A scrutiny of the percentage flow-mediated dilation index from a fundamental size-scaling perspective

1. Greg Atkinson and Alan M Batterham
Health And Social Care Institute
Teesside University
greg.atkinson@tees.ac.uk
SIZE MATTERS:
HOW A STATISTICIAN CAN HELP ENDOTHELIAL
FUNCTION RESEARCH

2. • Brachial FMD% is NOT “closely related” to coronary vasodilation,
especially in CHD patients (r = 0.26)
– Besides correlation is not the same as individual prediction error
which is what matters in the clinic
• Brachial FMD% is NOT deemed suitable for assessing CHD risk in
asymptomatic people
– (by the AHA - even without considering the issues raised here)
• FMD% does NOT indicate “function” per se
– Baseline artery size is easier to measure so relative importance of
size and “function” must be untangled
• Many claims about magnitude of changes/differences in FMD% ARE
biased without allometric adjustment
– Bias is usually that the differences/changes are larger than reality
• Other errors include shear rate normalisation and repeatability claims
This presentation is about statistics. But statistics are part of
scientific inference, so mistakes are being made

3. Endothelial
dysfunction
Endothelial dysfunction – a
precursor to atherosclerosis?

4. BASELINE
FMD
The flow-mediated dilation (FMD)
protocol - all about physiology
Dpeak
Dbase
Thanks to Helen Jones for these photos

5. The resulting measurements

6. The final step: Calculation of the
FMD% index (all about statistics)
FMD% = (Dpeak-Dbase) x 100
Dbase
= 5.0 – 4.0 x 100
4.0
= 25%
Where “D” is diameter of artery
4 mm

7. The final step: Calculation of the
FMD% index (all about statistics)
FMD% = (Dpeak-Dbase) x 100
Dbase
= 7.5 – 6.0 x 100
6.0
= 25%
Where “D” is diameter of artery
6 mmChange MUST be
proportional to Dbase
for FMD% to work, but
is this true? We’ll check
later

8. Publications on FMD% far outstrip its use in the clinic
or public health for risk appraisal, i.e. it’s “impact” in
UK REF terms
Source: Scopus
Celermajer et al. Lancet 1992

9. 2013 - Atkinson, G., Batterham, A.M., Thijssen, D.H.J., Green, D.J. A
new approach to improve the specificity of flow-mediated dilation for
indicating endothelial function in cardiovascular research. Journal of
Hypertension, 31: 287-291. Cited 67 times.
2013 - Atkinson, G., Batterham, A.M. Allometric scaling of diameter
change in the original flow-mediated dilation protocol.
Atherosclerosis, 226: 425-427. Cited 52 times.
2011 - Thijssen, D.H.J., Black, M.A., Pyke, K.E., Padilla, J., Atkinson, G.,
Harris, R.A., Parker, B., Widlansky, M.E., Tschakovsky, M.E., Green, D.J.
Assessment of flow-mediated dilation in humans: A methodological
and physiological guideline. American Journal of Physiology - Heart
and Circulatory Physiology, 300: H2-H12. Cited >400 times.
But it’s great if you want citations

10. FMD% seems prognostic for future CHD in
some studies (returned to later)
Yeboah et al. Circulation 2007;115:2390
FMD%
<Median
But on the balance of evidence, the AHA do not
recommend FMD% for risk appraisal in asymptomatic
people (even without the extra issues raised here). So
minimal impact potential in UK REF terms. Key
statistic AUC which is rarely reported.

11. Percentage flow-mediated
dilation
Time to translate the
evidence into clinical
practice?
No – Time to scrutinise
the evidence. No point
just having a research
tool if the research has no
impact

12. r2 = 62%
Celermajer et al. Lancet 1992; 340: 1111–1115.
Dbase-
dependency
A problem
right from the
start

13. “For arteries of diameter less than 6.0 mm, flow-mediated dilation is about 10% in
control subjects; however for arteries of more than 6.0mmin diameter, flow-mediated
dilation is small even in healthy subjects. . . .our method is best applied to the study
of smaller arteries in adults (such as the brachial or internal carotid) and larger
arteries in children”
(Celermajer et al.,1992)
Some convoluted solutions to the Dbase problem
“Reporting absolute change in diameter will minimize this [the Dbase-
dependency] problem … percent change might be the easiest method to use if
baseline diameter remains stable over time. However, the best policy may be to
measure and report baseline diameter, absolute change and percent change in
diameter.”
(Correttti et al., 2002)
“Objective comparison of %FMD is only possible between patients with the same
brachial artery size.”
(Milia-Stelic et al., 2007)
“Shear rate normalisation is essential for examining endothelial-dependent flow-
mediated dilation between groups differing in baseline arteries”.
(Pyke et al., 2004)

14. Lets just scale the change properly in
the first place

15. 15
Many allometric relationships have been established
between body size and organ weight as well as body
size and physiological process
Allometry – the study of size and
its consequences

16. The allometric relationship
between Dbase and Dpeak?
FMD% = (Dpeak-Dbase) x 100
Dbase
= Dpeak
Dbase
= Dpeak . Dbase-1
Where “D” is diameter of artery
Allometric
Exponent

17. One way to derive the allometric
exponent (log – log model)
Ln(PeakDiameter)
Ln (Baseline Diameter)

18. Atkinson and Batterham, Atherosclerosis 2013; 226:425-427
A new look at old data

19. Extracted data using DigitizeIt

20. Absolute flow-mediated response is
actually inversely proportional to Dbase!
Atkinson and Batterham, Atherosclerosis 2013; 226:425-427

21. Flow-mediated response is
inversely proportional to Dbase
Data re-analysed from Pyke et al. J Appl Physiol 2004; 97: 499-508.
This is the same data that was
used to conclude shear rate
normalisation is necessary. When
scaled properly, the Dbase
problem goes away anyway.

22. Study name Population Artery Sample size Statistics foreachstudy
Point Lower Upper
estimate limit limit
Atkinsonetal.,2013 Youngadults andchildren Brachial 64.000 0.890 0.845 0.935
AtkinsonandBatterham2013a Youndadults Femoral 14.000 0.860 0.765 0.955
AtkinsonandBatterham2013b Children Femoral 16.000 0.930 0.845 1.015
AtkinsonandBatterham2014 Adults (>45years) Brachial 3499.000 0.940 0.935 0.945
Atkinson,InPress Adults Brachial 44.000 0.820 0.780 0.860
0.937 0.932 0.942
Allometric exponents for various
FMD datasets

23. Comparison of models for Celermajer et
al. 1992
FMD% vs Allometry
Reanalysed data from Celermajer et al., 1992
Atkinson and Batterham, Atherosclerosis 2013; 226:425-427
FMD% is leading
us down false
trails

24. Some more
examples

25. Children vs Adults (again)
Atkinson et al. J Hypertens 2013;31:287-291.
So FMD% is NOT better in
children, so is it really an early
indicator of atherosclerosis? Yet
another paradox?

26. Age and Sex differences (MESA)
Atkinson and Batterham, Vasc Med 2013; 18: 354-365.
FMD% is
NOT
worse in
men

27. Healthy vs CVD disease (MESA)
Atkinson and Batterham, Vasc Med 2013; 18: 354-365.
Hypothesis: All claims
about FMD% are
compromised to some
degree

28. Two fundamental and oft-cited claims

29. But Dbase also predicts IMT progression

30. Is the brachial-coronary vasodilation correlation really
“close”? No – especially in the CHD patients that were
studied – time to stop regurgitating this in the literature?
r = 0.36

31. Dbase itself is also prognostic
Yeboah et al. Circulation 2007;115:2390
Low FMD%
FMD%
<Median
High Dbase
Dbase
>Median

32. So what is the causal pathway now?
Atkinson and Batterham, Vasc Med 2013; 18: 354-365.

33. Conclusions (1)
FMD%:
• Is a ratio (honestly – some referees argued not!)
• Misrepresents the apparent inverse relationship
between flow-mediated response and artery size
• Is dependent on Dbase for purely statistical reasons
• Can be a biased index of the flow-mediated D change
• Can cloud the causal pathway between flow-mediated
response per se and cardiovascular disease
• Is not adequately repeatable (but Dbase is) and is not
recommended by AHA for appraising risk of CHD in
asymptomatic people

34. Conclusions (2)
Allometric scaling:
• Removes the dependency on artery size in all datasets
if done properly
• Isolates the flow-mediated response per se
• Makes any other approaches to remove Dbase-
dependency redundant, including shear rate
normalisation
• Quantifies differences in the flow-mediated response
precisely
• Clarifies the causal pathway
• Is bad news for some

35. References
ATKINSON, G. & BATTERHAM, A. M. 2013. Allometric scaling of diameter change in the original flow-mediated dilation protocol.
Atherosclerosis, 226, 425-427.
ATKINSON, G. & BATTERHAM, A. M. 2013. The percentage flow-mediated dilation index: A large-sample investigation of its
appropriateness, potential for bias and causal nexus in vascular medicine. Vascular Medicine (United Kingdom), 18, 354-365.
ATKINSON, G. 2013. The dependence of FMD% on baseline diameter: A problem solved by allometric scaling. Clinical Science, 125, 53-
54.
ATKINSON, G. 2013. Impaired endothelial function in obstructive sleep apnoea: Allometric scaling can help estimate the true difference
in flow-mediated response. Heart, 99, 968-969.
ATKINSON, G. 2014. The difference in the flow-mediated response between steroid users and non-users. European Journal of
Preventive Cardiology, 21, 339.
ATKINSON, G. 2014. Shear rate normalization is not essential for removing the dependency of flow-mediated dilation on baseline artery
diameter: Past research revisited. Physiological Measurement, 35, 1825-1835.
ATKINSON, G. & BATTERHAM, A. M. 2012. The use of ratios and percentage changes in sports medicine: Time for a rethink?
International Journal of Sports Medicine, 33, 505-506.
ATKINSON, G. & BATTERHAM, A. M. 2013. Response to "Adjusting for brachial artery diameter in the analysis of flow-mediated
dilatation: Pitfalls of a landmark paper?". Atherosclerosis, 228, 282-283.
ATKINSON, G. & BATTERHAM, A. M. 2014. Response to: 'Allometric scaling of endothelium-dependent vasodilation: Brachial artery
flow-mediated dilation coming of age'. Vascular Medicine (United Kingdom), 19, 142-143.
ATKINSON, G. & BATTERHAM, A. M. 2014. When will the most important confounder of percentage flow-mediated dilation be reported
and adjusted for at the study level? International Journal of Cardiology, 172, 261-262.
ATKINSON, G. & BATTERHAM, A. M. 2015. The Clinical Relevance of the Percentage Flow-Mediated Dilation Index. Current Hypertension
Reports, 17.
ATKINSON, G., BATTERHAM, A. M., THIJSSEN, D. H. & GREEN, D. J. 2013. Reply to Stoner et al. regarding 'A new approach to improve
the specificity of flow-mediated dilation for indicating endothelial function in cardiovascular research'. Journal of Hypertension, 31,
1058.
ATKINSON, G., BATTERHAM, A. M., THIJSSEN, D. H. J. & GREEN, D. J. 2013. A new approach to improve the specificity of flow-mediated
dilation for indicating endothelial function in cardiovascular research. Journal of Hypertension, 31, 287-291.
ATKINSON, G., THOMPSON, A. & BATTERHAM, A. M. 2014. Baseline artery diameter: The hidden confounder in research syntheses on
human endothelial function? Heart Lung and Circulation, 23, 98-99.