System and method for predicting the onset of cardiac pathology using fractal analysis

• US 6,920,349 B2
• Filed: 07/01/2002
• Issued: 07/19/2005
• Est. Priority Date: 07/01/2002
• Status: Active Grant

• Current Assignee: VectraCor, Inc.
• Original Assignee: David M. Schreck
• Inventors: Schreck, David M.
• Primary Examiner(s): Schaetzle, Kennedy
• Assistant Examiner(s): Mullen, Kristen
• Application Number:
  US10/187,662
• Publication Number:
  US 20040002661A1
• Time in Patent Office: 1,114 Days
• Field of Search: 128923-925, 600508-510, 600512-513, 600515-518
• US Class Current: 600/512
• CPC Class Codes: A61B 5/318 Heart-related electrical modalities, e.g. electrocardiography [ECG]
• CPC Class Codes: A61B 5/349 Detecting specific parameters of the electrocardiograph cycle

Abstract

The onset of cardiac pathology can be predicted by first acquiring a plurality of lead values as a function of time for set of electrocardiogram leads and defining a spatial curve from the lead values for at least three leads. A fractal index for the spatial curve is calculated as a function of time and the time rate of change of the fractal index is monitored. A negative time rate of change is indicative of normal cardiac activity, while a positive time rate of change is indicative of pathological cardiac activity.

Claims

1. A method for predicting cardiac pathology comprising the steps of:

acquiring a plurality of lead values as a function of time for a set of electrocardiogram leads;

defining a spatial curve from the lead values for at least three leads;

calculating a fractal index as a function of time for the spatial curve; and

monitoring the time rate of change of the fractal index.

2. The method of claim 1, further comprising the step of calculating the lead values from electrode readings taken from electrodes attached to a patient.

3. The method of claim 1, wherein a negative time rate of change of the fractal index is indicative of normal cardiac activity, and a positive time rate of change of the fractal index is indicative of pathological cardiac activity.

4. The method of claim 1, wherein the set of electrocardiogram leads comprises from 3 to about 80 leads, and wherein the full set of electrocardiogram leads can be calculated from a subset of at least 3 electrocardiogram leads by using a universal transformation matrix.

5. The method of claim 1, wherein the fractal index is defined by the equation

FD(k)=log(k)/(log(k)+log(DD(t_k)/LSUM(t_k))),

wherein:

t_k=kδ

t is the time after k intervals of time unit δ

t;

$\mathrm{LSUM}<br><br>\left(t_k\right)=\mathrm{LSUM}<br><br>\left(t_{k-1}\right)+{\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>{\left(x_i<br><br>\left(t_k\right)-x_i<br><br>\left(t_{k-1}\right)\right)}^2\right)}^{\frac{1}{2}};<br><br>$$\mathrm{DD}<br><br>\left(t_k\right)=\max <br><br>\left({\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>x_i^2<br><br>\left(t_k\right)\right)}^{\frac{1}{2}},\mathrm{DD}<br><br>\left(t_{k-1}\right)\right);<br><br>$

N represents the number of electrocardiogram leads; and

x_i(t_k) represents the value of the i^th lead in the N-lead set at time t_k.

6. The method of claim 1, wherein the fractal index is defined by the equation

K1=(LSUM(t_k)^FD(k))/SumArea(t_k)

wherein

t_k=kδ

t is the time after k intervals of time unit δ

t;

$\mathrm{LSUM}<br><br>\left(t_k\right)=\mathrm{LSUM}<br><br>\left(t_{k-1}\right)+{\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>{\left(x_i<br><br>\left(t_k\right)-x_i<br><br>\left(t_{k-1}\right)\right)}^2\right)}^{\frac{1}{2}};<br><br>$ 

FD(k)=log(k)/(log(k)+log(DD(t_k)/LSUM(t_k)));

$\mathrm{DD}<br><br>\left(t_k\right)=\max <br><br>\left({\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>x_i^2<br><br>\left(t_k\right)\right)}^{\frac{1}{2}},\mathrm{DD}<br><br>\left(t_{k-1}\right)\right);<br><br>$$\begin{array}{c}\mathrm{SumArea}<br><br>\left(t_k\right)=<br><br>\mathrm{SumArea}<br><br>\left(t_{k-1}\right)+\\ <br><br>\frac{1}{4}<br><br>(\left(D<br><br>\left(t_k\right)+D<br><br>\left(t_{k-1}\right)+L<br><br>\left(t_k\right)\right)<br><br>(D<br><br>\left(t_k\right)-D<br><br>\left(t_{k-1}\right)+\\ <br><br>L<br><br>\left(t_k\right))<br><br>\left(-D<br><br>\left(t_k\right)+D<br><br>\left(t_{k-1}\right)+L<br><br>\left(t_k\right)\right)<br><br>(D<br><br>\left(t_k\right)+\\ {<br><br>D<br><br>\left(t_{k-1}\right)-L<br><br>\left(t_k\right)))}^{\frac{1}{2}},\end{array}$$\begin{array}{cc}\mathrm{where}& D<br><br>\left(t_k\right)={\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>x_i^2<br><br>\left(t_k\right)\right)}^{\frac{1}{2}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}\\ \text{\hspace{1em}<br><br>}& L<br><br>\left(t_k\right)={\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>{\left(x_i<br><br>\left(t_k\right)-x_i<br><br>\left(t_{k-1}\right)\right)}^2\right)}^{\frac{1}{2}};<br><br>\end{array}$

N represents the number of electrocardiogram leads; and

x_i(t_k) represents the value of the i^th lead in the N-lead set at time t_k.

7. The method of claim 1, wherein the fractal index is defined by the equation

K1=(PerimTot(t_k)^FD(k))/SumArea(t_k)

wherein

t_k=kδ

t is the time after k intervals of time unit δ

t;

$\mathrm{PerimTot}<br><br>\left(t_k\right)={\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>x_i^2<br><br>\left(t_k\right)\right)}^{\frac{1}{2}}+\mathrm{LSUM}<br><br>\left(t_k\right)$$\mathrm{LSUM}<br><br>\left(t_k\right)=\mathrm{LSUM}<br><br>\left(t_{k-1}\right)+{\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>{\left(x_i<br><br>\left(t_k\right)-x_i<br><br>\left(t_{k-1}\right)\right)}^2\right)}^{\frac{1}{2}};<br><br>$ 

FD(k)=log(k)/(log(k)+log(DD(t_k)/LSUM(t_k)));

$\mathrm{DD}<br><br>\left(t_k\right)=\max <br><br>\left({\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>x_i^2<br><br>\left(t_k\right)\right)}^{\frac{1}{2}},\mathrm{DD}<br><br>\left(t_{k-1}\right)\right);<br><br>$$\begin{array}{c}\mathrm{SumArea}<br><br>\left(t_k\right)=<br><br>\mathrm{SumArea}<br><br>\left(t_{k-1}\right)+\\ <br><br>\frac{1}{4}<br><br>(\left(D<br><br>\left(t_k\right)+D<br><br>\left(t_{k-1}\right)+L<br><br>\left(t_k\right)\right)<br><br>(D<br><br>\left(t_k\right)-D<br><br>\left(t_{k-1}\right)+\\ <br><br>L<br><br>\left(t_k\right))<br><br>\left(-D<br><br>\left(t_k\right)+D<br><br>\left(t_{k-1}\right)+L<br><br>\left(t_k\right)\right)<br><br>(D<br><br>\left(t_k\right)+\\ {<br><br>D<br><br>\left(t_{k-1}\right)-L<br><br>\left(t_k\right)))}^{\frac{1}{2}};<br><br>\end{array}$$\begin{array}{cc}\mathrm{where}& D<br><br>\left(t_k\right)={\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>x_i^2<br><br>\left(t_k\right)\right)}^{\frac{1}{2}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}\\ \text{\hspace{1em}<br><br>}& L<br><br>\left(t_k\right)={\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>{\left(x_i<br><br>\left(t_k\right)-x_i<br><br>\left(t_{k-1}\right)\right)}^2\right)}^{\frac{1}{2}};<br><br>\end{array}$

N represents the number of electrocardiogram leads; and

x_i(t_k) represents the value of the i^th lead in the N-lead set at time t_k.

8. The method of claim 1, further comprising the step of displaying the spatial loop in a heart monitor.

9. The method of claim 1, further comprising the steps of displaying the fractal index values in a heart monitor and storing said fractal index values in said heart monitor.

10. An apparatus for monitoring cardiac activity comprising:

means for acquiring a plurality of lead values as a function of time for a set of electrocardiogram leads;

means for defining a spatial curve from the lead values of at least three leads;

means for calculating a fractal index as a function of time for the spatial curve; and

means for monitoring the time rate of change of the fractal index.

11. The apparatus of claim 10, further comprising means for calculating the lead values from electrode readings taken from electrodes attached to a patient.

12. The apparatus of claim 10, wherein a negative time rate of change of the fractal index is indicative of normal cardiac activity, and a positive time rate of change of the fractal index is indicative of pathological cardiac activity.

13. The apparatus of claim 10, wherein the set of electrocardiogram leads comprises from 3 to about 80 leads, and further comprising means for calculating the full set of electrocardiogram leads from a subset of at least 3 electrocardiogram leads by using a universal transformation matrix.

14. The apparatus of claim 10, wherein the fractal index is defined by the equation

FD(k)=log(k)/(log(k)+log(DD(t_k)/LSUM(t_k))),

wherein:

t_k=kδ

t is the time after k intervals of time unit δ

t;

$\mathrm{LSUM}<br><br>\left(t_k\right)=\mathrm{LSUM}<br><br>\left(t_{k-1}\right)+{\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>{\left(x_i<br><br>\left(t_k\right)-x_i<br><br>\left(t_{k-1}\right)\right)}^2\right)}^{\frac{1}{2}};<br><br>$$\mathrm{DD}<br><br>\left(t_k\right)=\max <br><br>\left({\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>x_i^2<br><br>\left(t_k\right)\right)}^{\frac{1}{2}},\mathrm{DD}<br><br>\left(t_{k-1}\right)\right);<br><br>$

N represents the number of electrocardiogram leads; and

x_i(t_k) represents the value of the i^th lead in the N-lead set at time t_k.

15. The apparatus of claim 10, wherein the fractal index is defined by the equation

K1=(LSUM(t_k)^FD(k))/SumArea(t_k)

wherein

t_k=kδ

t is the time after k intervals of time unit δ

t;

$\mathrm{LSUM}<br><br>\left(t_k\right)=\mathrm{LSUM}<br><br>\left(t_{k-1}\right)+{\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>{\left(x_i<br><br>\left(t_k\right)-x_i<br><br>\left(t_{k-1}\right)\right)}^2\right)}^{\frac{1}{2}};<br><br>$ 

FD(k)=log(k)/(log(k)+log(DD(t_k)/LSUM(t_k)));

$\begin{array}{c}\mathrm{DD}<br><br>\left(t_k\right)=\max <br><br>\left({\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>x_i^2<br><br>\left(t_k\right)\right)}^{\frac{1}{2}},\mathrm{DD}<br><br>\left(t_{k-1}\right)\right);<br><br>\\ \begin{array}{c}\mathrm{SumArea}<br><br>\left(t_k\right)=<br><br>\mathrm{SumArea}<br><br>\left(t_{k-1}\right)+\frac{1}{4}<br><br>((D<br><br>\left(t_k\right)+D<br><br>\left(t_{k-1}\right)+\\ <br><br>L<br><br>\left(t_k\right))<br><br>\left(D<br><br>\left(t_k\right)-D<br><br>\left(t_{k-1}\right)+L<br><br>\left(t_k\right)\right)<br><br>(-D<br><br>\left(t_k\right)+\\ {<br><br>D<br><br>\left(t_{k-1}\right)+L<br><br>\left(t_k\right))<br><br>\left(D<br><br>\left(t_k\right)+D<br><br>\left(t_{k-1}\right)-L<br><br>\left(t_k\right)\right))}^{\frac{1}{2}},\end{array}\\ \begin{array}{cc}\mathrm{where}& D<br><br>\left(t_k\right)={\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>x_i^2<br><br>\left(t_k\right)\right)}^{\frac{1}{2}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}\\ \text{\hspace{1em}<br><br>}& L<br><br>\left(t_k\right)={\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>{\left(x_i<br><br>\left(t_k\right)-x_i<br><br>\left(t_{k-1}\right)\right)}^2\right)}^{\frac{1}{2}};<br><br>\end{array}\end{array}$

N represents the number of electrocardiogram leads; and

x_i(t_k) represents the value of the i^th lead in the N-lead set at time t_k.

16. The apparatus of claim 10, wherein the fractal index is defined by the equation

K1=(PerimTot(t_k)^FD(k))/SumArea(t_k)

wherein

t_k=kδ

t is the time after k intervals of time unit δ

t;

$\mathrm{PerimTot}<br><br>\left(t_k\right)={\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>x_i^2<br><br>\left(t_k\right)\right)}^{\frac{1}{2}}+\mathrm{LSUM}<br><br>\left(t_k\right)$$\mathrm{LSUM}<br><br>\left(t_k\right)=\mathrm{LSUM}<br><br>\left(t_{k-1}\right)+{\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>{\left(x_i<br><br>\left(t_k\right)-x_i<br><br>\left(t_{k-1}\right)\right)}^2\right)}^{\frac{1}{2}};<br><br>$ 

FD(k)=log(k)/(log(k)+log(DD(t_k)/LSUM(t_k)));

$\begin{array}{c}\mathrm{DD}<br><br>\left(t_k\right)=\max <br><br>\left({\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>x_i^2<br><br>\left(t_k\right)\right)}^{\frac{1}{2}},\mathrm{DD}<br><br>\left(t_{k-1}\right)\right);<br><br>\\ \begin{array}{c}\mathrm{SumArea}<br><br>\left(t_k\right)=<br><br>\mathrm{SumArea}<br><br>\left(t_{k-1}\right)+\frac{1}{4}<br><br>((D<br><br>\left(t_k\right)+D<br><br>\left(t_{k-1}\right)+\\ <br><br>L<br><br>\left(t_k\right))<br><br>\left(D<br><br>\left(t_k\right)-D<br><br>\left(t_{k-1}\right)+L<br><br>\left(t_k\right)\right)<br><br>(-D<br><br>\left(t_k\right)+\\ {<br><br>D<br><br>\left(t_{k-1}\right)+L<br><br>\left(t_k\right))<br><br>\left(D<br><br>\left(t_k\right)+D<br><br>\left(t_{k-1}\right)-L<br><br>\left(t_k\right)\right))}^{\frac{1}{2}};<br><br>\end{array}\\ \begin{array}{cc}\mathrm{where}& D<br><br>\left(t_k\right)={\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>x_i^2<br><br>\left(t_k\right)\right)}^{\frac{1}{2}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}\\ \text{\hspace{1em}<br><br>}& L<br><br>\left(t_k\right)={\left(\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>{\left(x_i<br><br>\left(t_k\right)-x_i<br><br>\left(t_{k-1}\right)\right)}^2\right)}^{\frac{1}{2}};<br><br>\end{array}\end{array}$

N represents the number of electrocardiogram leads; and

x_i(t_k) represents the value of the i^th lead in the N-lead set at time t_k.

17. The apparatus of claim 10, further comprising means for displaying the spatial loop.

18. The apparatus of claim 10, further comprising means for displaying the fractal index values and storing said fractal index values.