updated estimate of HbA1c is given by
eA 1 c ( t )=0.95* eA 1 c ( t −1 day)+0.05*ƒ(SMBG t ).
19. A non-transient computer-readable medium having stored therein computer-executable instructions for providing a real-time estimate of glycosylated hemoglobin (HbA1c) of a patient from a self-monitoring blood glucose (SMBG) measurement, and tracking changes in average glycemia of said patient over time, said instructions comprising instructions causing a computer to:
receive a fasting SMBG measurement from said patient;
compute a glycation value using said fasting SMBG measurement in a predetermined glycation equation;
output said glycation value as an initial estimate of HbA1c upon initialization of tracking of said patient's average glycemia;
update said glycation value by using an updated SMBG value in said predetermined glycation equation, said updated SMBG value being based on a subsequent fasting SMBG measurement from said patient;
compute an updated estimate of HbA1c using said initial estimate of HbA1c and said updated glycation value in a predetermined HbA1c estimation equation; and
output said updated estimate of HbA1c to a user.
20. The computer-readable medium of claim 19 , further including instructions for causing a computer to:
update said updated estimate of HbA1c by:
using a subsequent updated SMBG value in said predetermined glycation equation based on a further subsequent fasting SMBG measurement from said patient to compute a further updated glycation value; and
computing a further updated estimate of HbA1c using a last updated estimate of HbA1c and said further updated glycation value in a predetermined HbA1c estimation equation; and
output said further updated estimate of HbA1c to a user.
21. The computer-readable medium of claim 20 , wherein said predetermined glycation equation is given by:
f
(
SMBG
t
)
=
MAX
(
γ
*
(
4.7561
+
4.854
1000
*
mP
0
(
t
)
+
CalA
1
c
)
,
5
)
where
mP 0 (t) is the average fasting glucose over a predetermined period of time and is updated every time a new fasting glucose measurement is obtained from said patient,
CalA1c is a calibration offset, and
γ is a glycation efficacy parameter;
the initial estimate of HbA1c is given by
eA 1 c ( t 0 )=ƒ(SMBG t 0 ); and
the updated estimate of HbA1c is given by
eA 1 c ( t )=0.95* eA 1 c ( t −1 day)+0.05*ƒ(SMBG t ).
22. The computer-readable medium of claim 21 , wherein γ is set so that the last updated estimate of HbA1c, eA1c(t), is set to correspond to a reference HbA1c measurement obtained from said patient.
23. The computer-readable medium of claim 21 , wherein
CalA
1
c
=
6.507
1000
*
θ
1
+
4.353
1000
*
θ
2
,
θ 1 and θ 2 are predefined factors in a SMBG profile of said patient.
24. The computer-readable medium of claim 23 , wherein
θ 1 =0.4006*PG2+0.4645*PG3+0.3753*PG4+0.2411*PG5−0.1805*PG6−0.2528*PG7+0.0481*PG8, and
θ 2 =−0.1557*PG2−0.2077*PG3.1177*PG4+0.0341*PG5+0.5255*PG6+0.6014*PG7+0.2543*PG8.
25. The computer-readable medium of claim 19 , wherein said predetermined glycation equation is given by:
f
(
SMBG
t
)
=
MAX
(
γ
*
(
4.7561
+
4.854
1000
*
mP
0
(
t
)
+
CalA
1
c
)
,
5
)
where
mP 0 (t) is the average fasting glucose over a predetermined period of time and is updated every time a new fasting glucose measurement is obtained from said patient,
CalA1c is a calibration offset, and
γ is a glycation efficacy parameter;
the initial estimate of HbA1c is given by
eA 1 c ( t 0 )=ƒ(SMBG t 0 ); and
the updated estimate of HbA1c is given by
eA 1 c ( t )=0.95* eA 1 c ( t −1 day)+0.05*ƒ(SMBG t ).