One area of the diagnostic program which assesses the severity of a particular condition is in the identification of ST-T changes.
This area is notorious as one of the most difficult aspects of electrocardiography not least because the line dividing normal from abnormal is not sharp and normal ranges for components of the ST segment and T wave are wide (Macfarlane and Lawrie, 1989d). Clinically, there may be many possible causes of changes in the ST-T segment which further complicates any diagnosis.
This area will be discussed in a little more detail in Chapter 7 although reference will now be made to the interpretation of ST SLr,,*2,*3,Jt4)
depression and ST elevation since this is accomplished on the basis of the magnitude of two variables, namely ST amplitude and ST slope. Abnormalities of the ST segment are defined on the basis of the ST amplitude and slope, a clearly negative segment indicating marked ST depression and an obviously positive segment indicating significant ST elevation. Both ST depression and ST elevation are rather arbitrarily defined as moderate, marked or severe depending on the amplitude and slope, thereby providing a spectrum of the response. In this situation the response takes the form of a score which ranges from -3 to +3 describing the transition from marked ST depression through to significant ST elevation, i.e. there is a score function
S(x^,x2) defined by the rule:-
Xi < -1 0 0fjSJ an d x 2 <0° then jT 11 1 CO A 1 O and x2 < 0° then S(xl,x2) = - 2 o (N I V and x2 < 0° then S(xlfx2) = ~l
xx > 6QjuV and x2 > 0° then S(xltx 2) = 1
t i o oo A and x2 > 0° then S(xx, x2) — 2 r"io A then S(xt,x2) = 3 otherwise 5(x1,x2) = 0
where x, - ST Amplitude and x2 = ST slope. This is illustrated diagrammatically in Figure 5.11.
Figure 5 .1 1 0 -100 -50 -20 -2 -1 3 0" 25- 2 0' 15- 10- 5- -5 ■ o '0' -15- -2 0- -25- -30- 0 ST Amplitude 60 so 100 0 ( J _ S T Slope
Contour plot of the discrete ST Score 5(^ ,^ :2)
These criteria apply to lateral and inferior leads (I, II, III, aVL, aVF, V5 and V6) only. Slightly different threshold values for the amplitudes are used when considering leads V I, V2, V3 and V4.
Clearly there is potential for changes in the score due to small measurement changes especially the sudden jump from 0 to 3 in the lower right quadrant (see Figure 5.11). The methods which have been described earlier in this chapter can be used to form a smooth representation of namely 5*,«(x1,x2).
The negative contribution to 5*m(x,,x2) is calculated on the basis of the magnitude of the negative ST amplitude and the slope of the ST segment in the appropriate lead. This part of the score can range from 0 to -3 and may be expressed as follows :
S V * , , * , ) = - l x { ( l - F u) + ( l - F „ ) + ( l - F ls) } x ( l - * „ )
The positive contribution can be represented in a similar way.
where x x = ST Amplitude in lead of interest;
<jX) = estimated day - to-day variability in ST Ampl.;
x2 = ST Slope in lead of interest;
crt = estimated day - to-day variability in ST Slope.
F1‘ = . 6 ’ l + e n © o 1 II -cT II bx = 60; -C) ii <2, =0. » ^21 ~ a . * ^1 “ l + e 1x1
The overall smoothed score can now be calculated as the sum of the separate components (jcp j:2) and S*mt ( x l9x 2) since neither of these will contribute substantially to the other in the appropriate ranges, i.e.
S m ( X j , X 2 ) = S m, , X 2 j + 5 nij , X 2 ^
Figures 5.12 and 5.13 illustrate the surface plots of the score functions based on the discrete and on the new smoothed methods respectively. Figure 5.13 demonstrates the advantage that Smm(xx,x2)
has over S(x{,x2) ( see Figure 5.12) in terms of continuity.
5(^1 ,x2)
100
ST Slope 80 ST Amplitude
Figure 5 .1 3 Surface plot of Sm*(x:,x2)
5 .7 SUMMARY.
This chapter has introduced the concept of 'smoothing out' discrete thresholds by replacing them with continuous functions. These functions, which are based on cumulative distribution functions for computational convenience rather than on any principle of probability theory, are used to provide smoothed versions of previously discrete diagnostic indices in both the single and multiple threshold situations. They have an additional advantage of taking into account the natural day-to-day variability occurring in each ECG measurement which dictates the amount of 'steepness' associated with each new smoothed diagnostic index. !
Since many diagnostic decisions are based on collections of combined criteria we have also evolved a methodology for the
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treatment of such combinations. The union rule can be used to smooth out the diagnostic index in the situation where a certain action is to be taken when e i t h e r one of two conditions is met. Similarly, the intersection rule may be implemented if b o t h criteria are to be satisfied simultaneously before an action is taken. Combinations of the m a x i m a and m i n i m a rules may be manipulated to cater for situations when more than two conditions are being considered.
Basing an algebra of score construction on these criteria allows us to smooth out many complicated forms of 'discrete' rules which are encountered throughout the diagnostic process.
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