Friday, March 23, 2012

Fetal Tissue Doppler Z-Scores

Reference values and z-score calculations for fetal tissue Doppler E, A, and S waves added to new fetal echo z-score app.

I just wrapped up the design and implementation of a new fetal echo z-score site ( and as a test of the new modular design, I added the fetal tissue Doppler data from this recent article:

Gestational age- and estimated fetal weight-adjusted reference ranges for myocardial tissue Doppler indices at 24-41 weeks' gestation.
Comas M, Crispi F, Gómez O, Puerto B, Figueras F, Gratacós E.
Ultrasound Obstet Gynecol. 2011 Jan;37(1):57-64.

Although the article provides equations that adjust for fetal weight, since no pediatric cardiologist has ever asked me to estimate the fetal weight *wipes brow*, I have only included the gestational age-adjusted equations.

Jumping ahead for just a second, here is an example of the results page:

screenshot of fetal z-score app: results

fetal tissue Doppler z-scores for a 28wk4d fetus

and here is an example chart:

screenshot of fetal z-score app: TDI plot

fetal tissue Doppler LV TDI S vs. EGA


Implementing a class that provided a common interface for calculating a mean, range, and z-score was non-trivial for this reference. There are no fewer than 5 distinct models that govern the E’, A’, and S’ calculations:

  1. linear model with constant variance
  2. linear model with non-constant variance
  3. log-linear model with constant variance (log-normal)
  4. log-linear model with non-constant variance (NOT log-normal ?)
  5. log-polynomial model with non-constant variance (NOT log-normal?)

A second challenge was getting my calculations (based on the published data) to reconcile with the supplemental material (an Excel spreadsheet). In a few instances the spreadsheet used data with more significant digits than in the article, and in a few other instances the spreadsheet incorrectly exponentiates the “standard deviation” term. In the end, I figured that I had to go with the published data over the supplemental data. Also, it became clear after referring to the charts that the spreadsheet data was incorrect.


Apart from the multiple models and the occasional inconsistency in the formulae, there is also the small matter of the article failing to provide the typical correlation coefficients for the models, and, therefore, necessarily omitting the “R-squared” values. The R2 tell us about the goodness-of-fit or, sometimes, how much of the variance is explained by the model. For some of the dependent variables this seemed like an important omission as the models appear promising. I have included the data for the E’, A’, and S’ because they do look somewhat promising. I did not include the data for the derived values like the E’/A’,  E/E’ ratios or the MPI calculations because, to me, they seem dodgy—particularly without an R2.


  1. New fetal echo z-score calculator
  2. New calculations for fetal tissue Doppler
  3. I welcome your comments and criticisms

Sunday, March 4, 2012

The Problem with Indexing Volumes to BSA

Wherein the inappropriate indexation of cardiac volumes to BSA is explored, this time with charts!

For some time now I have been aware of and abiding by the following words of caution:
linear dimensions and volumes have a nonlinear relation to surface area and
are more appropriately indexed by surface area to the 0.5 and 1.5 power, respectively.

-- Gutgesell and Rembold, Am J Cardiol. 1990
But since I work mostly with echocardiography and echocardiography has, mostly, gotten this message I haven’t explored the problem much. Recently though, I have been reading some of the cardiac MRI literature. Plus, it’s hard not to see some reference to CMR even in the echo literature. A lot of the CMR literature seem to use a cutoff for ventricular chamber enlargement like:
170 ml/m2
And, in the search for improving the sensitivity of echo, many study designs pit echo measures against CMR measures.
So what is the problem?
What are the consequences of an inappropriate index?

I put together a few charts that helped me to understand the real hazards of what sounds like a mostly theoretical problem—maybe they will be useful to others as well:


This chart shows the expected nonlinear relationship between RVEDV and BSA: the predicted values (grey) and the somewhat arbitrary z-score upper limit of +4 (red) are those of Buechel et al.; the conventional cutoff values of 170ml/m2 are in yellow. Note that only at one place along the BSA spectrum is there an overlap of z-score and conventional indexed values: in this case, at somewhere around 1.7m2 (a medium –sized adult). Moving away from that intersection, for BSA values lower than 1.7, it is increasingly likely that a measured RV volume will be interpreted as “below the cutoff value", yet exceed a z-score of +4.
For BSA values above approximately 1.7m2, the reverse is true: it is increasingly likely that a measured RV volume will exceed the indexed cutoff value, yet fall below a z-score of +4.

Equivalent Z-Score for 170ml/m2 vs. BSA

This chart shows the equivalent z-score (Buechel et al.) for the conventional cutoff values of 170ml/m2 over the entire range of BSA.

The problem of using an inappropriately indexed value isn’t purely theoretical, and it isn’t just a matter of making it harder for echo researchers to find statistical significance—it is a matter of finding or, frankly, missing patients with important, real, abnormalities.