Lean body mass as a scaling variable in pediatric cardiology

lean body mass prediction equations based on height, weight, age, and gender are now available, providing insights into the practice of scaling of cardiovascular parameters to body size.
Recent critical reviews of reference values for pediatric cardiology are frankly sobering: we don’t have many studies with sufficient numbers of patients to draw reasonable conclusions, and the statistical methods are, at times, specious. I considered writing my own critical review of these critical reviews, but that just felt, well, a bit too meta. Please read this critical review of the many methodological limitations,  and this critical review of the statistical methods used in developing the current reference values. These are harsh but honest assessments of the current state of the art. Considering the criticism leveled against the community, it’s enough to make one wonder if anyone out there is even trying to generate worthwhile reference data.
Clearly, some folks are.
Canadians, mostly, by the looks of things.

background

Since the very first time a pediatric cardiologist realized that babies weren’t just tiny adults, and that their hearts are small but proportional to their bodies, we have been in a struggle to figure out how best to adjust for body size. The usual suspects have all been tried, with varying success: age, height, weight, body surface area, various allometric exponents of the same... Some groups advocate that weight alone is the best scaling variable; others argue convincingly that height is better; other groups go back-and-forth between the two (see the works from Mass General: 2009 and 1992 ).
Combining both height and weight, BSA has proven to be quite good as a scaling variable, with a defensible theoretic and empiric case for it’s use (see Sluysman and Colan, JAP 2005). But why should cardiac size scale with height, or weight, or BSA? What is the underlying physical principle that says heart size should be proportional to height? Could it be because tall people breathe thinner atmosphere? Because heavy people have to deal with more friction?
Lean body mass (or “Fat Free Mass”-- our brain, bones, and primarily, muscles) are what demand oxygen. If we were insects, we would just get our oxygen by moving the air right through our little exoskeletons. But most of us are not insects, and we get our oxygen instead via red blood cells, transported through our vast network of tubes, pumped from the heart. The heart has developed to pump oxygenated blood to the tissues that need it.
“Thank you very much, Captain Obvious” you say.
But there it is: the heart scales with lean body mass.
Yet, we don’t measure lean body mass. Nobody in the echo lab measures LBM. In fact, it’s a rare person in the echo lab that even knows how to measure it.
Traditionally, measurement of LBM required specialized equipment and training. Personally, I have never seen a pair of skinfold calipers in the cardiology department, and a dunk tank is almost entirely out of the question. I keep thinking a bioelectric impedance tool would somehow magically grow into this role, but I have yet to see that happen. Technically, I think you could measure it in the MRI scanner, but DEXA is probably the gold standard, and I am pretty sure we don’t have one of those machines on campus.
Height and weight (and BSA) may be poor surrogates for LBM, but at least they are easy to measure.

recent work

In the May-June issue of Annals of Human Biology, Foster et al. tackle the idea of developing a series of equations that could predict lean body mass from easily measured anthropometric measures. They measured lean body mass on over 800 children (using DEXA) and then performed some statistical kung-fu to develop their equations... and then validated those equations on another 300 or so patients. Using their prediction equations will get you within 5% of measured lean body mass, a feat that is about on par with some other available measurements (?bioelectric impedance??)

LBM estimated using this simple and inexpensive method may be useful in a variety of settings including ... characterization of the appropriateness of physiologic parameters that scale well to LBM such as resting energy expenditure, heart size, kidney function and drug dosing.

In an article in the current issue of JASE, the same group now apply these new lean body mass prediction equations to the age-old question of how best to determine left ventricular hypertrophy, a matter which they had previously covered and if I might add, raised the bar once already. They go on to demonstrate that— compared to values adjusted for lean body mass— height-adjusted LVM frequently over-estimates the incidence of LVH, and conversely, that BSA-adjusted values frequently under-estimate LVH (though less so than with height) They conclude the present investigation:

LBM is likely the best scaling variable and may be estimated reasonably accurately in children aged 5 to 21 years.
Only by scaling LV mass to LBM will we be able to determine the impact of obesity on heart size.

future directions

I think the ability to estimate LBM is going to be important to the field of reference values for echocardiography. It is, in effect, the holy grail of scaling variables for pediatric cardiology, and cardiology in general.
I believe that this is going to be so important to future research, I want to help you calculate lean body mass on your own data:

http://dev.parameterz.com/lbm/

In an effort to be completely transparent about the calculations, I have also provided a step-by-step worked example lean body mass calculation:

http://dev.parameterz.com/lbm/walkthrough/

And finally, a way to batch-process your data, adding lean body mass by the droves (upload your own csv data)

http://dev.parameterz.com/lbm/upload/

The Why and How of... What the?

Print is dead.

When the editorial process of a peer-reviewed journal deteriorates as it does in the January JASE issue, then I think it is safe to say print is dead.

What was destined to be The editorial concerning z-scores for echocardiography will now only make sense if we read the coming errata, which diffuses the point entirely. I considered writing a letter to the editor, but it is not obvious to me that they would bother to read the submitted material or, are at all familiar with the subject.

Not sure what I am driving at? Read the editorial yourself and see if you can make sense of how-- all of a sudden-- we are now supposed to be adjusting cardiac size for body mass index 
(Hint: we’re not. It’s a colossal misprint).

LVEDV Z-Scores

The second of two recent updates to app.parameterz.com is the addition of the left ventricular volume and dimension data supplied by this recent article:

Normalized end-systolic volume and pre-load reserve predict ventricular dysfunction following surgery for aortic regurgitation independent of body size.
Gentles TL, French JK, Zeng I, Milsom PF, Finucane AK, Wilson NJ.
JACC Cardiovasc Imaging. 2012 Jun;5(6):626-33.

(The equations are provided via an online supplement, supplied to me by the authors.)
Although the article describes equations for LV function and dimensions, I use only the dimensional z-scores. The form of these equations is that of an allometric relationship with BSA, with log-log transformation of both the measured value and the BSA.
The formula used for estimating BSA is not described within the article/supplement; I am awaiting a response from the authors on this. In the meantime, calculations are made using the Haycock formula.

LVEDD and LVESD

The allometric equations for the LVEDD and LVESD use exponents of around 0.4, which is slightly less than what would be expected by the theory of geometric similarity: 0.5. Numerous other authors have discovered linear relationships when correcting/adjusting linear dimensions (cm) to body surface area (m²). Additionally, the LVESD values seem a bit off when compared to other available sources:

(I have contacted the authors; awaiting their response)

LVEDV and LVESV

Data for the left ventricular volumes is also in the form of an allometric relationship with BSA, with an exponent of around 1.1. Again, this differs somewhat from what would be predicted by geometric similarity, and by other empirical evidence. The closer the exponent is to 1.0, the more the relationship is strictly linear with BSA, which is unexpected, particularly since the authors recognize this peril:

However, the relationship between body size and LV size is nonlinear

Yet, when you plot out the predicted values, it looks quite linear:

versus an allometric equation with an exponent of 1.38 (Lytrivi et al.):

Anyhow, given the paucity of ventricular volume z-score equations, these are now included among other pediatric echo z-score calculations at

app.parameterz.com

***update Dec 2012***

The author has advised me that there was an error with the online supplement.

"The intercept for ESD should be 2.56 NOT 3.56 as is on the web"

The app now uses the updated value.

Left Atrial Volume Z-Scores

Calculating BSA-adjusted z-scores of LA volume using an allometric equation
The first of two new calculations added to app.parameterz.com is based this recent article:

Normal values of left atrial volume in pediatric age group using a validated allometric model.
Bhatla P, Nielsen JC, Ko HH, Doucette J, Lytrivi ID, Srivastava S.
Circ Cardiovasc Imaging. 2012 Nov 1;5(6):791-6.

Similar to how this same group calculates z-scores for LV end-diastolic volume, they found an allometric equation that scales well with body size (in this case, two equations) and they index to that. For left atrial volume, there is one equation for BSA ≤ 1.0 and another equation for BSA > 1.0. The allometric exponent for the bigger kids, i.e., BSA^1.08, is not much different than just indexing to BSA, which strikes me as interesting.
I think the stratification into two groups would be more palatable if the interface was seamless, but in this case it is not. Let’s have a look at two patients with an LA volume of 34ml, one just under 1.0 meters squared and the other, just above.

1. BSA = 0.97; z = 0.74
2. BSA = 1.03; z = 1.65

And their accompanying plots:

BSA = 0.96

BSA = 1.03

For the smaller patient, the LA volume of 34 ml is well within the normal range, but for the slightly larger patient, the same LA volume is now at the upper limit of normal. Weird, huh?
Plus, it gets a little more interesting. If we assume that 125-131 cm is about the appropriate height for a 7 year old, and we plug the same data into another calculation, the indexed left atrial volume is definitely large, with a z-score of 3.5:

Anyhow (as always) I don’t pretend to have the answers— I just pose questions. Feel free to play around with this and other z-score calculations at:

app.parameterz.com

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 (fetal.parameterz.com) 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:

fetal tissue Doppler z-scores for a 28wk4d fetus

and here is an example chart:

fetal tissue Doppler LV TDI S vs. EGA

Challenges

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.

Concerns

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.

Summary

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

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:

RVEDV vs. BSA

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.

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CMR LVEDV Z-Score Mini-Smackdown

examining CMR references for LVEDV reveals interesting differences; doubt is cast upon the practice of generating z-scores for indexed values

I have been tinkering with z-scores for cardiac MRI and I thought it might be interesting to compare a couple of references for LV end-diastolic volume (I always think this stuff is interesting):

• Alfakih et al., (JMRI, 2003)
• Buechel et al. (JCMR, 2009)

So, what I did was create some tables (using the mean and ± 2SD limits), generated some charts, and then made a series of z-score calculations over a range of LVEDV values for two hypothetical patients (view the spreadsheet and calculations for this data HERE).

Data:

First, the Alfakih data: based on their published values for “younger men” using SSFP, the LVEDVi is 87.6 ± 15.6.

LVEDV Reference Values: Alfakih et al.

BSA (m2)	ULN (ml)	Mean (ml)	LLN (ml)
0.5	59	44	29
0.6	71	53	34
0.7	83	61	40
0.8	95	70	46
0.9	106	79	51
1.0	118	88	57
1.1	130	96	63
1.2	142	105	68
1.3	154	114	74
1.4	166	123	80
1.5	177	131	86
1.6	189	140	91
1.7	201	149	97
1.8	213	158	103
1.9	225	166	108
2.0	236	175	114

And then the Buechel data: based on their allometric equation, a * BSA^b, and their published values for boys: a = 77.5, b = 1.38, and using the z-score form of

... and their published value for the “SD” = 0.0426

LVEDV Reference Values: Buechel et al.

BSA (m2)	ULN (ml)	Mean (ml)	LLN (ml)
0.5	36	30	25
0.6	47	38	32
0.7	58	47	39
0.8	69	57	47
0.9	82	67	55
1.0	94	78	64
1.1	108	88	73
1.2	121	100	82
1.3	135	111	92
1.4	150	123	101
1.5	165	136	111
1.6	180	148	121
1.7	196	161	132
1.8	212	174	143
1.9	229	188	155
2.0	245	201	166

 

Charts:

 

Z-Scores:

 

Generated Z-Scores for Patient BSA = 0.7

LVEDV	Z: Alfakih	Z: Buechel
15	-4.3	-11.7
20	-3.9	-8.8
25	-3.4	-6.5
30	-2.9	-4.7
35	-2.5	-3.1
40	-2	-1.7
45	-1.5	-0.5
50	-1.1	0.6
55	-0.6	1.5
60	-0.1	2.4
65	0.3	3.2
70	0.8	4
75	1.3	4.7
80	1.7	5.3
85	2.2	6
90	2.7	6.5

 

Generated Z-Scores for Patient BSA = 1.4

LVEDV	Z: Alfakih	Z: Buechel
50	-3.4	-9.2
60	-2.9	-7.3
70	-2.5	-5.8
80	-2.0	-4.4
90	-1.5	-3.2
100	-1.1	-2.1
110	-0.6	-1.2
120	-0.1	-0.3
130	0.3	0.5
140	0.8	1.3
150	1.3	2.0
160	1.7	2.7
170	2.2	3.3
180	2.7	3.9
190	3.1	4.4
200	3.6	4.9

 

Summary

Buechel et al. sum it up nicely in their discussion:

cardiac volumes have a non-linear relation to body surface area, and since the exponential values are different for different cardiac parameters, it would not be appropriate to provide normal values simply indexed to BSA

The textbook Echocardiography in Pediatric and Congenital Heart Disease has an excellent and thorough description of the practice of “indexing”. Essentially, the problem boils down to this: for LVEDV, none of the assumptions for the relationship are met:

In order for the per-BSA method of indexing to work, three assumptions must be met. The relationship to BSA must be linear, the intercept of the regression must be zero, and the variance must be constant over the range of BSA.

If you had to choose a reference for LVEDV in children measured with cardiac MRI, I would have to wonder why anyone would not use the data from Buechel et al.— unless they just did not have those calculations handy.

Well, now they do:

cmr.parameterz.com

BSA Methods and Cardiac Z-Scores

A spreadsheet comparing different BSA calculations on various patients-- and the resulting BSA-adjusted z-scores-- reveals negligible differences.

Can we compare z-scores from various references when the methods for calculating BSA are different? How?

If a given group of z-score equations are BSA adjusted, and a given patient has a different BSA depending on the BSA formula, how do you perform a comparison? Meaning, if equation A uses BSA formula x, and equation B uses BSA formula y, to what extent are differences in the z-scores due to differences in BSA?

Which then spawns these questions:

• What is a clinically important difference in BSA?
  • a tenth of a meter²?
  • a hundredth?
  • a thousandth?!?
• How many significant digits are important when comparing z-scores?

I made this spreadsheet in an effort to examine some of these questions.

(the example z-score equation is from Kaiser et al., JCMR 2008.)

Looking over this data, I totally agree with Dallaire and Dahdah, JASE 2011, who noted:

There was virtually no difference when Z-score equations were derived from BSA estimated with different equations, and misclassification was rare.

Aortic Root and LV Volume Z-Score Calculators

Two new z-score calculators on Parameterz.com plus a paradigm shift or two

First, the z-score calculators:

1. LV End-Diastolic Volume z-scores, using the 5/6 A-L method
2. A consolidated Aortic Root z-score calculator

The paradigm shifts are these:

1. All calculations are now server-side, using Python
2. The Aortic Root calculator is a prototype for combining all available references into one calculator/results page

 

LV EDV Z-Score Calculator

These z-scores are based on the recent work Normal values for left ventricular volume in infants and young children by the echocardiographic subxiphoid five-sixth area by length (bullet) method, from the Feb 2011 JASE. This is a terrific approach to what is traditionally considered a difficult measurement to calculate and normalize. For one, ventricular volumes calculated by the traditional Simpson’s bi-plane technique are notoriously unreliable. To wit, the recent abstract from the PHN citing the 5/6 A-L technique as superioir:

Variability of LV size and function measurements in children with DCM is reduced when utilizing the 5/6 AL algorithm.

(Margossian et al., JASE; May 2010)

The authors cite their own previous work as demonstrating the 5/6 A-L technique to be valid with regards to correlating well with MRI volumes.

On another front, the equations presented in this article also dramatically simplify the very complex relationship of ventricular volume and size, thought to be multi-factorial based on ejection fraction, heart rate, cardiac output, and BSA. A theoretical allometric relationship between EDV and BSA was recently described to be approximately

...the predicted relationship is EDV ≈ BSA^1.4

Theoretical and empirical derivation of cardiovascular allometric relationships in children.
Sluysmans T, Colan SD.
J Appl Physiol. 2005 Aug;99(2):445-57

The allometric relationship described in this article is with BSA^1.38, which is, well, awesome.

The calculator itself is sort-of a hybrid calculator, in that the BSA and volumes are calculated with JS on the client, then the page is posted to the server and the z-scores are calculated using Python. Another novel aspect to this calculator is that, by virtue of the calculations being performed on the server, I can provide a running tab of recent calculations, resulting in a real-time plot of actual EDV vs. BSA data:

This is not the right calculator to be used for collecting normative data, but what I am learning about server-side programming-- like with this calculator-- is getting me much closer to realizing such a design.

Aortic Root Z-Score Calculator

This calculator is a combination of what I had learned from building the LVEDV calculator and from the prototype design of the multi-referenced coronary artery z-score calculator. The essence of the design is that the patient demographics and measurement data are entered once and the z-scores and reference ranges from each of several references are returned to you in what I hope is an easy  to use, sortable, results table:

http://aoroot.parameterz.com/calc?ht=128&wt=28&aov=15.5&sov=25&stj=18&aao=21

The data required to make the calculations are part of the url (i.e., the “query string”) so the results are essentially permanent and “linkable” should anyone find any need for such a feature.

The references for calculating aortic root z-scores use various BSA equations. This calculator applies the correct BSA formula to each calculation, and thus the z-scores between each reference should be comparable, even though the calculated BSA’s are slightly different. For posterity’s sake, the different BSA calculations are also provided, which therefore makes this a very elaborate BSA calculator:

http://aoroot.parameterz.com/calc?ht=128&wt=28

Also, since not all the references use the same measurement methodology, an allowance is made to show only the appropriate calculations based on your local methodology, i.e., I filter the results based on whether the user indicates the measurement of the vascular aspects of the aortic root were measured in systole or diastole.

To be sure, all of this could have been done on the client with JavaScript, but I thought it was time to grow up.

Reference Benchmarks

A look at evolving benchmarks for pediatric cardiac reference data

I read with some interest the article Optimal Normative Pediatric Cardiac Structure Dimensions for Clinical Use and was amused to see an off-hand reference to Parameter(z):

Pettersen et al’s paper does not specify which BSA formula was utilized; however, the cardiac dimensions they measured have been normalized using both the DuBois and the Haycock et al formula and are available elsewhere.

I am always curious about the context in which Parameter(z) might appear, and in this case I’d like to add my own two cents.

The authors of the paper set out to review the literature and recommend the “optimal normative data set” for cardiac structures/dimensions-- a familiar, if not worthy, cause. Along the way the authors note several criteria (I am going to call them benchmarks)  for consideration:

• sample size—larger studies are better
• normalization factor
  • allometric equation is best
  • Haycock BSA equation is best
• measurement technique/protocol—those according to current guidelines are best
• consideration for race and gender
• “sophisticated” analysis (like the LMS method) are mentioned (preferred?)

Race and gender considerations are mentioned, but it is not clear if these were separate criteria, or if they only had a bearing on which BSA formula to use. To give them the benefit of the doubt, I will leave them in as bonus benchmarks. The authors then go on to recommend the data from Detroit as the “optimal” data set.

While I don’t disagree with any of these benchmarks, I do think some clarification might be useful. An allometric equation is certainly a useful approach for describing the growth of structures-- the biologic relationship between structure and body size-- and I am a big fan of this approach. A “sophisticated” analysis like the LMS method is a completely different approach, independent and ignorant of any underlying biologic process. I am also a big fan of this type of analysis. The message here is that you either do a predictive analysis, preferably using an allometric equation OR you do a descriptive analysis, preferably using the LMS method.

The principle feature of the LMS method is that it accounts for things like skew and heteroscedasticity and results in valid, normally distributed z-scores. There are other ways to achieve this though, as was recently present in the manuscript New equations and a critical appraisal of coronary artery Z scores in healthy children. Here, the authors apply the Anderson-Darling goodness-of-fit test to determine if their data (derived from an allometric equation) depart from a normal distribution.

So, the first point is this—one of the benchmarks should read: equations result in valid, normally distributed data, either by use of the LMS (or similar) method, or by performing some type of analysis confirming a normal distribution.

The second point is this: I don’t think the Detroit data holds up well to these benchmarks and should not be described as “optimal”. Certainly, theirs is a large study (>700 patients), and they indeed followed current guidelines for the measurements. However, on every other point I believe they fail:

• they do not use an allometric equation (theirs is a polynomial equation)
• they do not use the preferred BSA equation (via a personal communication, I learned they used DuBois & DuBois)
• they do not include race or gender in their analysis (in fact, no demographic data is presented—at all)
• they did not use the LMS method, or perform any distribution analysis

Are they better than nothing? Absolutely. 
A step in the right direction? Agreed. 
But optimal?

 

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I will say this about the Detroit z-score calculator though: it is the most popular of all the calculators at Parameter(z). In the past 6 months:

• 19,165 pageviews; 15.26% of all site traffic
• average 160 visits per day
• average 3:56 time on page
• visited most by users in California, Virginia, Georgia, Chile, and North Carolina

The equations may not be optimal, but—for better or worse—they are getting a lot of use.

Q and A with Frédéric and Nagib

The January issue of JASE holds this gem of a manuscript:

New equations and a critical appraisal of coronary artery Z scores in healthy children.
Dallaire F, Dahdah N.
J Am Soc Echocardiogr. 2011 Jan;24(1):60-74. Epub 2010 Nov 13.

The title couldn’t be any more fitting-- it is a must-read for anyone interested in the matter of z-scores for pediatric cardiology.

The authors have graciously agreed to allow me to post their answers to my “follow up  questions”:

Q: Thanks for introducing us to the Anderson-Darling normal distribution test. However, why not include a few frequency vs. residuals histograms for the cavemen in the audience like me? We like pictures...

A: We used such histograms in our analysis to “visually” assess normality. Our article was however long and we had to cut down some of the text and figures. Here’s the frequency distribution for left main coronary artery Z scores (final model with square root of body surface area)

Q: Are there other normality tests? Why the Anderson-Darling test?

A: The Anderson-Darling test tests whether a sample fit to a given distribution. When used to test for departure from normality, it is one of the most powerful. SAS also gives the results for the Kolmogorov-Smirnov and Cramer-von Mises tests, which are less sensitive.

Q: The power model described in the article has the form: y = a +b₁x²+b₂x Why isn't that a polynomial model (quadratic)? I was expecting a model of the form: y : x^a  (see chart).

Is this just a matter of semantics, or is the power model misnamed?

A: Yes, we should have named it a polynomial model.

Q: Judging by the spread/skew of the +/- 2SD curves on the “exponential model”, it looks like a log-normal curve... how did you treat the SD with this model?

A: In the exponential model, body surface area and coronary diameter were both log-transformed and then the model was fitted. The SD used was thus the one of a linear model on log-transformed values. Even with the logarithmic transformation, there was residual heteroscedasticity and a weighted least-square model was used. The weight in the model was the inverse of the linear regression of the residuals (on log-transformed values).

Q: Your “exponential model” empirically arrived at an exponent of 0.544-- similar to your theoretical “square root model”: y = a + b₁x^0.5. However, the Boston and Washington, D.C. models are similar and have exponents of something like 0.3xx. Is the difference between the exponents attributed to your larger sample size, or could there be something else going on here?

A: Hard to say. I would guess that aside from the greater sample size, it is likely the better representation of small children and infants that made the difference. If the theoretical model of optimal cardiovascular allometry proposed by Sluysmans and Colan in 2004 is true, it seems logical that a good representation of children from all ages helped to produce a “real-life” model close to the theoretical model proposed by Sluysmans and Colan.

Q: The final models described in the article are very similar in form to many of the z-score equations from Boston: 2 regression equations; one for the mean, one for the SD. However, the Boston equations predict the SD by a regression against BSA. Your SD equations are run against the square root of the BSA. How does one determine the best model for the variance?

A: The best model for variance should be determined in the same way the model for the mean is. That is, one should ensure that the residuals are free of a trend (no association should exist between the residual and the independent variable). In other words, there should not be an association between the residuals of the residuals and the dependent variable. This was verified for our data but was apparently not done in previous series, including Boston’s.

Q: I keep wondering: if we took a hundred patients with the same BSA, what is the mean/median/mode/min/max/distribution of those measurements? What does that curve look like? Had you considered using something like the “LMS” method to do a group-wise evaluation?

A: The use of a Z score assumes that the coronary diameters of x patients with a given BSA are normally distributed. In fact, our modelisation supposes that for any given value of BSA, there exists a number of subjects that are normally distributed around the mean (see our figure). If so, the median, mode and mean should be the same. The important thing is that in the absence of such a distribution, the Z score cannot be used to estimated percentiles, which is its principal (only?) value. In the lab, one wants to know if a coronary diameters exceeds the 95th or 98th percentile for a given BSA to be able to answer the question “is that coronary abnormal?”. Such percentiles can only be estimated if the data is normally distributed.

Q: What do you think explains how the proximal RCA has a normal distribution in your analysis but the distal RCA does not?

A: The distal RCA has two particularities. 1) distal RCA is the most difficult to view and, therefore, to measure. We are confident all distal RCA measurements we use to compute our equations were properly imaged and measured (number of distal RCA samples are the lowest compared to the other segments in our report). The difficulty of obtaining good image might have played a part, but we do not think this is the main reason for the non normal distribution... 2) Essentially, the size of the distal RCA depends on whether or not the RCA is dominant or not (typically 2/3 vs 1/3 of normal humans). We think this is the most probable explanation for not perfectly symmetric variability among subjects. In brief, we believe that the dominance factor is the key answer. One way to verify this hypothesis is to take the adventure of measuring the distal circumflex (posterior rim) and compare with the distal RCA in a series of subjects...

Q: If you consider coronary arteries as a microcosm of the larger reference values issue in pediatric cardiology, what implications does your work have for the existing body of z-score equations?

A: Surprisingly, very little proper validation of reference values and normalisation has been done in paediatric echocardiography. We advocate for a close examination (and potentially a redo when appropriate) of nearly all equations so far available in the literature. Some of them are probably adequate, but in the absence of a good description of the final distribution, it is difficult to affirm with confidence.

Q: Do you have any advice for others, like the ASE, that are going forward with developing new models and z-score equations?

A: Simply fitting a modelled curve in the data is not enough. Since Z scores are dependent on the distribution of the data, one should absolutely test the Z score distribution obtained. One should also ensure that there is no residual trend and no residual heteroscedasticity. We believe that Z scores are a very useful tool for interpreting cardiac structure dimensions in paediatric settings. They must however be based on sound unbiased mathematical grounds.

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Naturally, a z-score calculator has been posted up at ParameterZ.com:

http://parameterz.blogspot.com/2010/11/montreal-coronary-artery-z-scores.html

I also made this into it’s own project, making comparisons between the new data and previous coronary artery z-score equations:

http://code.google.com/p/parameterz-coronaries/

-- more on that later.

I thank and congratulate the authors for their outstanding manuscript, and for their patience and generosity by way of indulging me and my questions.

Prototyping A Simple Database for Pediatric Echo Normal Values

A mashup of Google technologies to create a free, simple, open-access database.

The upcoming ASE Guidelines ”Recommendations for Quantification Methods During the Performance of a Pediatric Echocardiogram”, is intended to serve as The Standard for measurement techniques in pediatric echo. Getting everyone on the same page as far as making measurements is a prerequisite for moving forward with standardizing z-scores for pediatric echocardiography. Anticipating the guidelines, I built a mashup that could serve as a skeleton for a common database of normal values:

Normal Values Database Prototype: The Aortic Root

The above link is to a “working demo”. Feel free to enter any kind of data (fake or otherwise) in order to see it in action. Should I decide to do this “for real” there would likely be some preconditions for using the data form(s) but for now, feel free to use it with abandon.  Of course, I’d love to know what you think.

Kawasaki Disease Aneurysm Z-Scores: Another Smackdown

Boston Children’s versus Children’s National Medical Center for a “giant” knockout

When the Children’s National (CNMC) coronary artery z-score equations were published in 2008, I briefly compared them to the 2007 Boston data and noted their similarities. In my opinion, the manner in which the CNMC equations handle the “standard deviation” makes these incompatible with some newly proposed cutoffs. Let me explain.

Classifying Aneurysms

The current AHA criteria for classifying coronary artery aneurysms relies on a combination of z-scores and absolute diameters:

• any segment with a z-score of > 2.5 = abnormal
• <5 mm = small
• 5 – 8 mm = large
• ≥8 mm = giant

A recent article by Manlhoit et al. points out the folly of using absolute measurements in this instance. They then take the logical next step by introducing a classification system based on z-scores. Using their previously published data (from Boston, see above), the authors advocate the following coronary artery aneurysm z-score classification:

• ≥2.5 – <5 = small
• ≥5 – <10 = large
• ≥10 =  giant

The clinical science behind establishing these cutoff points is presented in the article and is beyond the scope of what I am trying to do here. However, it is worth noting that (at least to me) the proposed system has a certain elegance and symmetry— it just seems reasonable.

Z-Score Equations

The Boston and CNMC equations each predict very similar values for the BSA adjusted mean diameter by using an allometric model. The two equations also yield similar results out to about z-scores of +2. But the similarities end where coronary artery abnormalities begin. Using the new criteria proposed for giant aneurysms ( z ≥10 ) and applying the CNMC equations, patients who previously had giant aneurysms ( ≥8 mm) now only have large aneurysms.

(See this page for the interactive comparison)

The big difference between the two z-score equations (z = [score – mean] / standard deviation ) is in how they deal with the standard deviation. The Boston equations use a separate regression (on BSA) to predict the SD, while the CNMC equations use the regression mean square error (MSE) statistic as a substitute for the SD.

Residuals

I have always been bothered by the patent substitution of the regression MSE (usually, the square root of the MSE i.e., the RMSE) for the population SD— particularly for the purpose of calculating z-scores. While the “transform both sides” strategy is perfectly legitimate for stabilizing the variance (and indeed, for discovering the allometric relationship!), if you play around with the regression residuals and then back-transform (i.e., exponentiate) your calculations — you have just modeled positive skew.

Detecting skew shouldn’t be all that hard to do. If the values are distributed normally, then it stands to reason that the residuals (observed - predicted) are also normally distributed. A simple plot of the residuals should show us what is going on. Here is the frequency vs. residuals plot from the recent fetal echo reference values of Lee et al.:

 

(Similar residuals plots are provided by the crazy-cool online curve fitting at ZunZun.com.)

That’s not to say that skew doesn’t exist. Indeed, that is part of the point and elegance of the recently applied LMS method. It is imperative that we do something to examine the presence or absence of skew, and then describe how we intended to deal with it. Unfortunately, both of these investigations fail to mention this fundamental data characteristic in their respective manuscripts.

Bottom Line

Due to unexplored assumptions about the nature of the residuals/skew of the data, z-score cutoff values are not universal and are absolutely dependent upon their underlying reference z-score equations.

Aortic Root Z-Scores part deux

A new z-score calculator for the aortic root (annulus, sinuses of valsalva, sinotubular junction, ascending aorta) is now available at ParameterZ.com.

In addition to the online z-score calculator I have also created:

• an example calculation walk-through
• a sinuses of valsalva z-score comparison
• an ascending aorta z-score comparison

Caveats

A couple of things worth mentioning as far as methodology:

1. Measurement of the sinuses/st jct., AAO are in diastole
2. Measurements are taken from leading edge - leading edge

The authors claim that these are in accordance with The Guidelines, yet they seem like a break in convention to me.

New Fetal Echo Z-Score References

New fetal cardiac z-score equations from William Beaumont Hospital; new online calculator at OBSONO.org

Following up on their abstract from earlier this year, the group at William Beaumont Hospital in Royal Oak, Michigan produced what turns out to be the largest cross-sectional study of normative data for fetal cardiac measurements of all time:

Fetal echocardiography: z-score reference ranges for a large patient population.
Lee W, Riggs T, Amula V, Tsimis M, Cutler N, Bronsteen R, Comstock CH.
Ultrasound Obstet Gynecol. 2010 Jan;35(1):28-34.

Data from over 2700 normal pregnancies was used to construct z-score equations for the following fetal cardiac measures:

• LV minor
• RV minor
• Aortic annulus
• Pulmonary annulus
• Cardiac circumference

By way of comparison, the previous work from Royal Brompton used data from 130 normal pregnancies; the more recent "unpublished" equations from Boston are based on observations made on 232 normal pregnancies. This new data eclipses both of these studies by at least an order of magnitude. For the purpose of generating normative data, "n" is everything, so statistically speaking, this study is HUGE.

The William Beaumont z-score equations deal with the prediction of the standard deviation in a manner similar to that used by the Boston folks, by a separate regression, thus deliberately accounting and controlling for the natural spread of data (heteroscedasticity). And, for what has to be one of the first, if not only, time- the authors also present a beautiful frequency vs. residuals plot and convincingly demonstrate that their data conforms to a normal distribution- a predicate for all z-score comparisons.

To better examine the differences and similarities of the various z-score equations I provide these tools, allowing for side-by-side comparison of the predicted z-scores, mean values, and normal ranges:

Fetal Aortic Valve Z-Score Comparison

Fetal LV Minor Z-Score Comparison

The authors also provide their own online fetal cardiac z-score calculator ( one-upping ParameterZ.com by generating pretty z-score plots ! ) at  www.obsono.org.

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Speaking from the perspective of a pediatric cardiac sonographer, I have to recognize and thank the authors of this study for doing the work that we cannot do. Those of us in pediatric cardiology do not see a high volume of unselected, normal pregnancies and thus could never generate this kind of normative data.

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:

Notes:

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.

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References:

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.

Skew in Echocardiographic Reference Data

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

Skewness:

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...

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References

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.

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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

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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.

• Z-Score equations for fetal mitral valve, left ventricle, aortic valve, ascending aorta, and right ventricle are included. The ParameterZ.com z-score calculator is here:

  Fetal Echo Z-Scores: Boston Data

• The Smackdown, pitting the established equations from London against these 'new' equations, is here:

  Fetal Echo Z-Score Smackdown: Boston vs. Royal Brompton

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.

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:

ParameterZ.com Fetal Echo Z-Score Calculator

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.

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.