Method for forecasting the contrast medium flow in a living body

US 20060239917A1
Filed: 02/13/2006
Published: 10/26/2006
Est. Priority Date: 02/14/2005
Status: Active Grant

First Claim

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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;

${\tilde{c}}_{R} (t) = \frac{1}{F_{T}} \sum_{n = - \infty}^{\infty} \int_{- \infty}^{\infty} ⅆ t^{'} {\tilde{c}}_{R} (t + t_{0 T} - n Δ_{T} - t^{'}) b_{R}^{'} (t^{'}),$ {tilde over (c)}_R(t+t_0T−

nΔ

_T−

t′

) corresponds to the concentration displaced from the instant t to the instant t+t_0T−

nΔ

_T−

t′

, F_Tcorresponds 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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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: ${\tilde{c}}_{R} (t) = \frac{1}{F_{T}} \sum_{n = na}^{n = ne} \int_{x = xa}^{x = xe} ⅆ t^{'} {\tilde{c}}_{R} (t + t_{0 T} - n Δ_{T} - t^{'}) b_{R}^{'} (t^{'}) .$

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20 Claims

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;
  
  ${\tilde{c}}_{R} (t) = \frac{1}{F_{T}} \sum_{n = - \infty}^{\infty} \int_{- \infty}^{\infty} ⅆ t^{'} {\tilde{c}}_{R} (t + t_{0 T} - n Δ_{T} - t^{'}) b_{R}^{'} (t^{'}),$ {tilde over (c)}_R(t+t_0T−
  
  nΔ
  
  _T−
  
  t′
  
  ) corresponds to the concentration displaced from the instant t to the instant t+t_0T−
  
  nΔ
  
  _T−
  
  t′
  
  , F_Tcorresponds 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, 17, 18, 19, 20)
- - 2. The method as claimed in claim 1, wherein a contrast medium injection with constant flow over the injection time is used as test bolus and final bolus to be calculated, and the forecast of the concentration profile {tilde over (c)}_R(t) is calculated with the aid of the following formula:
    - $\begin{matrix} {\tilde{c}}_{R} (t) = \frac{1}{2 π} \frac{F_{R}}{F_{T}} \int_{- \infty}^{\infty} ⅆ ξexp (- ⅈξ (t - t_{0 R} + t_{0 T})) \\ (1 - \exp ({ⅈξΔ}_{R})) \sum_{n = 0}^{\infty} \exp (ⅈ n {ξΔ}_{T}) {\tilde{C}}_{T} (ξ) \\ = \frac{1}{2 π} \frac{F_{R}}{F_{T}} \sum_{n = 0}^{\infty} \int_{- \infty}^{\infty} ⅆ ξ (1 - \exp ({ⅈξΔ}_{R})) \\ \exp (- ⅈξ (t - t_{0 R} + t_{0 T} + n Δ_{T})) {\tilde{C}}_{T} (ξ) \\ = \frac{F_{R}}{F_{T}} \sum_{n = 0}^{\infty} ({\tilde{c}}_{T} (t - t_{0 R} + t_{0 T} - n Δ_{T}) - \\ {\tilde{c}}_{T} (t - t_{FR} + t_{0 T} - n Δ_{T})) \end{matrix}$ the following designations being used;
      
      F_Tflow rate of the contrast medium of the test bolus F_Rflow rate of the contrast medium of the correct bolus integration variable t_0Rstarting instant of the correct bolus t_0Tstarting instant of the test bolus.
  - 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.
  - 4. The method as claimed in claim 3, wherein the following system of differential equations is used as physiological calculation model:
    - $\frac{\partial}{\partial t} b (x, t) + v \frac{\partial}{\partial x} b (x, t) - D \frac{\partial^{2}}{\partial x^{2}} b (x, t) = F δ^{(1)} (x) Θ (t - t_{0}) Θ (t_{F} - t),$ 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
      
      (t_F−
      
      t) Heaviside step function for describing the end of the injection.
  - 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:
    - $b (x, t) = c_{0} + C Θ (t - t_{0 T}) (Θ (t_{FT} - t) (1 - Erf (A \frac{B - (t - t_{0 T})}{\sqrt{(t - t_{0 T})}})) + Θ (t - t_{FT}) (Erf (A \frac{B - (t - t_{FT})}{\sqrt{(t - t_{FT})}})) - Erf (A \frac{B - (t - t_{0 T})}{\sqrt{(t - t_{0 T})}}))$ 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;
      
      $b (x, t) = c_{0} + C \frac{F_{R}}{F_{T}} Θ (t - t_{0 R}) (Θ (t_{FR} - t) (1 - Erf (A \frac{B - (t - t_{0 R})}{\sqrt{(t - t_{0 R})}})) + Θ (t - t_{FR}) (Erf (A \frac{B - (t - t_{FR})}{\sqrt{(t - t_{FR})}})) - Erf (A \frac{B - (t - t_{0 R})}{\sqrt{(t - t_{0 R})}})$ 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, c₀enhancement value before the injection of the contrast medium bolus, Erƒ
      
      ( ) error function, F_Rflow rate of the contrast medium of the correct bolus, F_Tflow rate of the contrast medium of the test bolus, t_FRfinal instant of the correct bolus, t_FTfinal instant of the test bolus, t_0Rstarting instant of the correct bolus, t_0Tstarting instant of the test bolus, x observed location, Θ
      
      Heaviside step functions for describing the beginning and the end of the bolus injections.
  - 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.
  - 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.
  - 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.
  - 9. The method as claimed in claim 8, wherein the following system of differential equations is used as physiological calculation model:
    - $\frac{\partial}{\partial t} b (x, t) + υ \frac{\partial}{\partial x} b (x, t) - D \frac{\partial^{2}}{\partial x^{2}} b (x, t) = F δ^{(1)} (x) Θ (t - t_{0}) Θ (t_{F} - t),$ 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
      
      (t_F−
      
      t) Heaviside step function for describing the end of the injection.
  - 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:
    - $b (x, t) = c_{0} + C Θ (t - t_{0 T}) (Θ (t_{FT} - t) (1 - Erf (A \frac{B - (t - t_{0 T})}{\sqrt{(t - t_{0 T})}})) + Θ (t - t_{FT}) (Erf (A \frac{B - (t - t_{FT})}{\sqrt{(t - t_{FT})}})) - Erf (A \frac{B - (t - t_{0 T})}{\sqrt{(t - t_{0 T})}})$ 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;
      
      $b (x, t) = c_{0} + C \frac{F_{R}}{F_{T}} Θ (t - t_{0 R}) (Θ (t_{FR} - t) (1 - Erf (A \frac{B - (t - t_{0 R})}{\sqrt{(t - t_{0 R})}})) + Θ (t - t_{FR}) (Erf (A \frac{B - (t - t_{FR})}{\sqrt{(t - t_{FR})}})) - Erf (A \frac{B - (t - t_{0 R})}{\sqrt{(t - t_{0 R})}})$ 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, c₀enhancement value before the injection of the contrast medium bolus, Erƒ
      
      ( ) error function, F_Rflow rate of the contrast medium of the correct bolus, F_Tflow rate of the contrast medium of the test bolus, t_FRfinal instant of the correct bolus, t_FTfinal instant of the test bolus, t_0Rstarting instant of the correct bolus, t_0Tstarting instant of the test bolus, x observed location, Θ
      
      Heaviside step functions for describing the beginning and the end of the bolus injections.
  - 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:
    - $b (x, t) = c_{0} + C Θ (t - t_{0 T}) (Θ (t_{FT} - t) (1 - Erf (A \frac{B - (t - t_{0 T})}{\sqrt{(t - t_{0 T})}})) + Θ (t - t_{FT}) (Erf (A \frac{B - (t - t_{FT})}{\sqrt{(t - t_{FT})}})) - Erf (A \frac{B - (t - t_{0 T})}{\sqrt{(t - t_{0 T})}})$ 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;
      
      $b (x, t) = c_{0} + C \frac{F_{R}}{F_{T}} Θ (t - t_{0 R}) (Θ (t_{FR} - t) (1 - Erf (A \frac{B - (t - t_{0 R})}{\sqrt{(t - t_{0 R})}})) + Θ (t - t_{FR}) (Erf (A \frac{B - (t - t_{FR})}{\sqrt{(t - t_{FR})}})) - Erf (A \frac{B - (t - t_{0 R})}{\sqrt{(t - t_{0 R})}})$ 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, c₀enhancement value before the injection of the contrast medium bolus, Erƒ
      
      ( ) error function, F_Rflow rate of the contrast medium of the correct bolus, F_Tflow rate of the contrast medium of the test bolus, t_FRfinal instant of the correct bolus, t_FTfinal instant of the test bolus, t_0Rstarting instant of the correct bolus, t_0Tstarting instant of the test bolus, x observed location, Θ
      
      Heaviside step functions for describing the beginning and the end of the bolus injections.
  - 12. The method as claimed in claim 10, 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:
    - $b (x, t) = c_{0} + C Θ (t - t_{0 T}) (Θ (t_{FT} - t) (1 - Erf (A \frac{B - (t - t_{0 T})}{\sqrt{(t - t_{0 T})}})) + Θ (t - t_{FT}) (Erf (A \frac{B - (t - t_{FT})}{\sqrt{(t - t_{FT})}})) - Erf (A \frac{B - (t - t_{0 T})}{\sqrt{(t - t_{0 T})}})$ 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;
      
      $b (x, t) = c_{0} + C \frac{F_{R}}{F_{T}} Θ (t - t_{0 R}) (Θ (t_{FR} - t) (1 - Erf (A \frac{B - (t - t_{0 R})}{\sqrt{(t - t_{0 R})}})) + Θ (t - t_{FR}) (Erf (A \frac{B - (t - t_{FR})}{\sqrt{(t - t_{FR})}})) - Erf (A \frac{B - (t - t_{0 R})}{\sqrt{(t - t_{0 R})}})$ 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, c₀enhancement value before the injection of the contrast medium bolus, Erƒ
      
      ( ) error function, F_Rflow rate of the contrast medium of the correct bolus, F_Tflow rate of the contrast medium of the test bolus, t_FRfinal instant of the correct bolus, t_FTfinal instant of the test bolus, t_0Rstarting instant of the correct bolus, t_0Tstarting instant of the test bolus, x observed location, Θ
      
      Heaviside step functions for describing the beginning and the end of the bolus injections.
  - 13. 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.
  - 14. 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.
  - 15. 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.
  - 16. 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.
  - 17. 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.
  - 18. A computer program, adapted to, when executed on a computer, cause the computer to carry out the method as claimed in claim 1.
  - 19. A computer program product, including the computer program of claim 18.
  - 20. A computer readable medium including program segments for, when executed on a computer, causing the computer to implement the method of claim 1.

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Current Assignee
Siemens Healthcare GMBH (Siemens AG)
Original Assignee
Siemens AG
Inventors
Rauscher, Annabella, Klotz, Ernst

Granted Patent

US 7,477,929 B2
Time in Patent Office

Days
Field of Search
US Class Current

424/9.300
CPC Class Codes

A61B 6/481 involving the use of contra...

A61B 6/504 for diagnosis of blood vess...

Method for forecasting the contrast medium flow in a living body

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Method for forecasting the contrast medium flow in a living body

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