Wolfram Blog
Koji Maruyama

Distinguishing Risks of Modes of Cardiac Death in Heart Failure with Machine Learning

November 20, 2020 — Koji Maruyama, Sales Engineer

Distinguishing Risks of Modes of Cardiac Death in Heart Failure with Machine Learning

In medical fields like cardiology, the Wolfram Language continues to help researchers make discoveries and predictions. I recently coauthored a study that uses the machine learning functionality of the Wolfram Language to predict risks of deaths due to heart failure. In it, we aimed to build a classifier that is capable of distinguishing the probabilities of cardiac death caused by end-stage heart failure (HFD) and severe arrhythmic events/sudden death (ArE). What follows is a summary of the paper we published earlier this year.

Reliable risk stratification models are coveted for selecting appropriate therapies in the treatment of chronic heart failure, a serious health problem in current aging societies. Despite the substantial progress in pharmacological treatment and various devices, the mortality rate is still high. The therapeutic management of high-risk patients is also very difficult and costly, involving implantable cardioverter defibrillators and resynchronization therapy. With these concerns in mind, we studied the applicability of machine learning techniques, with the help of the Wolfram Language, to distinguish the risks of HFD and ArE in patients with chronic heart failure.

Significance of Each Outcome and Important Parameters

In the supervised learning we have implemented, the inputs are comprised of 13 clinical variables, such as age, sex, severity of heart failure (functional class defined by the New York Heart Association), etc., and the output has three classes, namely: (1) heart failure death (HFD); (2) fatal arrhythmic events (ArE); and (3) survival (alive) during a two-year period of follow-up.

When a patient with chronic end-stage heart failure dies, it is classified as HFD. In such patients who are typically elderly and/or associated with heart diseases, the pumping ability is deteriorating and the ventricular ejection fraction is low. Deaths due to ArE consist of sudden cardiac arrests and deaths, and also include appropriate functioning of a defibrillator against life-threatening arrhythmic events, because an irremediable consequence must have been inevitable without the therapy by defibrillator.

Let us briefly describe 123I-metaiodobenzylguanidine (MIBG) scintigraphy and an index obtainable thereby before showing the result. It is one of the diagnostic tests in which radioisotopes are labeled to substances that accumulate in a specific organ and the distribution of gamma ray radiation is detected to form an image, i.e. a scintigram. Among other things, it has been found that the heart-to-mediastinum ratio (HMR) calculated from 123I-MIBG can be a useful indicator for cardiac mortality risk, when combined with other clinical parameters. Therefore, we want our classifier to be able to show distinct probabilities for the three classes, i.e. HFD, ArE and Survival, as a function of 123I-MIBG HMR. Nevertheless, the HMR alone is not very useful for our purpose, thus 12 other parameters are incorporated into the set of predictor variables.

The HMR is calculated as the ratio Ch/Cm, where Ch and Cm are the mean pixel values of areas corresponding to the heart and the upper part of the mediastinum, respectively, in the 123I-MIBG image. The mediastinum is, roughly speaking, the area surrounded by the two lungs. Since the edges of organs in scintigrams are rather blurred, it is in general hard to select the relevant regions and compute the pixel values systematically. Following is a quick Wolfram Language app to facilitate the region selection and automatic evaluation of the HMR as well as other indices. This may be widely welcomed once further improvements, such as automatic region selection, are implemented.

This sample app provides a GUI, with which one can select the regions corresponding to the heart (circle) and mediastinum (rectangle) in the given DICOM image, and the results of calculations using pixel values in those regions are simultaneously displayed:

img = CloudGet
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"], {{0, 256}, {256, 0}}, {0, 65535},
ColorFunction->GrayLevel],
BoxForm`ImageTag[
      "Bit16", ColorSpace -> "Grayscale", Interleaving -> None],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSize->Automatic,
ImageSizeRaw->{256, 256},
PlotRange->{{0, 256}, {0, 256}}]\)*1000; igs = ImageAdjust[img]

dk = ColorNegate
&#10005

dk = ColorNegate[Graphics@Disk[]];
p10 = {155, 120}; p11 = {160, 138};
p20 = {123, 160}; p21 = {133,
  180};                                                               \
                                                                      \
         Dynamic[
 trm1rct =
  ImageTrim[igs, {p10 - Norm[p10 - p11], p10 + Norm[p10 - p11]}];
 (* extract circular region around heart:  trm1*)
 trm1 = ImageMultiply[trm1rct,
   ImageResize[dk, ImageDimensions[trm1rct][[1]]]];
 (* extract rectangular region in mediastinum: trm2 *)

 trm2 = ImageTrim[igs, {p20, p21}];
 (* select pixel values that are larger than zero *)

 mat1 = Select[Flatten@ImageData[trm1], # > 0 &];
 mat2 = Select[Flatten@ImageData[trm2], # > 0 &];
 mean1 = Mean[mat1];
 mean2 = Mean[mat2];
 max1 = Max[mat1]; max2 = Max[mat2];
 min1 = Min[mat1]; min2 = Min[mat2];
 std1 = StandardDeviation[mat1]; std2 = StandardDeviation[mat2];
 Column[{Show[
    HighlightImage[
     Image[igs,
      ImageSize -> 500], {EdgeForm[{Green, Thickness[Medium]}],
      Graphics[Rectangle[p20, p21]]}],
    Graphics[{Line[{p10, p11}], {White, Thickness[Small],
       Circle[p10, Norm[p10 - p11]]},
      Locator[Dynamic[p10], Appearance -> Small,
       Background -> LightPink],
      Locator[Dynamic[p11], Appearance -> Small,
       Background -> LightBlue],
      Locator[Dynamic[p20], Appearance -> Small,
       Background -> LightPink],
      Locator[Dynamic[p21], Appearance -> Small,
       Background -> LightBlue]}, PlotRange -> {0, 152},
     ImageSize -> 600]],
   Grid[{{"", "Mean", "Std dev", "Max", "Min"}, {"Heart", mean1, std1,
       max1, min1}, {"Mediastinum", mean2, std2, max2,
      min2}, {"H/M Ratio", mean1/mean2, "", "", ""}}, Frame -> All]}]]

Applying Machine Learning

We have performed receiver operating characteristic (ROC) analysis to select the most suitable method for modeling the cardiac risk evaluation. By area-under-the-curve (AUC) analysis, using 75% of the data for training and 25% for validation, we have found logistic regression best for our purpose.

Now that we have chosen logistic regression as the method, the rest is simply the generation of a classifier function using Classify in the Wolfram Language. The data to be fed is a set of lists of the form:

{var1, var2, var3, var4, var5, var6, var7, var8, var9, var10, var11, \var12, var13, outcome}

For example:

{62, m, 2, 87, 40, 1.62, 35, 0, 1, 11.2, 1, 0, 0, 0, ArE},{52, m, 1, 70, 28, 2.29, 30, 0, 0, 15.6, 0, 0, 0, 1, HFD},{69, f, 1, 40, 48, 1.16, 31, 1, 0, 13.7, 4, 1, 0, 0, Alive},...

For this study, we have used data from 105 cases of HFD and 37 cases of ArE from a cohort of CHF patients in Japan. Having randomly chosen 75% of the data to be the training set (trainingSet in the following), the training is done automatically by:

cs = Classify
&#10005

cs = Classify[trainingSet, Method -> "LogisticRegression", ValidationSet -> testSet]

… where testSet is the test set, i.e. the remaining 25% of the data. (Note that the training and test data cannot be disclosed here, so this section only demonstrates the study’s method.)

Detailed information, e.g. the final value of the loss function and “learning curve,” can be checked with:

Information
&#10005

Information[cs]

Now we can evaluate the accuracy and other indices of the classifier with the test set:

measTestc = ClassifierMeasurements
&#10005

measTestc = ClassifierMeasurements[cs, testSet]measTestc[{"Accuracy", "AreaUnderROCCurve"}]

When the function ClassifierMeasurements is applied to the training set, it returns:

ClassifierMeasurements

This shows that the degree of overfitting is rather mild and the accuracy of 0.827 for the test set is quite high. Not only the value itself, but also the quantitativeness of the risk evaluation is the point. The deviation of a judgement criterion is inevitable as far as we rely on individual human eyes, while we may be able to expect a more quantitative diagnosis for a patient’s condition, when more clinical data is accumulated.

The following figure is the plot of computed probabilities of each class of outcomes as a function of 123I-MIBG HMR, together with other parameters that are made discrete and shown as buttons on the left. The classifier function is the one obtained previously and the plot shown here is a snapshot of the output:

Manipulate
&#10005

Manipulate[
 Plot[{cs[{age, sex, nyha, gfr, ef, hx, wr, hd, isc, hb, bnp, ht, dm},
     "Probability" -> "Alive"],
   cs[{age, sex, nyha, gfr, ef, hx, wr, hd, isc, hb, bnp, ht, dm},
    "Probability" -> "HFD"],
   cs[{age, sex, nyha, gfr, ef, hx, wr, hd, isc, hb, bnp, ht, dm},
    "Probability" -> "ArE"]}, {hx, 1, 3}, PlotRange -> {0, 1},
  PlotLegends -> {"Surviving", "HFD", "ArE"}, GridLines -> Automatic,
  AspectRatio -> 1,
  LabelStyle -> Directive[Black, 14, ImageResolution -> 480],
  AxesLabel -> {"MIBG HMR", "Probability"},
  PlotStyle -> {Purple, Blue, Red},
  ImageSize -> Medium], {{age, 60.}, {50., 60., 70., 80.}}, {{sex,
   "m"}, {"f", "m"}}, {{nyha, 3}, {1., 2., 3., 4.}}, {{gfr,
   45.}, {30., 45., 60.}}, {{ef, 35.}, {20., 35., 50.}}, {{wr,
   20.}, {0., 20., 40.}}, {{hd, 0.}, {0., 1.}}, {{isc, 1.}, {0.,
   1.}}, {{hb, 10.}, {8., 10., 12.}}, {{bnp, 1}, {0., 1., 2., 3.,
   4.}}, {{ht, 0.}, {0., 1.}}, {{dm, 0.}, {0., 1.}}]

A noteworthy observation here is that the curve for ArE has a peak at an intermediate level of HMR. This tendency has been known only empirically, and our present result verified the speculation based on data. Moreover, although the conditions for this bell-shaped distribution to be realized have been unknown, our analysis sheds light in this respect quantitatively. For instance, such distributions are likely to occur for patients with intermediate New York Heart Association (NYHA) functional classes, which is consistent with the multi-facility research conducted with the data of NYHA classes 2 and 3 (out of 4) in the United States.

Next Steps

With the handiness of not only data manipulation, but also machine learning and the visualization of its results by the Wolfram Language, we were able to obtain a risk evaluation model for estimating the likelihood of death from heart failure and fatal arrhythmic events. The probability of fatal arrhythmic events has been segregated for the first time, especially with respect to the 123I‑MIBG HMR, among other clinical variables.

Since the resulting model is easy to export as an app, we expect that Wolfram Language–based apps or tools could be accessed by those who are in charge of making diagnoses and decisions as to subsequent therapeutic options.

For additional details and deeper analysis of the data and findings, read more about the study in our published paper.

Check out machine learning courses via Wolfram U or get full access to the latest Wolfram Language functionality with a Mathematica 12.1 or Wolfram|One trial.

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