**Errors in Mayo Clinic Paper**

September 2006

Dear Sir or Madam,

I am very concerned about the
accuracy the article by *(Sorenson et al, 2006)
*__Electrophysiological
findings in a cohort of old polio survivors__
Eric J. Sorenson, Jasper
R. Daube, and Anthony J.Windebank published in Journal of the
Peripheral Nervous System 11:241–246 (2006)

I've reviewed the article and if the math is done correctly, one gets entirely different results.

Page 242 bottom of first column to top of second column describes in detail the method for calculating the rate of decline. Dr. Sorenson's group describe using the first order kinetic formula. The one at the bottom of the page gives (ln MUNE(5)) = (ln MUNE(0)) (-kT) which is not right.

The change in P with respect to time, dP/dt = k*P is the first order kinetic formula.

Integrating,
one gets P(t) = P(0)*e(to the power k*t) *(Stewart, 2003) *so

** ****kt
=ln (MUNE(t) /MUNE(0) ) **is
the correct formula (Divide first __then
__take
the natural log)

Dividing by the time t gives us k = 1/t * [ ln (MUNE(t) /MUNE(0)) ]

Using the study data, k = 1/5 * (ln (331 / 407) ) = -.0413 using the 5 year data and

k = 1/15 * (ln (226/ 407) ) = -.0392 using the 15 year data

k
is the relative growth rate (a negative value indicates loss) and
since t is in years, expressing k as a percentage gives MUNE declines
at a rate of **4.13% per year **using the 5 year data or **3.92%
per year** using the 15 year data.

The
authors state that the “While neither model of loss
(proportional or linear) closely matches the data, the stronger
correlation and better coefficient of variation would favor the
proportional model over the linear model.” After concluding the
loss was proportional, at the top of page 245, they give us
“a rate of decline of 2.9%
annually” (with
no supporting calculations). Using the model they recommend and the
given data, 2.9% is wrong. The rate of decline is **4.13%
per year **using the 5 year data or
**3.92% per year**
using the 15 year data as show in the calculations above.

The
study (*Doherty et al, 2003)*
is cited as the source of "However, in a cross-sectional study
of normal subjects, there was a decline in the thenar MUNE counts
from a mean of 288 to 139 between
the ages of 40 and 60 years *(Doherty
et al., 2003)*. This represents
approximately a 50% decline, or 2–3%
per year." The study then compares
2.9% to the “normal” value calculated using the MUNE mean
values from *(Doherty et al, 2003) *.
If the authors used data other than their MUNE means to calculate
their rate of decline, the data are not comparable.

I reviewed the study by Doherty
et al. They very appropriately didn't even try to give a rate of
decline per year. In their study, the two groups are described as "a
group of younger (20 - 40 years) and
older (60 to 80 years) healthy
subjects." The two groups are better described in *(Doherty et
al, 1993)* "In 37 trials from 17 younger subjects (20-40
years), the mean MUE was 288 +/- 95 SD based on negative peak area
and, in 33 trials from 20 older subjects, mean values were 139 +/-
68.” These are the numbers used to calculate "normal MUNE
losses" at the bottom of page 244 of *(Sorenson et al, 2006).*

Using the
proportional model and (lacking more data,) the __middle__ of the
age ranges instead of the upper extreme of one range and the lower
extreme of the other, one gets a change from 288 to 139 from age 30
to 70. (40 years)

k
= 1/40 ((ln (139 / 288) ) = -0.018 or a decline of **1.8%
per year.**

or,
using the more general conclusion in *(Doherty et al, 2003)*
that “on balance, average MUNE values in groups over 60 years
of age show reduction of about 50% in comparison to younger controls”
and the formula on page 242 of *(Sorenson et al, 2006).*

k
= -0.693/(t ½) = -0.693/(40) =-0.0172 or a decline of **1.72%
per year.**

The
data do not support the conclusion “our
polio cohort did not age any differently than a normal population.
This suggests that the most likely cause for the decline in our polio
survivors is aging alone.” *(Sorenson
et al, 2006)* The polio
survivors' MUNE losses of **4.13%
per year **using the 5
year data or **3.92% per
year** using the 15 year
data were more than twice the rate of **1.72%
per year **or **1.8%
per year **in a “normal”
population. This is what McComas found as stated on page 244.
“McComas reported that the
loss of motor units in their subjects was approximately twice that
seen in their normal population *(McComas
et al., 1997)*.”

On page 243,
*(Sorenson et al, 2006), *the
authors state “There
was no association between the magnitude of decline in either the
summated CMAP amplitude or the summated MUNE and the presence of
symptomatic progression.” and “There was a mean decline
in MUNE of 229
(SD 43) for the asymptomatic group
and a mean decline of 120
(SD 24) for the symptomatic
group (p ¼ 0.09).” Either this is wrong or Table 2 (on
the same page) is wrong. Table 2 shows MUNE decline of 229
in the symptomatic group
and 120
in the asymptomatic
group. The numbers in Table 2 are internally consistent, but the
15 year MUNE values are switched in Table 2 and the paragraph on page
243 cited above.

Using MUNE values in Table 2 and the formula for proportional loss,

**All
subjects** decline at
4.1% (5 years) and 3.9% (15 years)

**Symptomatic**
at 3.5%
(5 years) and 6.2% (15 years)

**Asymptomatic**
at 2%
(5 years) and 1.68% (15 years)

According
to Table 2, over the 15 year period, the symptomatic group are losing
motor units at **3.7
times the rate** of the
asymptomatic group. The fact that “only seven subjects
remained asymptomatic” probably means that this is not
statistically significant so no conclusions can be drawn, not that no
association exists. Either the
table is wrong, or the conclusions are wrong.

I have only looked at the MUNE data in detail so I can not comment on the CMAP data.

I am Dr. Mavis Matheson, M.D. (UBC), B Sc. (hon) Mathematics (U of Saskatchewan). I had polio at age 16 months and live with the late effects of polio.

**References:**

**Doherty**
TJ*, *__The
estimated numbers and relative sizes of thenar motor units as
selected by multiple point stimulation in young and older adults.__
Muscle & Nerve [Muscle Nerve], (1993) Apr; Vol. 16 (4), pp.
355-366.

Doherty TJ, Stashuk DW, Brown WF,
__MUNE measurement of age-related changes.__ J Clin Neurophysiol,
(2003) 55:158–163.

McComas AJ, Quartly C, Griggs RC,
__Early and late losses of motor units after poliomyelitis__
Brain, (1997), 120, 1415-1421.

Stewart J, __Exponential growth
and decay__. Calculus 5e,
(2003), 10.4:647-655.

Sorenson
EJ, Daube JR,Windebank AJ, __A
15-year follow-up of neuromuscular function in patients with prior
poliomyelitis.__ Neurology
[Neurology], 2005 Mar 22; Vol. 64 (6), pp. 1070-1072.

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