Mohs math – where the error hides
© Ellis et al; licensee BioMed Central Ltd. 2006
Received: 18 August 2006
Accepted: 06 December 2006
Published: 06 December 2006
Mohs surgical technique allows a full view of surgical margins and has a reported cure rate approaching 100%.
A survey amongst Mohs surgeons was performed to assess operator technique. In addition, an animated clay model was constructed to identify and quantify tissue movement seen during the processing of Mohs surgical specimens.
There is variability in technique used in Mohs surgery in regards to the thickness of layers, and the number of blocks layers are cut into. A mathematical model is described which assesses the clinical impact of this variability.
Our mathematical model identifies key aspects of technique that may contribute to error. To keep the inherent error rate at a minimum, we advocate minimal division and minimal physical thickness of Mohs specimens.
Over the past sixty years, Mohs micrographic surgery has become the standard of care in the management and treatment of many skin cancers. Unlike standard vertical sectioning, the horizontal sectioning utilized by Mohs technique allows a full view of surgical margins  and has a reported cure rate between 88 to 100% [2–7]. Differences in operator technique are already known [8, 9], however their impact into the ability to fully view the surgical margins have not been defined. This paper is divided into two parts; Part I: A survey of the techniques of practicing Mohs Surgeons. Part II: A mathematical model is described which assesses the clinical impact of technique variability.
1. How many years have you been performing Mohs Surgery?
2. Who cuts your excised layer into blocks?
3. For specimens ranging from 1–4 cm, on average
a. How many blocks is the excised layer cut into when processing?
b. What is the thickness (depth) of your first Mohs layer?
Mathematical model methods
To best appreciate the following mathematical model, it is crucial for one to be familiar with the processing of tissue in Mohs surgery. For those not involved with Mohs surgery on a daily basis, this can be challenging to visualize. As such, a clay animation of ideal Mohs tissue processing is provided to clarify the geometry of expected tissue movement during processing [see Additional file 1].
The question remains... does it matter? A mathematical model was created to assess the importance of these Mohs technique variables.
Mathematical model results, derivation of a mathematical proof
Careful analysis of tissue movement in "ideal" processing, and the errors that may occur when tissue is processed allows one to derive a mathematical expression. This is a useful exercise because analysis of the expression can allow one to draw conclusions related to the specific aspects of the technique that contribute most to potentiating error.
Step 1: Calculation of ideal area (Figure 19)
Abase = Πr2
Aside = (d)(r1) + 1/2(d)2
Total area of the side walls = (N) × (Aside)
Step 4: A false negative is the ideal area (Abase) minus a percentage of Aside. And a false positive is the idea area plus a percentage of Aside.
Let k = the percentage roll, falling between 0 and 1.
Abase - k(Aside)(N)
Abase + k(Aside)(N)
Πr2 - k(Aside)(N)
Πr2 + k(Aside)(N)
Πr2 - k((d)(r1) + 1/2(d)2)(N)
Πr2 + k((d)(r1) + 1/2(d)2)(N)
Πr2 - k((d)((r - d/0.851)) + 1/2(d)2)(N)
Πr2 + k((d)((r - d/0.851)) + 1/2(d)2)(N)
r = r1 + r2
r1 = r - r2
Sin (45) = d/r2
r2 = d/Sin (45) = d/0.851
r1 = (r - d/0.851)
Step 5: We can place the expression of error over the ideal area, to create a mathematical formula that predicts error. This formula will produce the value that is equal to the percentage of tissue that is lost from the ideal preparation of a specimen. If we assume only a 5% roll (k = 0.05), we have the following expression (see Figure 23) (Note: for simplicity, let us assume that k is the same on each side)
Is recurrence of a tumor after Mohs surgery always a result of error? Persistent tumor may be related to "difficulties of anatomic site, tumor size and histological subtype, as well as observer error in histological interpretation and potential tumor multifocality" . There are also many processing errors that may occur including inaccurate mapping, tissue staining, and tissue preparation for sectioning. It is clear that in order to maximize the value of the technique, processing of tissue must be as ideal as possible.
The importance of processing tissue in an 'ideal way' is not a new one. The benefits of processing a layer as one block have been previously described . In addition, several authors have suggested techniques to facilitate obtaining quality and complete horizontal sections [15–17].
It seems prudent to anticipate some questions that this paper may raise, and provide answers at this time. One frequently asked question is "Wouldn't you notice missing tissue (i.e.: edge role)" The answer is simply no. Remember that the clay models show an exaggerated event to help illustrate a potential event. If only 5% of the tissue rolled, this would unlikely be perceivable. Even if it were perceived that this tissue seemed "smaller", it would be easy to disregard this fact as anticipated tissue shrinkage .
Another question often asked relates to tissue dyes. In the models presented, the clay was not marked with an orientation dye. If the edge lifted, wouldn't the marked edge be lost? The answer is that it depends. As we know, the orientation dye we use is far from precise, and often "bleeds" slightly. It is easy to imagine tissue could be removed form the plane of section, while some orientation dye remains. One must remember that the only absolute edge is an epidermal edge; it is the non-epithelial edges that are subject to the errors we have demonstrated. As tissue dyes do "bleed", they cannot be considered absolute boundary markers.
Finally, curetting or debulking a tumor may have additional benefit related to processing. Though this is controversial amongst Mohs surgeons, removing the bulk of a tumor will serve to significantly decrease the thickness of a Mohs layer. In doing so, it may serve to decrease the likelihood of the processing errors described here.
The model presented in this paper could be adapted to any layer of Mohs surgery, with or without debulking. The conclusions will always be the same. A variety of processing errors can be significantly reduced by taking thin layers, and processing tissue in the least number of blocks possible.
As previously described, variability exists in the technique of Mohs Surgery. This paper represents the first known attempt to quantitate in a mathematical way the consequence of some components of this variation. Evidence is provided which suggests that minimizing the number of blocks an excised layer is cut into when processing, and minimizing the thickness or depth of an excised layer can dramatically improve the cure rate of Mohs Surgery.
- r = r1 + r2 :
radius of Abase
- r1 :
length of base
- r2 :
length of side wall
Number of blocks
- Cottel WI, Bailin PL, Albom MJ, Bernstein G, Braun M 3rd, Hanke CW, Sutnick TB, Swanson NA: Essentials of Mohs micrographic surgery. J Dermatol Surg Oncol 1988, 14: 11–3.View ArticlePubMedGoogle Scholar
- Leibovitch I, Huilgol SC, Selva D, Richards S, Paver R: Basal cell carcinoma treated with Mohs surgery in Australia I. Experience over 10 years. J Am Acad Dermatol 2005, 53: 445–51. 10.1016/j.jaad.2005.04.083View ArticlePubMedGoogle Scholar
- Leibovitch I, Huilgol SC, Selva D, Richards S, Paver R: Basal cell carcinoma treated with Mohs surgery in Australia II. Outcome at 5-year follow-up. J Am Acad Dermatol 2005, 53: 452–7. 10.1016/j.jaad.2005.04.087View ArticlePubMedGoogle Scholar
- Malhotra R, Huilgol SC, Huynh NT, Selva D: The Australian Mohs database: periocular squamous cell carcinoma. Ophthalmology 2004, 111: 617–23. 10.1016/j.ophtha.2003.07.020View ArticlePubMedGoogle Scholar
- Malhotra R, James CL, Selva D, Huynh N, Huilgol SC: The Australian Mohs database: periocular squamous intraepidermal carcinoma. Ophthalmology 2004, 111: 1925–9.PubMedGoogle Scholar
- Malhotra R, James CL, Selva D, Huynh N, Huilgol SC: The Australian Mohs database, part II: periocular basal cell carcinoma outcome at 5-year follow-up. Ophthalmology 2004, 111: 631–6. 10.1016/j.ophtha.2003.11.004View ArticlePubMedGoogle Scholar
- Malhotra R, Huilgol SC, Huynh NT, Selva D: The Australian Mohs database, part I: periocular basal cell carcinoma experience over 7 years. Ophthalmology 2004, 111: 624–30. 10.1016/j.ophtha.2003.12.003View ArticlePubMedGoogle Scholar
- Silapunt S, Peterson SR, Alcalay J, Goldberg LH: Mohs tissue mapping and processing: a survey study. Dermatol Surg 2003, 29: 1109–12. 10.1046/j.1524-4725.2003.29347.xPubMedGoogle Scholar
- Hanke CW, Lee MW: Cryostat use and tissue processing in Mohs micrographic surgery. J Dermatol Surg Oncol 1989, 15: 29–32.View ArticlePubMedGoogle Scholar
- Panje WR, Ceilley RI: The influence of embryology of the mid-face on the spread of epithelial malignancies. Laryngoscope 1979, 89: 1914–20. 10.1288/00005537-197912000-00003View ArticlePubMedGoogle Scholar
- Robins P: Chemosurgery: my 15 years of experience. J Dermatol Surg Oncol 1981, 7: 779–89.View ArticlePubMedGoogle Scholar
- Dzubow LM: Chemosurgical report: recurrence (persistence) of tumor following excision by Mohs surgery. J Dermatol Surg Oncol 1987, 13: 27–30.View ArticlePubMedGoogle Scholar
- Dzubow LM: False-negative tumor-free margins following Mohs surgery. J Dermatol Surg Oncol 1988, 14: 600–2.View ArticlePubMedGoogle Scholar
- Randle HW, Zitelli J, Brodland DG, Roenigk RK: Histologic preparation for Mohs micrographic surgery. J Dermatol Surg Oncol 1993, 19: 522–4.View ArticlePubMedGoogle Scholar
- Dogan MM, Snow SN, Lo J: Rapid skin edge elevation using the OCT compound droplet technique to obtain horizontal microsections in Mohs micrographic surgery. J Dermatol Surg Oncol 1991, 17: 857–60.View ArticlePubMedGoogle Scholar
- Franks JW: A precision machine for mounting tissue for Mohs micrographic surgery. Dermatol Surg 1998, 24: 989–93. 10.1016/S1076-0512(98)00097-1PubMedGoogle Scholar
- Nouri K, O'Connell C, Alonso J, Rivas MP, Alonso Y: The Miami Special: a simple tool for quality section mounting in Mohs surgery. J Drugs Dermatol 2004, 3: 175–7.PubMedGoogle Scholar
- Gardner ES, Sumner WT, Cook JL: Predictable tissue shrinkage during frozen section histopathologic processing for Mohs micrographic surgery. Dermatol Surg 2001, 27: 813–8. 10.1046/j.1524-4725.2001.01017.xPubMedGoogle Scholar
- The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-5945/6/10/prepub
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