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