To The Editor:
The article "Multiplier Method for Predicting Limb-Length Discrepancy" (82-A:
1432-1446, Oct. 2000), by Paley et al., provides a valuable contribution to
accurate prediction of growth in the lower extremity. The simplicity
and accuracy of prediction that this method affords on the basis
of just one or two measurements make it useful. Also, the authors
point out that it does not matter whether chronological or skeletal
age is used, and I certainly agree. The authors compare their method
favorably with Moseley’s conversion of the Anderson growth
curve1, which they refer to as
the gold standard. It has been suggested, however, that the Moseley method
may not be the most accurate2,3.
The authors provide a formula that can be used to predict the percentage
of total bone growth remaining on the basis of measurements of the
distal physis of the femur and the proximal physis of the tibia. They
assume that 71% of the growth of the femur comes from the
distal physis and that 57% of the growth of the tibia comes from
the proximal physis. The authors used the work of Anderson et al.4 for these percentages. Anderson et
al. derived these numbers from measurements made in a group of 206
individuals measured between the ages of ten and fifteen years only.
Three consecutive radiographs of temporary growth-arrest lines were
used to make their estimates. These were not the same subjects that
they followed longitudinally for their tables and graphs. Additional
work by our group has suggested that the percentage of growth that
occurs at each physis is not constant throughout growth5. In fact, the percentage changes with
each age. For instance, the proportion of growth at the distal femoral
growth plate in girls varies from 60% at the age of seven
years to 90% at the age of fourteen. The contribution of
the proximal tibial growth plate varies in boys from 50% at
the age of seven years to 80% at the age of sixteen. Over
the entire growth period, the two figures of 71% and 57% become reasonable
approximations but are not accurate at any given age.
Finally, the authors cite my work as indicating that ethnic origin, socioeconomic
status, and when individuals grew up are important in predicting
growth5. When the multiplier method
is used, these variables are unimportant. The authors suggest that
they may extend their method to provide predictions of spine length, height,
foot length, and upper-limb length. In the case of upper-extremity
growth, my work and that of others suggest that ethnic origin and
other factors may be important.
D. Paley, A. Bhave, J.E. Herzenberg, and J.R. Bowen reply:
We are familiar with Dr. Pritchett’s important contributions
to the study of lower and upper-limb-length growth. According to
his article5, the proportion of
growth from the distal femur and the proximal tibia is not the same
at each age. The proportion of growth occurring in the distal femoral physis
in girls varies from 60% to 90% between the ages
of seven and fourteen years, respectively, and in boys, from 55% to
90% between the ages of seven and sixteen years, respectively.
The growth contribution of the proximal tibia in girls varies from
50% at the age of nine years to 80% at age fourteen;
the growth contribution of the proximal tibia in boys varies from
50% at the age of ten years to 80% at the age
of sixteen. This is an annual increase of approximately 4% in both
boys and girls for femoral growth and an annual increase of 5% in
boys and 6% in girls for tibial growth. If one assumes
that the proportion of growth of the proximal and distal physes
of the femur and tibia vary with age as described above, stating
that the distal femur contributes a constant 71% and the
proximal tibia, a constant 57% is an oversimplification.
This oversimplification may be one of the factors leading to variability and
error in growth prediction with epiphysiodesis2,6-9.
To make Dr. Pritchett’s concept simple to use, we derived
simple equations that describe the overall average percentage of growth
from the distal femoral or proximal tibial physis for both boys
and girls until skeletal maturity (Table). For example, a boy’s
distal femur at the age of twelve years would be expected to grow
at a remaining average growth rate of ([2 12] + 59)%,
or 83%. It is this average growth percentage that is multiplied
by the growth remaining. Using the multiplier method, 83% is
multiplied by the formula G = L(M-1), in which G = the
growth remaining, L = the current length of the long limb, and
M = the multiplier for the current chronological age. In comparison,
the average growth rate for the distal femur as computed by the
method of Anderson et al. would be 71%. Therefore, the
Anderson method underestimates the amount of growth remaining from
the distal femoral physis when compared with the growth remaining according
to the Pritchett method. The maximum difference between the two methods
in the percentages of growth remaining occurs near the age of skeletal
maturity, and the least difference occurs at the youngest age for
calculation. For example, the difference between the two methods
in the percentage of the growth rate of the distal femoral physis
relative to the growth rate of the entire limb is 2% (73% according
to the Pritchett5 method versus
71% according to the method of Anderson et al.4) at age seven compared with 20% (91% according
to the Pritchett method versus 71% according to the Anderson method)
at age sixteen. The difference in calculated growth remaining is
minimal because the amount of growth remaining diminishes with increasing
age. Therefore, when the difference in the two methods is the greatest,
the amount of growth remaining is the least, and when the difference
between the methods is the least, the amount of growth remaining
is the greatest. Furthermore, epiphysiodesis is generally recommended
only for five centimeters or less of equalization of limb-length discrepancy.
Therefore, the error that occurs by using the approximation of Anderson
et al. is limited for all practical purposes. In an earlier draft
of our manuscript, we had included the above-noted information and
formulae. However, we elected to delete this because we felt that
it would be overly complex, given the fact that the practical implications
of these growth-percentage adjustments are minimal for the typical
epiphysiodesis patient. We do nonetheless acknowledge that these
modifications are technically more accurate. We are currently testing
the difference between the methods of Anderson et al. and those
of Pritchett in a large group of patients who have undergone epiphysiodesis,
and the results will be the subject of a future publication.
We have calculated multipliers for height and for upper-extremity
growth as well. For height, there are many databases, and, as with
the lower-extremity data, there is little difference in the multipliers
for different races and nationalities. There are fewer databases
for the upper-extremity measurements, and therefore we have been
unable to test whether these multipliers are different for different
national and racial groups. We would, however, be surprised if the upper
extremity did not follow the same pattern that the lower extremity
and height have.