Journal of Dermatological Science 67 (2012) 15–19

New insights into therapy by mathematical analysis: Recalcitrant granulatedimproved more than sclerotic venous leg ulcers with amelogenin treatment§

Regina Renner a,*, Jan C. Simon b

a Hautklinik Erlangen, Universitatsklinikum Erlangen, Germanyb Klinik fur Dermatologie, Venerologie und Allergologie, Universitatsklinikum Leipzig A.o.R., Germany

A R T I C L E I N F O

Article history:

Received 19 October 2011

Accepted 17 April 2012

Keywords:

Mathematical model

Prediction

Wound treatment

Amelogenin

Xelma1

Recalcitrant wounds

Venous insufficiency

Modern wound treatment

Chronic wounds

Visual analogue scale

Pain intensity

A B S T R A C T

Background: Chronic wounds are both time consuming as well as costly. A new therapeutic option for

those wounds might be amelogenin, which supplies a temporary matrix to the fibroblasts and

keratinocytes.

Objective: To prove the hypotheses for a divergent therapeutic outcome, we treated granulated vs.

sclerotic chronic venous leg ulcers with amelogenin (Xelma1) 1�/week for 5–8 weeks.

Methods: The analysis of the treatment was performed by applying a recently published mathematical

model. This model can predict and evaluate different wound treatment methods by treating only few

patients which is even more practicable for diseases with different influencing factors within patients

groups because it is easier to collect only a small homogenous number of patients than multiple.

Results: We treated 12 granulated vs. 16 sclerotic ulcerations. 5 (42%) of the granulated ulcerations with

a mean initial wound area of 18.3 cm2 showed optimal wound healing (>90% epithelization). The

average area of new epithelia was 11.9 cm2.

Nine (56%) of the sclerotic ulcerations showed optimal wound healing with an initial wound area of

7.5 cm2 and a total average area of 4.1 cm2 with new epithelia. For comparison of those groups, we

extrapolate to a hypothetic mean sclerotic wound area of 18.3 cm2 analogue to the granulated

ulcerations. This calculates to a mean neoepithel of only 6 cm2 for sclerotic ulcerations. Further on, we

calculated about 2% of the wound area that proliferated in contrast to about 3% in granulated wounds.

Conclusions: Although sclerotic ulcerations show higher growth rates, Xelma1 seems to be more

effective in granulated ulcerations. For larger sclerotic ulcerations the mean maximal covered wound

area with neoepithelia is reduced to about 33% in contrast to 65% in granulated ulcerations.

� 2012 Japanese Society for Investigative Dermatology. Published by Elsevier Ireland Ltd. All rights

reserved.

Contents lists available at SciVerse ScienceDirect

Journal of Dermatological Science

jou r nal h o mep ag e: w ww .e lsev ier . co m / jds

1. Introduction

The majority of chronic ulcerations are venous or venous-arterialleg ulcers which account for about 50–70% of chronic ulcerations[1,2]. A particular challenge is a subgroup of wounds that do not healdespite optimized wound treatment and sufficient compressiontherapy. In the past years, the focus has been placed on theimportance of the extracellular matrix (ECM) for wound healing [3].In 2008, we reported on a small case series involving the clinicaleffects of an amelogenin containing hydrogel (Xelma1) [4].

Amelogenin is produced by ameloblasts and is normally foundin developing embryonal tooth enamel in different mammals.

§ The investigation was supported by the Molnlycke Health Care AB, Goteborg,

Sweden.

* Corresponding author at: Hautklinik Erlangen, Universitatsklinikum Erlangen,

Ulmenweg 18, 91054 Erlangen, Germany. Tel.: +49 9131 85 33851.

E-mail address: Regina.renner@uk-erlangen.de (R. Renner).

0923-1811/$36.00 � 2012 Japanese Society for Investigative Dermatology. Published b

http://dx.doi.org/10.1016/j.jdermsci.2012.04.007

Amelogenin is a hydrophobic 20 kDa protein that, because of itsbipolar characteristics, can aggregate under physiological condi-tions to larger stable hydrophobic ECM structures and build up asurrogate matrix [5]. This temporary matrix should providegrowth structures for the fibroblasts, stimulate their migrationand adhesion and finally lead to healing of the wound [6,7]. Thissupports the hypothesis that there may be a divergent result aftertreatment of granulated or sclerotic ulcerations and especially thatsclerotic ulcerations may benefit more from the treatment becauseof their reduced potential to build up granulation tissue [8,9].Additionally, we tried to analyse whether there is a correlationbetween pain intensity (measured via the visual analogue scale)and response to treatment.

The evaluation of the treatment was carried out by using arecently published mathematical formula for predicting andevaluating different wound treatment methods [10]. Mathematicmodelling is not the same like a statistical analysis. For mathematicmodelling, it is not necessary to treat many patients but only a fewof about 15 patients with measurements once or twice a week.

y Elsevier Ireland Ltd. All rights reserved.

R. Renner, J.C. Simon / Journal of Dermatological Science 67 (2012) 15–1916

With this data, it is possible to adapt the healing trajectories to thereviewed group and to compare the results. To collect smallnumbers of patients are even more practicable for diseases withinhomogenity within their groups instead of the multiple forstatistical analysis, e.g. leg ulcers with many different influencingfactors like divergent persistence of ulcer durations or divergentulcer areas and so on. Also, this method seems possible for analysisfor maybe more hazardous treatment regimes, because it is notnecessary to expose many patients with the therapy to see adifference.

2. Patients

2.1. Conditions

All patients were suffering from at least one or more chronicvenous leg ulcers that had been recalcitrant under various kinds oftreatment. Allocation to one of the two groups was performed by awound treatment specialist according to the clinical appearance ofthe wound.

In the group with granulated ulcerations (G), there were 8patients with a total of 12 recalcitrant wounds and, in the groupwith sclerotic ulcerations (S), there were 7 patients with a total of16 ulcerations. We treated all wounds with amelogenin once aweek for at least 5 and for a maximum of 8 weeks corresponding tothe clinical improvement and willingness of the patient (details seeTable 1a).

2.2. Definitions

A ‘‘granulated wound’’ was defined as one with a wound groundcompletely or almost completely (>80%) covered by newly formedsoft vascular pink or red granulation tissue.

A ‘‘sclerotic wound’’ was defined as one with a wound groundcovered only marginally – or not at all – with granulation tissue(<0%). Instead of this, the wound ground was hard, firm andindurated like a scar.

We included only wounds dating back to �6 months that wereunder continuing adequate and causative treatment but showedrecalcitrant wound healing, which means that all patients (n = 15)were obliged to carry out consistent and sufficient compressiontherapy, and it was required that the wound dressing used beforestarting amelogenin treatment (at least >4 weeks for amelogenintreatment) had not improved wound status. These wounds weconsidered to be ‘‘recalcitrant wounds’’.

Table 1aData of the included patients and their ulcerations.

Granulated

Patients 8

Female:male 5:3

Mean age of the patients 65 years (minimum 53, maxi

Ulcerations 12

Mean ulcer duration 28 months (minimum 9, max

Table 1bResults of the ulcerations and their observed and calculated healing course under ther

Granulated

Evaluated ulcerations 9

Healed (>90% wound coverage) 5 (42%)

Mean ulcer area (cm2) 18.3 (minimum 0.8, maximum 59)

Mean wound coveragea 64%

Insufficient effect 3 (25%)

a Wound coverage ¼ area of neoepithelwound area .

3. Materials and methods

Xelma1 consists of a mixture of 3% amelogenin in propyleneglycol alginate and water. It totally degrades within one week. It isa hydrogel with a transparent, slightly yellowish appearance that isof lower viscosity at room temperature and higher viscosity atrefrigerator temperature. Xelma1 was appropriately stored in therefrigerator at a max. of 8 8C throughout the complete treatmentperiod.

Wound area was measured two dimensionally with ImageAccess (Version Enterprise 10, Imagic Bildverarbeitung AG,Glattbrugg, Switzerland) by photographs that were taken duringthe treatment period.

3.1. Basics of the mathematic model

To allow a better understanding of the context, we would like torecapitulate some elementary points of our mathematical model.In this model, we suggest that an area of fibroblasts andkeratinocytes at the edge of the wound is activated to proliferateby the treatment provided to the wound. At a later stage, weassume that intercellular interaction puts the proliferating cellsunder stress. This will influence the further growth rate of the cells.They compete against each other, e.g. in terms of nutrition. Finally,cell growth will stagnate although the wound area might not betotally covered with neoepithelia. This hypothesis results in thefollowing growth function [10]:

PðtÞ ¼ K � P0

a � P0 þ ðK � a � P0Þ � e�b�K�t (1)

P(t) characterizes the area of neoepithelia in cm2 at time point t, P0

defines the area of cells in cm2 that proliferate from the edge of thewound at the beginning of treatment t = 0, K represents the initialwound area in cm2, and b defines the growth rate and parameter a

takes the stress situation into account which varies from ulcerationto ulceration.

t ! 1 leads to Pð1Þ ¼ K

aand

Pð1ÞK

¼maximal neoepithelia

wound area¼ 1

a; (2)

respectively, which represents the maximal wound coverage.Only the parameter of the wound area at the time point t = 0 is

measurable directly at the beginning of treatment. All otherparameters have to be calculated and adapted to the equation by

Sclerotic

7

4:3

mum 73) 65 years (minimum 49, maximum 86)

16

imum 84) 24 months (minimum 6, maximum 69)

apy with Xelma1.

Sclerotic Sclerotic (extrapolation)

6 –

9 (56%) –

7.5 (minimum 3.8, maximum 13) 18.3

55% 33%

7 (44%) –

Parameter a vs. granulated ulcer area Ka= 0.03*K + 1

R2 = 0 .93

1

1.5

2

2.5

3

6050403020100

Ulcer area K in cm2

Para

mete

r a

a

R. Renner, J.C. Simon / Journal of Dermatological Science 67 (2012) 15–19 17

‘‘best fitting’’ so that the temporal sequence of the observed datawill be described exactly by this growth function. The values of K,P0, a and b describe the healing curve of each ulcerations.

Within one patient group, these parameters show a character-istic course in relation to wound area K and the age of theulceration. For example: a vs. K is a linear correlation. P0 vs. K istheoretically proportional to

ffiffiffiffi

Kp

but can be described simplifiedalso by a linear function.

The characteristics of a group are reflected by the functionalcourse of their parameters of wound area and wound duration.If the course of an exemplary group 1 is described byaGroup1 = ma1 � K + 1, their slope factor ma1 is characteristic for aspecific attribute of the group. The data of the comparison groupcan be described also by the equation aGroup2 = ma2 � K + 1 but witha divergent slope factor ma2. A similar behaviour can be shown forall other parameters.

3.2. Pain evaluation

We used the visual analogue scale (VAS) with a 10 cm baselineof a graphic rating scale with the extreme markers of ‘‘no pain atall’’ and ‘‘maximum pain’’. The wound pain was measured on theflip side of the VAS (min. 0 = no pain at all, max. 10 = maximumpain). Patients were canvassed at every visit for their pain intensityby using the VAS scale. The corresponding numeric value on theback of the scale was documented and evaluated.

4. Results

4.1. Observations

All patients suffered from chronic venous insufficiency and wedocumented 3.6 not necessary wound related additional diagnosesin the G group as well as 3.8 additional diagnoses in the S group.Details to our population are shown in Table 1a. Unfortunately, wecould not use the same wound dressing in the treatment of allpatients due to different local wound conditions. However, thewound dressing used during treatment with amelogenin had beenused before inclusion in the programme for more than 4 weekswithout observing any improvement to the wound.

According to clinical criteria, no wound was infected in anypatient during the amelogenin application. Wound marginsshowed no increased maceration. We evaluated only dataobserved for which we could generate the healing trajectories ofP(t) vs. time (t) (see Fig. 1).

On the basis of the parameter ‘‘wound area reduction’’ from thebeginning to the end of the treatment, we observed (see Table 1b)in the G group, 7 of 12 ulcerations (58%) showed a very goodhealing process, and 5 of these ulcerations showed wound area

Neoepithel area vs. time

0

1

2

3

4

0 20 40 60 80

time in days

Ne

oe

pith

eliu

m in

cm

2

observed calculated

Fig. 1. Example of a growth function with observed K = 6.5 cm2 and calculated

values P0 = 0.073 cm2, a = 1.79 and b = 0.018 of a patient in the group of granulated

(G) ulcerations.

coverage of >90%. In the S group, 9 of 16 ulcerations (56%)demonstrated a very good healing process (>90% epithelization).Within this group, 3 ulcerations healed during the treatmentperiod, but could not be taken into account for the functionalanalysis because of too few measurement values.

4.2. Extrapolation

Initially, the mean value of the granulated ulcer areas was18.3 cm2 (minimum 0.8 cm2, maximum 59 cm2). We calculatedfrom the corresponding diagram a vs. K (Fig. 2a) and with Eq. (2)the parameter a = 1.55 and expected a mean wound area coverageof 64%, which corresponds to an area of neoepithelia of 11.9 cm2.

In the sclerotic group, the mean value of the initial wound areawas 7.5 cm2 (minimum 3.8 cm2, maximum 13 cm2). As before inFig. 2a, we found in Fig. 2b that the corresponding value a = 1.8leads to a calculated 55% coverage with neoepithelia, whichcorresponds to 4.1 cm2 of neoepithelia. The value calculatedmatches the data we observed. However, the S group comparespoorly with the G group: therefore we extrapolate regarding Fig. 2bto the mean value of wound area of 18.3 cm2 equivalent to the realvalue of the G-group. This would result in a = 3. The maximumwound coverage is therefore (Eq. (2)) 33%. This means that if theinitial wound area of sclerotic wounds would be 18.3 cm2, wecould expect 6 cm2 of neoepithel. But, the mean area of neoepithelof granulated ulcerations (Fig. 2a) is 11.9 cm2 (see Table 2).

P0 is the area of cells that are stimulated to proliferate.Granulated ulcerations mobilize about 3–5.5% of their ulcer areadependent on the initial wound area as opposed to only about 2% inthe case of sclerotic ulcerations. This area is described by theequation

P0ffi 2 �ffiffiffiffiffiffiffiffiffiffiffi

p � Kp

� d (3)

Parameter a vs. sclerotic ulcer area K

a = 0.12 *K+0.89 R2 = 0.81

1

1.5

2

2.5

14121086420

Ulcus area K in cm 2

Para

mete

r a

b

Fig. 2. Graphical illustration of a vs. K of the (a) granulated ulcerations and (b)

sclerotic ulcerations, including the coefficient of determination R2.

Table 2Comparison of the mathematic results of the granulated and sclerotic ulcerations.

Granulated

ulcerations

Sclerotic ulcerations

a vs. K a = 0.03 � K + 1 a = 0.12 � K + 0.89

Slope factor 0.03 0.12

P0 vs. K P0 ¼ 0:205 �ffiffiffiffi

Kp

P0 ¼ 0:035 �ffiffiffiffi

Kp

Viable cell layer (t = 0) d = 0.6 mm d = 0.1 mm

Mean epithel coverage 64% Extrapolated value 33%

Mean increase of neoepithel 11.9 cm2 Expected: 6 cm2

R. Renner, J.C. Simon / Journal of Dermatological Science 67 (2012) 15–1918

In this case, the essential parameter is the width d of the activatedlayer of the edge of the wound. By means of Fig. 3a and b we cancalculate the value of d. Granulated ulcerations show a muchhigher value (d = 0.6 mm) then sclerotic ulcerations (d = 0.1 mm).According to our model, d also influences the growth rate of theneoepithel. In the diagrams of Fig. 3a and b, we choose thegraphical illustration of the root function to present the variation ofthe viable cells P0.

4.3. Pain evaluation

Finally, we asked patients about their individual wound painlevels using the visual analogue scale. We compared woundhealing process and pain intensity continuously. Thus, wecompared each visit to the previous and following, and not onlyfirst to last visit. Before treatment, the patients with granulatedulcerations complained about pain with a mean VAS of 5.7, inthe group with sclerotic ulcerations with a mean VAS of 3. At theend of treatment, VAS in the granulated group was 3.1, and 1 inthe patients with sclerotic ulcerations. So, we observed a trendtowards higher pain values in the G group than in the S group.We could not find a correlation between pain improvement andtherapeutic improvement in individual patients, although meanpain scores were reduced over the course of therapy.

P0 vs. granulated ulcer area KP0 = 0.03 *K + 0.25

R2 = 0.91

0

0.5

1

1.5

2

6050403020100

Ulcer area K in cm2

P0 in

cm

2

P0 vs. sclerotic ulcer area K P0 = 0.02 *K - 0 .01

R2 = 0 .87

0

0.05

0.1

0.15

0.2

0.25

1412108642

Ulcer area K in cm2

Po in

cm

2

b

a

Fig. 3. Area of cells in simplified linear description in the (a) granulated wounds and

(b) sclerotic wounds that proliferate at the beginning of the therapy, including the

coefficient of determination R2.

5. Discussion

In chronic wounds there is a defective reorganization of theECM [11,12]. The integrity of the ECM seems to be essential inorder to avoid complications in wound healing. If necessary matrixstructures are missing it is possible that centripetal migration offibroblasts is impeded and induction of granulation tissue andneoepithelization is prolonged. Turn-over of the ECM is a multi-factorial sequence [3], decrease of the ECM is a result of a disturbedratio of growth and pro-inflammatory cytocines via overexpres-sion of matrix metalloproteinases that finally lead to a chronicinflammatory reaction which damages the newly generated ECM.By applying amelogenin, a temporary matrix is provided forfibroblasts and keratinocytes to which they can adhere.

5.1. Benefit of our mathematic modelling

We can detect marked differences in group characteristicsespecially for small groups of patients by our mathematic model.We do not observe results that we can accept or decline later on byuse of thesis, antithesis or level of significance. Our basic concept ismathematic equations. For example, Eq. (1) describes thechronological progress of wound healing by means of theparameter K, P0, a and b, wherein each ulcer is defined by specificresults of these parameters. It is obvious in Figs. 2–4, that theseresults are depended in a typical way of the wound area K.

Parameter a can take on values �1 according to our mathematicmodel. Its dependency on K is described perfectly by the equationa = ma � K + 1. An essential parameter for our predication is thevalue of the slope factor ma. Granulated ulcerations show clearlydivergent values compared to sclerotic ulcerations.

The quality of the observed and measured functions in Figs. 1–4is defined by the correlating factor R2. R2 = 1 means that the givenfunctional equation correlates exactly with our observed values. Inour case, we can characterize our observed values with values ofR2 = 0.9 with minimal variations.

5.2. Evaluation of our results

Direct evaluation of both groups is not comparable becausesclerotic wounds have higher chances for healing because of theirrelatively small wound areas. Our mathematic model offers thepossibility of extrapolation to similar baseline levels of both woundareas. Fig. 2b shows the individually calculated parameter a for eachulceration in correlation to K. If calculated on the basis of a meanvalue of wound area of 18.3 cm2, this results in a more effectiveepithelization of granulated wounds (11.9 cm2 vs. 6 cm2, see Section4) Therefore, Xelma1 is more effective in granulated ulcerations.

ß vs. ulcer area K

R2 = 0.95

0

0.01

0.02

0.03

0.04

0.05

6050403020100

Ulcer area K in cm 2

Para

mete

r ß

granulate d sclerotic

Fig. 4. Growth rates b of granulated vs. sclerotic ulcerations, including the

coefficient of determination R2.

Table 3Comparison with the data of Vowden et al. [14].

Healed Up to 50% reduced

wound area

Insufficient effect

Comparison group 35% 35% 30%

Our patients (total) 42% 33% 25%

R. Renner, J.C. Simon / Journal of Dermatological Science 67 (2012) 15–19 19

Fig. 4 present changes of the growth rate b for different woundareas. It is obviously that the value of b is nearly twice as high forsclerotic wound areas in contrast to granulated wound areas. Butfinally, they show decreased epithelization rates if applied to largerulcer areas. This might be due to reduced neovascularizationwithin the sclerosis [13].

This hypothesis is supported by the additional analysis whichcalculates the percentage of proliferating cells in the wound duringtherapy (Fig. 3a and b).

5.3. Comparison with other results

If we compare our data with previously published data forXelma1, the results are very interesting. For example, we analysedthe data of Romanelli et al. [14,15] by means of our mathematicalformula. Romanelli et al. [15] published details of three patientgroups treated with Xelma1, and observed a mean woundcoverage of 22% at 3 weeks, 48% at 6 weeks and 72% at 12 weeks.We summarized these patients and their ulcerations, respectively(n = 29), working on the assumption that these three groups aresimilar. If we calculate our growth function parameters for these29 ulcerations, there is an excellent result of P0 = 0.074 cm2,a = 1.33 and b = 0.064. Romanelli et al. [14,15] treated ulcerationswith a wound area <30 cm2. According to our calculation we canassume that their mean ulcer area was about 10 cm2. This leads tofurther conclusions for these ulcerations: treatment with Xelma1

stimulated about 1% of the wound area to proliferate in theseulcerations. Furthermore, we can predict a maximum of 75% meanwound coverage of the wound area in this example. Thiscorresponds very well to the data of our group of granulatedwounds. However, comparison would only be possible if thepatients of Romanelli [14,15] and our group have undergone thesame pre-conditions. Unfortunately, this could not be verifiedbecause of missing information in the published data.

In addition, we can confirm the results of the study of Vowdenet al. [16], cited by Romanelli et al. [14] (see also Table 3). As in thepreviously mentioned study, we based our comparison solely onthe parameter ‘‘reduction of wound area’’ working on theassumption that both of the groups reported on are comparable.However, according to our mathematic model [10], maximumwound coverage is not only dependent on the initial wound area,but also on the age of the ulcer as demonstrated before [17].

5.4. Pain evaluation

The pain scores decreased during treatment in the G group aswell as in the S group. The results of the VAS in general showedhigher pain values in the G group than in the S group. This is inaccordance with clinical observations that show, for example, thatcurettage is possible in patients with sclerotic ulcers mostlywithout topical anaesthesia. However, we could not find acorrelation between pain improvement and therapeutic improve-ment as a marker for healing in individual patients, maybe due tothe small number of patients. The pain score reduction duringtreatment without wound improvement might be caused byunspecific effects of the hydrogel-structure of Xelma1 (e.g. cooling,minimizing discomfort because of dry wound surface). In thestudies of Vowden et al. [18,19] pain reduction was significant towound improvement, but only in subgroup-analysis. Also, theycompared placebo vs. amelogenin, and also first to last visitconcerning pain evaluation. We did not compare placebo vs.amelogenin, but two groups with the same treatment.

6. Conclusion

Treatment with amelogenin is more successful in granulatedulcerations than in sclerotic ulcerations. Sclerotic ulcerations havea higher growth rate at the beginning of the treatment but on theother hand in larger ulcerations their maximally covered woundarea with neoepithelia is reduced. Finally, sclerotic ulcerations>10 cm2 will show a wound coverage with neoepithelia of <50%.

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