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Description  |
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BACKGROUND OF THE INVENTION
The present invention relates to the field of electronic signal processing,
and more particularly to a method and an apparatus for characterizing the
unknown state of a physical system having a variant history, the
characterization being made with reference to a known state of like
physical systems.
For many physical systems, the ability to predict accurately the future
state of the system is as important as, and in some instances more
important than, knowledge of the present state of the system. For example,
in the field of medical science, the ability to predict future medical
problems of seemingly healthy individuals is of paramount importance.
Although this ability is extremely desirable, such predictions based on
presently known techniques are often inaccurate.
Illustrative of this problem is the current limited ability to predict with
or without early symptoms the onset of coronary problems in the future in
a seemingly normal individual who presently exhibits a negative
electrocardiographic reading and who has no prior history of heart disease
or problems typically associated therewith. Currently, techniques exist
for analyzing electrocardiographic data. For example, an article by
Teichholz et al., 35 The American Journal of Cardiology 531-36 (April,
1975), entitled "The Omni Cardiogram, New Approach To Detection Of Heart
Disease In Patients With A Normal Resting Cardiogram", discusses a
technique for analyzing and detecting subtle degrees of abnormality not
apparent in raw electrocardiographic data. Although the analytical
technique described in this article possesses certain desirable attributes
and results in a better understanding of the underlying data, it still has
certain drawbacks and limitations. More specifically, it does not enable
one to predict accurately and quantitatively the future onset of coronary
disease in a patient possessing an apparent normal electrocardiogram. It
is believed that prior to the present invention this problem has gone
unsolved.
Accordingly, it is a general object of the present invention to overcome
the drawbacks and limitations of known signal processing systems for
characterizing the state of a physical system when it is unknown.
It is a specific object of the present invention to provide a method and an
apparatus for evaluating the present state and/or predicing the future
state of a physical system.
It is another object of the present invention to provide a method and an
apparatus for characterizing the state of a medical system with reference
to a known state of like systems.
It is another object of the present invention to provide a method and an
apparatus for characterizing chemical compounds with reference to a known
state of like systems.
SUMMARY OF THE INVENTION
The foregoing and other objects and advantages which will be apparent in
the following detailed description of the preferred embodiment, or in the
practice of the invention, are achieved by the invention disclosed herein,
which generally may be characterized as a method and an apparatus for
characterizing the unknown state of a physical system, the
characterization being made with reference to a known state of like
physical systems.
In accordance with the teachings of the present invention, a response
signature representative of the unknown system state is obtained and
compared to a standard signature representative of the known system to
determine whether or not the system being characterized is in the known
state.
The standard signature comprises a multi-dimensional region within a
pre-defined, transformed coordinate system having an inner and outer
boundary. If the response signature lies wholly within the bounded region
the system being characterized is deemed to be in the known state.
Conversely, if this criteria is not satisfied the system is deemed to be
in a state other than the known state. The ability to characterize the
state of a physical system may be enhanced by adjusting the coordinate
transformations of the standard signature and the response signature by an
offset factor and by subsequently subjecting both signatures to a
topological transformation which produces a standard signature comprising
two concentric geometric figures.
BRIEF DESCRIPTION OF THE DRAWINGS
Serving to illustrate an exemplary embodiment of the invention are the
drawings of which:
FIG. 1 illustrates a normal EKG.
FIG. 2 illustrates a seemingly normal EKG.
FIG. 3 illustrates the normalized integration of EKGs.
FIG. 4 illustrates transformed normalized integration of EKGs in polar
coordinates.
FIG. 5 illustrates a normal EKG template with isoclines.
FIG. 6 illustrates a transformed normal EKG within the normal EKG template.
FIG. 7 illustrates a transformed seemingly normal EKG outside the normal
EKG template.
FIG. 8 illustrates a plot of the point function P.sub.1.
FIG. 9 illustrates a block diagram of a signal processing system for
carrying out the present invention.
FIGS. 10A and B illustrate a flowchart of the method of the present
invention.
FIG. 11 illustrates the joint angles used to analyze the gait of a test
subject.
FIG. 12 illustrates a series of walk cycle steps comprising one complet
walk cycle.
FIG. 13 illustrates a plot of the joint angles shown in FIG. 1 versus walk
cycle fraction of a single walk cycle.
FIG. 14 illustrates a response signature representative of a normal gate
for the left knee of a test subject, and the corresponding standard
signature template therefor.
FIG. 15 illustrates a response signature representative of an abnormal gait
for the right knee of a test subject, and the corresponding standard
signature template therefor.
FIG. 16 illustrates a topological transformation of the data shown in FIG.
14.
FIG. 17 illustrates a topological transformation of the data shown in FIG.
15.
FIG. 18 illustrates a response signature representative of an abnormal gait
for the left hip of a test subject, and a corresponding offset standard
signature template therefor.
FIG. 19 illustrates an offset topological transformation of the data shown
in FIG. 18.
FIG. 20 illustrates a response signature representative of a normal gait
for the left knee of a test subject, and a corresponding offset standard
signature template therefor.
FIG. 21 illustrates an offset topological transformation of the data shown
in FIG. 18.
FIG. 22A illustrates a typical EKG for a normal subject.
FIG. 22B illustrates an offset geometric transformation of the data of FIG.
22A.
FIG. 23A illustrates a typical EKG for a diabetic subject.
FIG. 23B illustrates an offset geometric transformation of the data of FIG.
23A.
FIG. 24A illustrates a typical EKG for a cancerous subject.
FIG. 24B illustrates an offset geometric transformation of the data of FIG.
24A.
FIG. 25 illustrates a typical spectral graph for tetradecane.
FIG. 26 illustrates a normalized integration of spectrographic data.
FIG. 27 illustrates typical transformed spectrographic data.
FIG. 28 illustrates transformed spectrographic data for multiple organic
compounds in a functional group superimposed on the same coordinate
system.
FIG. 29 illustrates an organic compound functional group template derived
from the data of FIG. 28.
FIG. 30 illustrates the determination of average percent transmittance from
a typical spectral graph.
FIG. 31 illustrates a response signature representative of an organic
compund belonging to the same functional group as the template.
FIG. 32 illustrates a response signature representative of an organic
compound that does not belong to the same functional group as the template
.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
The teachings of the present invention are applicable to the
characterization of various types of physical systems having a variant
history. Although, it will be described primarily in conjunction with the
analysis of electrocardiographic data obtained from animate subjects,
other applications for the present invention will also be discussed.
FIG. 1 illustrates an electrocardiogram 11 taken from a truly normal
subject. As shown therein, the electrocardiographic signal is time varying
and periodic, i.e., it starts at a time t.sub.0 and ends at a time
t.sub.1, at which point it repeats itself. Electrocardiographic signal 11
is exemplary of actual electrocardiograms taken from a human control group
consisting of caucasian males between the ages of 28 and 72. As one
skilled in the will appeciate, the electrocadiographic data representative
of other major groups of medical subjects may differ somewhat from this
particular control group.
FIG. 2 illustrates an electrocardiogram 12 taken from a seemingly normal,
i.e., pre-coronary, subject. It is also a periodic time-varying signal,
and is exemplary of electrocardiograms taken from a human control group
consisting of caucasian males between the ages of 28 and 72, all of whom
had a coronary episode within five years after the taking of their
electrocardiogram.
Visually, electrocardiographic signal 11 does not appear to differ
significantly from electrocardiographic signal 12. However, as noted
above, the members of the control group from which the data presented in
FIG. 1 was obtained did not experience a coronary eposide within ten
years, if at all, after the taking of their electrocardiogram, whereas the
members of the control group from which the data presented in FIG. 2 was
obtained did experience a coronary episode within five years after the
taking of their electrocardiogram. Hence, this former data is
characterized as being taken from a seemingly normal subject.
According to the present invention the differences between data obtained
from a truly normal subject, exemplified by FIG. 1, and data obtained form
a seemingly normal, or latent coronary subject, exemplified by FIG. 2, can
be enhanced by plotting the data in polar coordinates obtained using the
following non-linear transformation:
##EQU1##
where V(t) is the time-varying signal of the electrocardiogram;
.vertline.V(t).vertline. is the absolute value of V(t);
t is the variable time;
t.sub.0 is the point in time at which the electrocardiographic data
acquisition process is initiated;
t.sub.1 is the point in time at which the waveform V(t) repeats itself;
.phi. is the integrated, normalized representation of the time varying
signal V(t);
r is the radius vector of the transformed
.theta. is the angle of the radius vector r;
T equals (t/t.sub.1); and
f(T) is an arbitrarily selected predetermined function of the normalized
variable T which may be chosen as a straight line (see FIG. 3) or the
average of a group of normal curves, or the average of a group of
non-normal curves.
When Equations (2) and (3) are plotted in polar coordinates for data
representing electrocardiograms obtained from truly normal subjects,
curves such as the curves 13 illustrated in FIG. 4 are obtained. Once the
data representative of a sufficient number of normal cases has been
plotted, a corresponding standard signature composite template can be
formed. The template 14 for curves 13 is shown in FIG. 5. It includes a
primary signature portion comprising a closed two dimensional region 15
within a pre-defined transformed coordinate system having an inner
boundary 16 and outer boundary 17 derived from the curves 13 of FIG. 4;
and a secondary signature portion comprising segments or isoclines 18 of
some of the normal curves 13 which are substantially, or nearly, parallel.
These segments or isoclines are emphasized in FIG. 5.
Isoclines 18 further subdivides the "normal" region 15 between the inner
and outer boundaries thereof, and are utilized as follows. Referring to
FIG. 6, the standard signature tempate 14 shown in FIG. 4 is shown therein
in phantom to emphasize that a truly normal electrocardiographic signal
plot 19 lies wholly within the inner and outer boundaries 16 and 17 of the
closed region 15 comprising the primary portion thereof and does not cross
any of the secondary isoclines 18 situated therein. In contrast, a
seemingly normal electrocardiographic signal plot 20 obtained from a
pre-coronary subject will, as shown in FIG. 7, either fall, partially or
entirely, without bounded region 15 of template 14 (also shown in phantom
for emphasis purposes), or if entirely within the bounded region will
cross one or more of the isoclines 18 situated therein. It is these
characteristic conditions which identify pre-coronary subjects who would
otherwise appear normal using known diagnostic techniques.
In accordance with the present invention, a response signature (polar plot)
is made for each of the standard electrocardiographic leads utilized to
obtain data from a test subject, and compared to a corresponding standard
signature template. Although there are twelve standard
electrocardiographic leads, the principles of the present invention will
be illustrated in conjunction with a discussion of the I, II, V.sub.4 and
V.sub.6 leads. However, it is noted that the teachings of the present
invention may be applied to as few as one or many as twelve
electrocardiographic leads.
Comparisons between the response signatures of the utilized cardiographic
leads and the corresponding standard signature template is readily
effected by overlaying the transformed response signature and its
corresponding standard signature template. If a transformed response
signature for any of the above-noted electrocardiographic leads falls
without the boundaries of the corresponding standard signature template or
crosses one or more isoclines situated within the bounded region therein,
it is deemed positive and assigned a value of +1. Similarly, if a
transformed response signature for any of the above-noted
electrocardiographic leads falls entirely within the boundaries of the
corresponding standard signature template and does not cross any of the
isoclines situated within the bounded region, it is deemed negative and
assigned a value of -1. For any transformed response signatures for which
none of the above conditions are apparent it is deemed inconclusive and
assigned a value of zero.
The present invention also utilizes point functions which, contrast to what
might be characterized as path functions which display an entire signal
waveform as a transformed line, compress essential geometric features of
an original signal waveform or a transformed signal waveform into single
points. Illustrative examples, as applied to the subject of the present
discussion, are the area of he electrocardiographic signal, the arc length
of the electrocardiographic signal, the area of the .phi., T signal, the
arc length of the .phi., T signal, the area of the r, .theta. curve, and
the arc length of the r, .theta. curve.
It has been found that better predictive results are achieved when the
above-identified point functions are combined in a non-dimensionalized
form and plotted with respect to one another. Illustrative examples of
such point functions by coordinates are the following:
P.sub.1 =[(electrocardiographic signal arc length).sup.2
.div.(electrocardiographic signal area), versus (.phi., T arc
length).sup.2 .div.(.phi., T area)]
P.sub.2 =[(electrocardiographic signal arc length).sup.2
.div.(electrocardiographic signal area), versus (r, .theta. arc
length).sup.2 .div.(r, .theta. area)]
P.sub.3 =[(.phi., T arc length).sup.2 .div.(.phi., T area), versus (r,
.theta. arc length).sup.2 .div.(r, .theta. area)]
It is noted that point functions, P.sub.1, P.sub.2 and P.sub.3 are
exemplary and do not represent the total number of possible point
functions for a given signal waveform. Nevertheless, for
electrocardiographic data evaluation it has been found that optimum
results, i.e., a maximum detection rate and a minimum false positive rate,
are obtained by utilizing seven sets of data obtained from the test
subject, i.e., data obtained from the I, II, V.sub.4 and V.sub.6
electrocardiographic leads and the point functions, P.sub.1, P.sub.2 and
P.sub.3, defined above.
The data exhibited in FIG. 8 were obtained by calculating and plotting
P.sub.1 for a large group of test subjects. As shown therein, the data
fell into three definable regions. One region 21 contains a clustering of
data points, (denoted by N's) obtained from normal test subjects; another
region 22 contains a clustering of data points (denoted by C's), obtained
from pre-coronary test subjects, and the third region 23 contains a mixed
clustering of N's and C's and thereby precludes meaningful data
discriminations. The three regions of FIG. 8 are separated by curved lines
which may be fitted to the plotted data by means of curve fitting
techniques for maximum accuracy.
The same procedure previously described for the electrocardiographic lead
is followed for each of the point functions. Using data obtained from a
test subject, or transformed data representative thereof, the P.sub.1,
P.sub.2 and P.sub.3 point functions are calculated and plotted on the
standard P.sub.1, P.sub.2 and P.sub.3 plots, respectively. If the
calculated point function yields a value which falls within the
pre-defined clustering of N points 21 it is deemed negative and assigned a
value of -1; if the calculated point function yields a value which falls
within the pre-define clustering of C points 22 it is deemed positive and
assigned a value of +1; and if the calculated point function yields a
value which falls within the pre-defined clustering of N and C points 23
it is deemed inconclusive and assigned a value of zero.
Multiplicative weighting factors, which may vary for each of the
electrocardiographic leads and point functions, are assigned to the
numerical constants .+-.1 or zero. In general, these weighting factors are
developed using empirical data obtained from actual population samples.
Specifically, electrocardiogram data are obtained for each of the
individuals in the population sample. The subsequent coronary history of
each of the sample members is then monitored to identify a sub-sample
group of "normal" individuals. A normal standard signature template is
then developed from this sub-sample group.
The specific weighting factors are obtained by trial and error using a
computer to carry out multiple iterations of number substitutions until
corresponding results are achieved. The final selection of the weighting
factors is based on the desired detection rate and/or the false positive
rate. The detection rate is defined as the percentage of sick subjects
detected as sick, while the false positive rate is defined as the
percentage of normal subjects detected as sick. Depending upon the
particular application, the weighting factors will be selected to adjust
one variable or the other.
For example, where the present invention is used to screen potential pilots
for the Air Force, it is desirable to select the weighting factors to
maximize the detection rate. In this instance there would be little effort
to minimize the false positive rate.
For an insurance company seeking to screen potential insureds the weighting
factors would be selected to minimize the false positive rate. In this
instance a relatively low detection rate would be satisfactory. As one
skilled in the art will appreciate, the two variables are interdependent,
but not complimentary.
Thus, for the four lead, three point functions electrocardiographic system
described above, the weighting factors selected would depend upon the
particular application in which the present invention is used and the
selection of the population to which the test subject belonged.
The weighted sum of the test data, i.e., electrocardiographic test lead
data and calculated point functions values, is designated as the Lundy
index and is given by the following expression:
##EQU2##
where n=the number of different tests utilized;
w.sub.i =i.sup.th weighting factor; and
N.sub.i =i.sup.th numerical constant (0, {1).
As will be illustrated in more detail below, the value, i.e., magnitude and
sign, of the Lundy index provides a valuable tool in analyzing and
predicting the likelihood that a particular test subject is going to
experience a future coronary episode.
The data obtained in Table 1 below illustrates the teachings of the present
invention to test data obtained from six different test subjects. As
illustrated therein, seven types of data were obtained for each of the
test subjects. In particular, evaluation data were obtained from the I,
II, V.sub.4 and V.sub.6 electrocardiogram test leads; and, in addition the
P.sub.1, P.sub.2 and P.sub.3 point functions were calculated in
conjunction with the electrocardiographic data obtained from the leads.
Examining the data from Table I obtained for the second subject illustrates
the teachings of the present invention. Specifically, since the
transformed response signal corresponding to the data obtained with the
electrocardiographic lead I was found to lie wholly within the bounded
region of the composite standard signature template for lead I and did not
cross any of the isoclines situated therein, it was deemed to be negative
and was assigned a value of -1. Since the transformed response signal
corresponding to the data obtained with the electrocardiographic lead II
was found to be wholly within the bounded region of the composite standard
template for lead II but crossed one or more of the isoclines situated
therein, it was deemed to be positive and was assigned a value of +1.
Similarly, since the transformed response signal corresponding to the data
obtained with the electrocardiographic lead V.sub.4 was found to be not
wholly within the bounded region of the composite template for lead
V.sub.4, it was deemed to be positive, and assigned a value of +1. And
finally, since the transformed response signal corresponding to the data
obtained with the electrocardiographic lead V.sub.6 was not found to
satisfy clearly any of the above conditions, it was deemed to be
inconclusive and assigned a value of zero.
The three point functions, P.sub.1, P.sub.2 and P.sub.3, were calculated
and plotted on the respective response templates for the P.sub.1, P.sub.2
and P.sub.3 functions. Since each one was found to fall in the C
(pre-coronary) region (e.g., region 22 of FIG. 8), it was deemed to be
positive and assigned a value of +1.
The next step was to calculate the value of the Lundy index for the test
subject. To determine this value the respective numberal constants were
multiplied by the corresponding weighting factors. As noted in Table I,
the factors for the I, II, V.sub.4 and V.sub.6 electrocardiograph leads
were empirically determined in accordance with the criteria articulated
above to be 2, 5, 3 and 1, respectively. Similarly, the factors for the
P.sub.1, P.sub.2 and P.sub.3 point functions were determined to be 2, 1
and 3, respectively.
Accordingly, the Lundy index, L, for this subject is equal to the weighted
sum of (2)(-1)+5(+1)+(3)(+1)+(1)(0)+2(+1)+1(+1)+3(+1) or +12. Since this
number is positive, this case is designated as a coronary candidate.
Accordingly, the significance of the Lundy index as a diagnostic tool in
indicating the probability that, and the approximate length of time before
a coronary episode will occur in the absence of medical intervention is
apparent. In particular, an inverse relationship between the Lundy index
and the length of time before an episode is indicated, i.e., a large
positive Lundy index indicates a short interval to the coronary episode.
Conversely, a direct relationship between the Lundy index and the
probability of a future coronary episode is indicated, i.e., a large
positive Lundy index indicates a strong probability that a coronary
episode will occur. The larger this index, the greater the probability and
the shorter the time. A negative Lundy index, indicates freedom from heart
disease. The more negative it is, the greater is the degree of certainty
regarding the absence of heart disease.
FIG. 9 is a block diagram of a system that can be utilized to implement the
exemplary embodiment of the present invention. The heart of the system is
a microprocessor based computer 25.
FIGS. 10A and 10B illustrate a flow chart of the method of the present
invention. It can be used as the basis for a program utilized by
microprocessor 25 to carry out the method of the present invention. As
shown in FIGS. 10A and 10B, the method steps of the invention include the
acquisition, integration, normalizaton, transformation and comparison of
data representative of a pre-defined physical state. These steps will be
discussed in detail in conjunction with both the block diagram of the
system illustrated in FIG. 9 and some of of the other figures included
herein.
Referring to FIG. 9 first, illustrated therein are a series of leads 26
which correspond to electrocardiograph leads I, II, V.sub.4 and V.sub.6.
These leads are used to obtain electrocardiographic data from a test
subject from whom it is desirous to predict the possibility of a furture
coronary episode.
The information obtained by probes 26 is fed into a macro-shock protection
circuit 27, a safety feature incorporated to protect a test subject from
the possibility of electrical shock. The output of this circuit is then
suitably amplified and filtered by a preamplifier 28 and an amplifier 29,
and a low pass filter 30, respectively. Because the raw
electrocardiographic signal is in analog form, it is necessary that it
first be converted to a suitable digital format prior to it being input
into microcomputer 25. An A/D converter 31 performs this function.
As indicated by program step 32 of FIG. 10A, an electrocardiograph signal
V(t) is measured for each of leads I, II, V.sub.4 and V.sub.6 over one
complete cycle and stored by microcomputer 25 in a floppy disc storage 33,
or alternatively, in an audio-cassette storage 34. For program execution
purposes only, these electrocardiographic leads are then assigned lead
numbers 1-4 as indicated at step 36.
Taking the response signal for electrocardiographic lead I first,
microcomputer 25 in accordance with the method of the invention integrates
the absolute value of the electrocardiographic data over time (step 37).
This integral is then normalized in step 38 by calculating .phi. in
accordance with equation 1. An example of this calculation is illustrated
in FIG. 3 by curve 39, depicted more heavily than similar curves 40 also
illustrated therein. Using equation 2 and the pre-determined function
f(T), microcomputer 25 then calculates the differences between f(T) and
curve 39 for T=0-1 (step 41). The result, r, is the radius vector of the
transformed electrocardiographic data obtained from the test subject.
Upon completing the calculations for the radius vector r, microcomputer 25
then computes the corresponding radius vector angle .theta. using equation
3 for the values of T=0-1 (step 42). Once the polar coordinates r and
.theta. have been calculated, they are plotted using a display unit 43,
which may be an oscilloscope or an x-y plotter (step 44).
Operating in conjunction with a D/A converter 45, unit 43 traces a response
signature 46 for curve 39 (shown in FIG. 4). Once this plot has been
completed, point functions P.sub.1, P.sub.2 and P.sub.3 are computed for
signature 46 by microcomputer 25 as indicated by step 47. At step 48
signature 46 is then superimposed on the corresponding standard signature
template for normal EKGs for lead I, which is similar to the template
shown in FIG. 5.
The result as indicated by step 49, is then displayed via display unit 43.
If the plot is within the corresponding template, a negative weight is
assigned to lead I and stored by microcomputer 25 (step 50). Conversely,
if the plot is outside the template a positive weight is assigned to lead
I and stored for further use (step 51). Where neither condition is
apparent, signature 46 is deemed inconclusive and assigned a weight of
zero (step 52).
Thereafter, microcomputer 25 proceeds to superimpose the point functions
calculated in step 47 on the point function plots for point functions
P.sub.1, P.sub.2 and P.sub.3 for lead I as generally indicated by routine
53. If a point function falls in pre-coronary region 22 it is assigned a
positive weight and stored at step 54. In contrast, at 55 if a point
function falls in the normal region 21, it is assigned a negative weight
and stored. Where the point function falls in the no test region 23,
microcomputer 25 | | |
