Dear Editor:

We would like to echo Dr. Gilman’s comments [Letter to the Editor, WOUNDS 2003;15(7):A16–18] regarding the article, “Healing rate as a prognostic indicator of complete healing: A reaapraisal” [WOUNDS 2003;15(3):71–76]. The equation that Dr. Gilman derived is correct and provides a rate independent of wound size or shape. Dr. Falanga’s equation gives the average radius of a wound between the two time periods. One equation determines the speed of healing; the other resembles the measure the Food and Drug Administration (FDA) requires: time to heal, which is dependent on the size and shape of the wound and is a measure of size rather than a rate. Now, the derivative of Dr. Falanga’s equation becomes a rate similar to the Gilman equation akin to the relationship between distance traveled and velocity.

Dr. Goldman’s equation (Letter to the Editor, WOUNDS 2003;15(7):A14] also has problems. The premise that the change in area is proportional to the area is not correct. The wound heals by the cells moving toward the middle at potentially a constant rate. The change in area over area is not a constant and actually increases over time. In actuality, the K he measures is the true rate divided by the average radius that Dr. Falanga measures. The change in area is proportional to the average radius or average perimeter as used in Dr. Gilman’s equation.

Although this might seem like quibbling over minutia, in actuality a lot is at stake. If clinicians cannot agree on a true healing rate and still use it as an indicator of healing (as Dr. Falanga states) that must be validated, the FDA will never accept this as an outcome measure and we will always have to report time to heal.

Without getting “too involved with the mathematics” (a concern of Dr. Falanga) we can see some of the differences using a simple geometry—a circle (note it works similarly for any shape). The time component is removed to simplify the equations (the actual rate is obtained by dividing the answer by the time interval between the two measurements).

Dr. Gilman’s equation is:
?A/ (P1+ P2)/2

For a circle, it becomes:
[r12-r02]/[2r1+2r0]/2
(r12-r02)/2(r1+r0)/2
(r1-r0)(r1+r0)/2(r1+r0)/2
(r1-r0)
= ?r

Dr. Falanga’s equation is:
?A/?P

For a circle it becomes:
?A/(P1-P2)
(r12-r02)/2(r1-r0)
(r1-r0)(r1+r0)/(r1-r0)
(r1+r0)/2
=ravg

Dr. Goldman’s equation is:
?A/?T=kA

For a circle it becomes:
(r12-r02)=Kr02
(r1-r0)(r1+r0)=Kr02
2ravg?r/r02=K
2?r/ravg=K

Again, although the differences between the three approaches is subtle, much depends on the distinction. Only one gives a true healing rate (Gilman); the other two give measures related to average size (Falanga and Goldberg). Measures related to average size would have to be validated to prove they relate to time to heal—a healing rate does not because it is already an outcome measure. Again, until clinicians agree on a true healing rate, the FDA will never accept this as an outcome measure and we will always have to report time to heal. As all of these investigators are trying to achieve a healing rate, they see the problems with time to heal—wounds of different sizes, even if they heal at the same rate, heal at different times, which makes time to heal a noisy parameter. What we should shoot for is a healing rate to complete healing. This, we believe, has led to a delay in seeking FDA approval for treatments for wounds that heal, like pressure ulcers, in which the goal is to speed healing. This has forced us to pursue approval for wounds that typically do not heal (e.g., diabetic foot ulcers) unless we use the proposed intervention.

Dale Feldman, PhD
J. Amber Jennings, MS
Department of Biomedical Engineering
University of Alabama at Birmingham
Birmingham, Alabama