Sunday, November 29, 2009

Pediatric RV Function (TAPSE) Z-Score Calculator

Z-Scores for RV systolic function.

Using data published in the June 2009 JASE, this calculator determines the age-adjusted Tricuspid Annular Plane Systolic Excursion (TAPSE) z-scores:



For the purpose of calculating the z-score, I used the published mean and "-3SD" lower limit to calculate each SD ([mean – lower limit] / 3)- which is a little bit off-label. That is, the standard deviation by itself is not published— only the ±2 and ±3 ranges are published— and there is some variation in how those back-calculate to "1 SD". Even though the title of the article suggest using the data for calculating z-scores, it is not perfectly clear how we are supposed to do this.

For the purpose of drawing the plot, I used the published ±2 SD values (the 2.5 – 97.5 percentiles).

While the authors note the independent influence of BSA on TAPSE (they also provide a separate graph for BSA vs. TAPSE), it is not clear to me how we are supposed to apply this information. For each age group, a TAPSE/BSA index value is determined by dividing the mean TAPSE by the mean BSA for each age group. The indexed values are noted to decrease with increasing age/BSA. However, no range of normal indexed values is given. The manner in which BSA was estimated for the study is not presented. The BSA vs. TAPSE data used to construct their graph are not published.


Right ventricular function in infants, children and adolescents: reference values of the tricuspid annular plane systolic excursion (TAPSE) in 640 healthy patients and calculation of z score values.
Koestenberger M, Ravekes W, Everett AD, Stueger HP, Heinzl B, Gamillscheg A, Cvirn G, Boysen A, Fandl A, Nagel B.
J Am Soc Echocardiogr. 2009 Jun;22(6):715-9. Epub 2009 May 7.

Wednesday, November 11, 2009

Skew in Echocardiographic Reference Data

some offhand observations about the treatment of skewness in pediatric echo reference data.

1. asymmetry in a frequency distribution.
2. a measure of such asymmetry.


Underlying the use of z-scores is an assumption about the symmetric nature of the distribution: the use of "Z" is because the normal distribution is also known as the "Z distribution". However, as noted elsewhere[1, 2], cardiac growth data are skewed to the right. Here are a few examples that I find remarkable.

Left Atrial Diameter

Neilan et al.[3] examined the nature of the relationship of body size to cardiac structures using the left atrial diameter as measured in over 15,000 normal patients. Their plot of LA diameter against body weight—and the underlying rightward skew—can be examined here: left atrial diameter vs. body weight. Although the chart is presented in the source article with logarithmic axes, "back transforming" the axes into natural units reveals the magnitude and direction of the skew.


Left Ventricular Mass

Using the LMS technique to deliberately account for skew (and non-constant variance), Foster et al.[4] provide the data used to construct the following curves: left ventricular mass vs. height (I used ±1.65 for the upper and lower bounds). Interestingly, while the LMS method handles the skew and variance in a discrete (although smoothed) fashion, applying a log transformation appears to control both phenomenon as well.


Fetal Data

Comparing the recently published[5] fetal echo z-score data with the earlier reference[6] reveals one obvious difference: the Boston data is modeled as having a normal distribution, with no obvious skew. What, I wonder, happens if the underlying data really does have rightward skew, but is modeled as a normal distribution? Hmm...



  1. Sluysmans T and Colan SD (2009). Structural Measurements and Adjustment for Growth. In Wyman Lai [et al.] (Eds.), Echocardiography in Pediatric and Congenital Heart Disease: From Fetus to Adult . Oxford: Wiley-Blackwell
  2. Abbott RD, Gutgesell HP. Effects of heteroscedasticity and skewness on prediction in regression: modeling growth of the human heart.
  3. Neilan TG, Pradhan AD, Weyman AE. Derivation of a size-independent variable for scaling of cardiac dimensions in a normal adult population.
  4. Foster BJ, Mackie AS, Mitsnefes M, Ali H, Mamber S, Colan SD. A novel method of expressing left ventricular mass relative to body size in children.
  5. McElhinney DB, Marshall AC, Wilkins-Haug LE, Brown DW, Benson CB, Silva V, Marx GR, Mizrahi-Arnaud A, Lock JE, Tworetzky W. Predictors of technical success and postnatal biventricular outcome after in utero aortic valvuloplasty for aortic stenosis with evolving hypoplastic left heart syndrome.
  6. Schneider C, McCrindle BW, Carvalho JS, Hornberger LK, McCarthy KP, Daubeney PE. Development of Z-scores for fetal cardiac dimensions from echocardiography.

Monday, November 2, 2009

More Fetal Echo Reference Values

Seems like I spent most of the month of October thinking about fetal echos in one form or another. Apart from the earlier release of the Fetal Echo Z-Scores: Femur Length calculator, I also developed a couple of "helper" routines:

  • A calculator to cross-check the femur length against the EGA derived from dates. Also Gives reference values for fetal thoracic circumference:

    Fetal Biometry

  • A remake of the CHOP calculator- useful for describing the hemodynamic status of the recipient twin in twin-twin transfusion syndrome (TTTS). Good stuff for reminding me about the various manners in which heart failure can be categorized by fetal echo:

    CHOP Fetal CV Profile Score

  • A calculator for fetal LV/RV/IVS wall thicknesses. In the absence of any published z-score equations, these two sources (one uses autopsy data) seem to be our only recourse:

    Fetal Ventricular Wall Thickness Reference Values

Additionally, the October 13 issue of Circulation brought a new fetal echo z-score reference:

Predictors of technical success and postnatal biventricular outcome after in utero aortic valvuloplasty for aortic stenosis with evolving hypoplastic left heart syndrome.
McElhinney DB, Marshall AC, Wilkins-Haug LE, Brown DW, Benson CB, Silva V, Marx GR, Mizrahi-Arnaud A, Lock JE, Tworetzky W.
Circulation. 2009
Oct 13;120(15):1482-90. Epub 2009 Sep 28.

I won't attempt an analysis beyond the smackdown itself because, as the authors reveal, these new z-score equations are based on

unpublished fetal norms…

Still, it is interesting (to me) to see the data published at all, and I think the smackdown sheds some interesting light on the two groups of equations.


Tuesday, October 13, 2009

Fetal Echo Z-Score Calculator: Updated

Cardiac valve, chamber, and arch z-scores based on femur length; predicted LMP/EDD/EGA; LV/RV size discrepancy ratios.

This update provides the following functionality:

Fetal cardiac z-scores calculated from femur length

According to the source article, each of the independent variables (EGA, FL, BPD) had similar performance, with the regressions based on femur length being slightly superior. I have not yet compared the z scores across the two calculations- it is likely that minor differences exist between z-scores based on femur length, and those based on the derived EGA.

Femur length estimates of EGA, EDD, and LMP

Since the ICAEL guidelines require reporting of the EGA (and manner of determination), this is estimated according to this common citation: New charts for ultrasound dating of pregnancy. Without getting wrapped up in the subtleties of another field entirely, this reference seemed suitable . From the looks of it though, EGA predictions by femur length alone are open to some criticism.

Size discrepancy ratios

A common referral for fetal echocardiography is the discovery on routine ultrasound of a "size discrepancy" between the left and right ventricles. The authors of this new article Left Ventricle to Right Ventricle Size Discrepancy in the Fetus: The Presence of Critical Congenital Heart Disease Can Be Reliably Predicted suggest the use of easily calculated ratios as a simple manner for stratifying the various underlying lesions. Ratios of 0.6 for each of the sites (MV/TV, LV/RV, AoV/PV) appear to have good predictive value- particularly when used in combination with the transverse arch measurement and descriptions of the flow across the atrial septum.

The topic of z-scores is touched upon briefly with reference to the transverse arch. Although the data presented suggests that the arch z-scores were significantly different between groups (intervention vs. not), no cutoff values for the z-score are suggested. It is interesting (to me) that the stated z-scores in the intervention vs. non groups is –4.7 vs. –3.2 (or, the difference between the 0.0001 percentile and the 0.0687 percentile !!). If one uses the normal boundaries of the 5th and 95th cumulative percentiles (z-scores of ±1.65), or the more liberal 2.3-97.3 percentiles (z scores of ±2), even the non-intervention group seems way out there.

It is also interesting to me that the chamber size and valve z-scores weren't discussed- at all. Many of the referrals for 'size discrepancy' seem more imagined than real, and z-scores of the left heart structures ought to provide evidence of normality, even if things appear discrepant. Along those lines, I am looking forward to the manuscript to follow this abstract: Fetal Cardiac Growth: New Z-Score Ranges From 3,000 Normal Pregnancies.

You can find the updated z-score calculator here: Fetal Echo Z-Score Calculator

Sunday, August 2, 2009

Pediatric Echo Z-Score Calculator: Children's Mercy Hospital

Calculate z-scores and normal ranges for 80+ echocardiographic measures including m-mode, 2D, and Doppler; generate z-score graphs.

While browsing, I more-or-less stumbled upon a great website put together by the good folks at Children's Mercy Hospital (Kansas City, MO). The depth and breadth of measurements is astonishing, as is the number of observations from which the reference values are generated.

CMH generated z-score graph

I understand an article is forthcoming— destined to be the largest and most encompassing work to date on normative values for pediatric echocardiography.

CMH Pediatric Echo Z-Score Calculator

Also worth reading, their newsletter announcement: Creating New Growth Charts


Congratulations (and thanks!) to Dr. Drake and his staff for creating an incredible resource and service.

Thursday, June 4, 2009

LV Mass Reference Values: Smackdown

I am starting to think I should change the tagline for this blog to:
more questions than answers
I am in the midst of building another smackdown calculator:

LV Mass Smackdown

I hope that it use is self-explanatory and that it requires no introduction- because I am now out of time (heading out to the ASE meeting!).
This is still a 'work in progress' (I seem to have lots of these). Upon my return from the nation's capitol, I plan to add additional functionality:
  • tips on measurement technique
  • input validation
  • automatically detecting discrepancies between references
  • allowing users the opportunity to provide feedback in the cases where there are discrepancies
I think this is going to be very interesting ...

Saturday, April 18, 2009

Critical Aortic Stenosis: Echo Calculations

Calculators for Critical Aortic Stenosis: Rhodes Score, Discriminant Score, and CHSS Survival Benefit

In a previous post I presented my first version of the Discriminant Score calculator. Since then, we (sonographers) still get asked to calculate a Rhodes Score (this score has achieved virtual Brand Name recognition at this point) for patients with what appear to be borderline anatomy- even though the Discriminant Score now updates and improves upon the older score. In the process of developing the calculator for the Rhodes Score I was also clued-in to the Congenital Heart Surgeons Society (CHSS) Survival Benefit score. So, I thought I could present calculators based on each of these manuscripts (references included):

A few procedural notes related to the actual calculations are probably worth mentioning:

  • Rhodes Score
    • an erratum was published in 1995 (the original article was published in 1991). This is not to be missed, as is corrects the misprinted formula for the area of an ellipse used to calculate the MV (annulus) area, thus the indexed MV area, and thus the overall score
    • I omit the calculation of LV mass as the authors note the technical difficulty of the measurement (particularly, I might add, in patients where the LV is misshaped)
  • CHSS Survival Benefit Score
    • this is not the CHSS's current survival benefit calculator (I still can't figure that one out); they prefer you not play "what if..." with theirs  :)
    • necessary calculations of the z-scores use the only published data available at the the time: the Wessex z-score data (discussed previously here)
    • swapping the aortic root z-score equations for the competition (i.e., the Boston data) can have a pronounced effect (try it yourself)

It is this last point that I find both fascinating and more than a little disturbing: the CHSS survival benefit score, the way it is published- referring to the Wessex z-score data- appears to have a built in bias against biventricular repair. That is to say, in my experience (see for yourself) the Wessex data has a small standard deviation, and thus, less tolerance for deviations from the mean, and calls "abnormal" too soon. Way, way too soon. So, if the choice to go down the single ventricle pathway is (somewhat) dependent upon the relative size of the measured structures, and the relative size is gauged by the z-score, and the z-scores are biased...

If the choice of z-score equations perches neonates on the balance of biventricular vs. univentricular repair, we should probably be thinking pretty hard about how and where we want to derive our reference values.

A consensus *cough* Z-Score Writing Project *cough* can't come soon enough.

Sunday, March 22, 2009

Pediatric Echo Z-Score Graphs

I have been working on different visualizations of the data we see and use every day in the pediatric echo lab.

Consider the following hypothetical patient data:

  t0 t1 t2 t3
Height(cm): 55 58 65 75
Weight(kg): 3.5 3.9 4.5 7
LMCA (mm): 2.9 2.95 3.2 3.5

A simple graph of these individual measurements over time- particularly for pediatric patients- is potentially a bit misleading:

Coronary Artery Measurement Time Series Graph

While the graph clearly conveys the information that the coronary artery size changes over time, unless you also happen to know what the normal values are for each point in time, there is no way to know if the change in size is pathologic, or simply due to somatic growth.

This is the entire reason we use z-scores.

So, maybe more to the point- at least for the purpose of trending- would be to graph the z-scores over time:

Coronary Artery Z-Score Time Series Graph

(This simple LMCA graphing routine can be found here.)

However, neither graph is entirely satisfactory for me.
I want to see both the absolute values and their relationship to normal values… more like this:

LMCA ZScore Plot

Using the coronary artery z-score data published from Boston and the enormously cool JavaScript plotting library, flot,  I built a few more z-score graphing routines:

They're not perfect (I'd like the z-score to show as a 'tooltip' when hovering over individual data points, and the axes need labels...), but they are a lot more fun. If they seem useful, I may release more of them into the wild.

I'd love to know what anyone else thinks about graphing their pediatric echo data.

(special thanks to the authors of "Normal values for aortic diameters in children and adolescents – assessment in vivo by contrast-enhanced CMR-angiography" for the inspiration)

Thursday, March 12, 2009

3D Lament (a haiku)

" give back the green" 
billing is not collecting
elevation plane

Wednesday, February 18, 2009

Digital Imaging Protocols for Pediatric Echo


This was the explanation I was given, very early in my introduction to "digital echo", about why we record These Views in This Order. At the time, I was coming from a lab that did things proper: starting with the subcostal views. The only sense this new "parasternal images 1st" protocol made was that it supposedly made reading the studies easier.
How convenient.

For you.

Who is this protocol for anyhow?

I insist that the marriage of the image acquisition protocol with the ordered reviewing of said images is a potential liability. Always starting with the parasternal view is fine for most hearts— most hearts are nearly normal. The problem, in my opinion, with starting with the parasternal view is: it presumes that things are normal, or are nearly normal, or that I can at least make something up to look passably normal.

If things are not normal (this is what we're supposed to be particularly good with in Peds, isn't it?) this type of protocol presumes too much: that I already know enough about the heart to make some sense of the parasternal views. Try this on: what is the PLAX view for a patient with dextrocardia, DORV, and pulmonary atresia supposed to look like? How about HLHS? In order to record meaningful parasternal long axis views of these types of abnormal hearts, the sonographer has to either:

  • immediately recognize the pathology from this one clip
  • spend time scanning from subcostals and apicals first (in order to sort it out) then return to the "starting point"- the parasternal views.

The first option is not a fair predicament for most sonographers (including physicians), and the second- grossly inefficient.

The Images are for Physicians

Certainly, I appreciate that in order to report the anatomy, arrangement, size, and function of the examined heart some considerable structure is required. There must be images that support and document our conclusions. And, as we are increasingly moving towards structured reporting, the structure of the underlying, supporting images must also evolve. I have no problem with this, in fact, I embrace it. It's the "absence of evidence is not evidence of absence" philosophy, taken to it's logical conclusion. We don't want anyone to report anything that our images can't substantiate. The fact that physicians will determine and require a certain, precise collection of images is undisputed. They may choose and prefer to review them in any particular order. Bully for them.
Our obligation is to provide these images.

I simply prefer to do it in a manner that is most efficient for me.

The Protocol is for Sonographers

What is really needed to improve our exam consistency is a system that allows for the flexible acquisition of any prescribed (minimum) set of images. On a small scale, we are already doing this with stress echo, particularly with exercise stress echo: you grab what you can, when you can, and sort it out later. The order of collection is irrelevant, but the presentation of the images, in order, is everything. I can't tell you how many fetal echos I have done that would have been greatly improved by the ability to collect the images as I saw them, and then sort them into a logical arrangement later. Not to mention every "new blue" dextrocardia-aortic-atresia-single-ventricle-goat-wreck (Goat Rodeo + Train Wreck, contracted form), I have done since the inception of the current "parasternals 1st" protocol.

I am eager to see what the new Philips iE33's SmartExams are all about.

Lately, I have been tinkering about with a collection of image acquisition protocols suitable for pediatric echo.
In addition to providing a basis for building our own structured, protocol-driven exams, I believe these could also turn into a fairly useful teaching tool (I still need more descriptions/images though).

Tuesday, January 13, 2009

Line Fitting for Pediatric Cardiology (and everyone else)

Described as "one of the fundamental tasks of scientific inquiry", model selection could consume the better part of an afternoon and an important part of one's budgeted time with a statistician.


If you're looking for quality curve fitting and surface fitting, this is the site for you!

The power law applied by Sable et al. in their description of coronary artery reference values caught my attention. Particularly, the scaling exponents for the individual coronary arteries are all different, and not what I would have intuitively guessed them to be, based on the principle of geometric similarity. So, I wanted to test a theory: perhaps the coronary arteries scale well with something besides BSA.

Consider this small data set of 10 hypothetical patients:

Ht (cm) WT (kg) BSA (Haycock)
57 6.1 0.3187
61 7 0.3525
83 12.6 0.5464
98 14.2 0.6223
104 16.6 0.6930
120 20.5 0.8215
148 41 1.2961
172 88.6 2.0820
176 58 1.6729
178 65.5 1.7940

From this I predicted the diameter of the LAD and height-based LV mass for each hypothetical subject.
I then constructed a second table of super hypothetical data:

LV Mass (g) LAD (mm)
16.86 1.38
19.19 1.44
34.42 1.72
45.69 1.82
50.17 1.90
63.28 2.04
99.64 2.46
149.46 2.99
158.99 2.73
163.79 2.81

Then I did some line fitting:

hypothetical LAD vs. LVM

The model fitted is:

y = a * xb

The reported coefficients are:

a =  5.2619076425282296E-01
b =  3.3269001508780827E-01

The "b" term is the scaling exponent: 0.333.
That is to say, in this small sample of hypothetical data, the LAD (a linear measure) scales with LV mass (a volumetric measure) to the 1/3 power.
Maybe that is just random.
Or, maybe that is just… cool.


Of course, selection of the best model depends on numerous factors some of which are the regression "fit" statistics and things like the "Bayesian information criterion". Excel won't report these bits, but throws a bunch at you.

It's free, by the way- unlike the statistician's time.