Method for forecasting the contrast medium flow in a living body
First Claim
1. A method for forecasting the contrast medium flow in a living body, comprising:
- injecting a defined test bolus with a contrast medium into the body;
observing and determining a time concentration profile of the contrast medium over a limited time period with a number of measuring instants at at least one location in the body with the aid of a tomographic method;
forecasting a time profile of the contrast medium concentration of another contrast medium dose from the measured data obtained via the distribution of the contrast medium, with the aid of a linear cause/effect formulation; and
using the following calculation formula for forecasting the time concentration profile {tilde over (c)}R(t) of the contrast medium at at least one of the previously measured locations of the body;
in which{tilde over (c)}R(t+t0T−
nΔ
T−
t′
) corresponds to the concentration displaced from the instant t to the instant t+t0T−
nΔ
T−
t′
,FT corresponds to the flow rate of the contrast medium of the test bolus,b′
R(t′
) corresponds to the time derivative of the profile of the contrast medium bolus administered,t corresponds to the forecast instant, andt′
corresponds to the integration variable.
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Accused Products
Abstract
A method is disclosed for forecasting the contrast medium flow in a living body, in particular in a patient, in which a defined test bolus with a contrast medium is injected, preferably intravenously and with a known injection flow profile, into the body, preferably into a blood vessel. The time concentration profile of the contrast medium is observed and determined over a limited time period with a number of measuring instants at at least one location in the body with the aid of a tomographic method. The time profile of the contrast medium concentration of another contrast medium dose is forecast with the aid of a linear cause/effect formulation from the measured data obtained via the distribution of the contrast medium. The following calculation formula is then used for forecasting the time concentration profile {tilde over (c)}R(t) of the contrast medium at at least one of the previously measured locations of the body:
26 Citations
18 Claims
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1. A method for forecasting the contrast medium flow in a living body, comprising:
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injecting a defined test bolus with a contrast medium into the body; observing and determining a time concentration profile of the contrast medium over a limited time period with a number of measuring instants at at least one location in the body with the aid of a tomographic method; forecasting a time profile of the contrast medium concentration of another contrast medium dose from the measured data obtained via the distribution of the contrast medium, with the aid of a linear cause/effect formulation; and using the following calculation formula for forecasting the time concentration profile {tilde over (c)}R(t) of the contrast medium at at least one of the previously measured locations of the body; in which {tilde over (c)}R(t+t0T−
nΔ
T−
t′
) corresponds to the concentration displaced from the instant t to the instant t+t0T−
nΔ
T−
t′
,FT corresponds to the flow rate of the contrast medium of the test bolus, b′
R(t′
) corresponds to the time derivative of the profile of the contrast medium bolus administered,t corresponds to the forecast instant, and t′
corresponds to the integration variable.- View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
the following designations being used; FT flow rate of the contrast medium of the test bolus FR flow rate of the contrast medium of the correct bolus ξ
integration variablet0R starting instant of the correct bolus t0T starting instant of the test bolus.
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3. The method as claimed in claim 1, wherein, in order to forecast instants for which no measured values from a test bolus injection are present, the contrast medium concentration is forecast using a physiological calculation model.
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4. The method as claimed in claim 3, wherein the following system of differential equations is used as physiological calculation model:
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the following designations being used; b(x,t) concentration profile of the bolus at location x at time t, F flow of the contrast medium, δ
(1) delta function,Θ
(t−
t0) Heaviside step function for describing the beginning of the injection,Θ
(tF−
t) Heaviside step function for describing the end of the injection.
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5. The method as claimed in claim 3, wherein in order to forecast instants for which no measured values from a test bolus injection are present, the measured concentration profile is firstly approximated after a test bolus injection with the aid of the following function:
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and subsequently the expected concentration profile is estimated using the parameters A, B, C and c—
0 thus calculated with the aid of the following formula;the following designations being used; A first function constant, substantially indirectly proportional to the width of the test bolus curve, B second function constant, substantially proportional to the peak of the test bolus curve, b(x, t) concentration profile of the bolus at location x at time t, C third function constant, proportional to the area under the test bolus curve, c0 enhancement value before the injection of the contrast medium bolus, Erƒ
( ) error function,FR flow rate of the contrast medium of the correct bolus, FT flow rate of the contrast medium of the test bolus, tFR final instant of the correct bolus, tFT final instant of the test bolus, t0R starting instant of the correct bolus, t0T starting instant of the test bolus, x observed location, Θ
Heaviside step functions for describing the beginning and the end of the bolus injections.
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6. The method as claimed in claim 3, wherein a mean value of the two forecast values is used for instants at which forecasts from the linear model and the physiological model are present.
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7. The method as claimed in claim 3, wherein a weighted mean value of the two forecast values is used for instants at which forecasts from the linear model and the physiological model are present.
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8. The method as claimed in claim 2, wherein, in order to forecast instants for which no measured values from a test bolus injection are present, the contrast medium concentration is forecast using a physiological calculation model.
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9. The method as claimed in claim 8, wherein the following system of differential equations is used as physiological calculation model:
-
the following designations being used; b(x,t) concentration profile of the bolus at location x at time t, F flow of the contrast medium, δ
(1) delta function,Θ
(t−
t0) Heaviside step function for describing the beginning of the injection,Θ
(tF−
t) Heaviside step function for describing the end of the injection.
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10. The method as claimed in claim 8, wherein in order to forecast instants for which no measured values from a test bolus injection are present, the measured concentration profile is firstly approximated after a test bolus injection with the aid of the following function:
-
and subsequently the expected concentration profile is estimated using the parameters A, B, C and c—
0 thus calculated with the aid of the following formula;the following designations being used; A first function constant, substantially indirectly proportional to the width of the test bolus curve, B second function constant, substantially proportional to the peak of the test bolus curve, b(x, t) concentration profile of the bolus at location x at time t, C third function constant, proportional to the area under the test bolus curve, c0 enhancement value before the injection of the contrast medium bolus, Erƒ
( ) error function,FR flow rate of the contrast medium of the correct bolus, FT flow rate of the contrast medium of the test bolus, tFR final instant of the correct bolus, tFT final instant of the test bolus, t0R starting instant of the correct bolus, t0T starting instant of the test bolus, x observed location, Θ
Heaviside step functions for describing the beginning and the end of the bolus injections.
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11. The method as claimed in claim 4, wherein in order to forecast instants for which no measured values from a test bolus injection are present, the measured concentration profile is firstly approximated after a test bolus injection with the aid of the following function:
-
and subsequently the expected concentration profile is estimated using the parameters A, B, C and c—
0 thus calculated with the aid of the following formula;the following designations being used; A first function constant, substantially indirectly proportional to the width of the test bolus curve, B second function constant, substantially proportional to the peak of the test bolus curve, b(x, t) concentration profile of the bolus at location x at time t, C third function constant, proportional to the area under the test bolus curve, c0 enhancement value before the injection of the contrast medium bolus, Erƒ
( ) error function,FR flow rate of the contrast medium of the correct bolus, FT flow rate of the contrast medium of the test bolus, tFR final instant of the correct bolus, tFT final instant of the test bolus, t0R starting instant of the correct bolus, t0T starting instant of the test bolus, x observed location, Θ
Heaviside step functions for describing the beginning and the end of the bolus injections.
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12. The method as claimed in claim 4, wherein a mean value of the two forecast values is used for instants at which forecasts from the linear model and the physiological model are present.
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13. The method as claimed in claim 4, wherein a weighted mean value of the two forecast values is used for instants at which forecasts from the linear model and the physiological model are present.
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14. The method as claimed in claim 5, wherein a mean value of the two forecast values is used for instants at which forecasts from the linear model and the physiological model are present.
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15. The method as claimed in claim 5, wherein a weighted mean value of the two forecast values is used for instants at which forecasts from the linear model and the physiological model are present.
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16. The method as claimed in claim 1, wherein the injecting of a defined test bolus with a contrast medium is done intravenously and with a known injection flow profile, into a blood vessel of the body.
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17. A computer program stored on a computer program product and adapted to, when executed on a computer following the injection of a defined test bolus with a contrast medium into the body, cause the computer to carry out steps of:
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observing and determining a time concentration profile of the contrast medium over a limited time period with a number of measuring instants at at least one location in the body with the aid of a tomographic method; forecasting a time profile of the contrast medium concentration of another contrast medium dose from the measured data obtained via the distribution of the contrast medium, with the aid of a linear cause/effect formulation; and using the following calculation formula for forecasting the time concentration profile {tilde over (c)}R(t) of the contrast medium at at least one of the previously measured locations of the body; in which {tilde over (c)}R(t+t0T−
nΔ
T−
t′
) corresponds to the concentration displaced from the instant t to the instant t+t0T−
nΔ
T−
t′
,FT corresponds to the flow rate of the contrast medium of the test bolus, b′
R(t′
) corresponds to the time derivative of the profile of the contrast medium bolus administered.t corresponds to the forecast instant, and t′
corresponds to the integration variable.
-
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18. A computer readable medium including program segments for, when executed on a computer following the injection of a defined test bolus with a contrast medium into the body, causing the computer to implement steps of:
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observing and determining a time concentration profile of the contrast medium over a limited time period with a number of measuring instants at at least one location in the body with the aid of a tomographic method; forecasting a time profile of the contrast medium concentration of another contrast medium dose from the measured data obtained via the distribution of the contrast medium, with the aid of a linear cause/effect formulation; and using the following calculation formula for forecasting the time concentration profile {tilde over (c)}R(t) of the contrast medium at at least one of the previously measured locations of the body; in which {tilde over (c)}R(t+t0T−
nΔ
T−
t′
) corresponds to the concentration displaced from the instant t to the instant t+t0T−
nΔ
T−
t′
,FT corresponds to the flow rate of the contrast medium of the test bolus, b′
R(t′
) corresponds to the time derivative of the profile of the contrast medium bolus administered.t corresponds to the forecast instant, and t′
corresponds to the integration variable.
-
Specification