| 1 Background and objective Congenital concealed penis is a common disease in the pediatric genitourinary system,ranked only second to phimosis and redundant prepuce.It was circumcised by mistake in the past because of the lack of professional knowledge.Children were always failed to get the right treatment.Concealed penis shows shorter penile shaft caused by congenital factors,and its basic character is the separation between the prepuce and the shaft of penis.All patients’ skin and penis are not attached,the part of penile shaft will be extended visibly if pressed on the pubic area,but the penis will be retracted back to the original appearance supposing that the pression is removed.The pathogenesis of the disease is universally recognized as the dysplastic membrane directly attached on the front end of the penis,which forms a fiber cable without elasticity that limits the penile shaft and increased the concealed degree.On account of the out rigion of prepuce is narrow,which makes the glan can’t be observed,these factors cause the unique appearance.Since the penis outside mouth is stricture,concealed penis often suffers from the balanitis,dermatitis and wrapping dirties accumulated within the prepuce that is difficult to be cleaned up.The long-term development will inevitably affect the penile growth.Many boys begin to pay close attention to their external genital organs in prepuberty.Even if some concealed penis can be self-healing,children can still meet mood disorders in the process of waiting for self-healing.Most parents are willing to select the time of surgical treatment in children within 3 years old or even earlier.Firstly,the parents worry about that the short penis would influence the sexual and reproductive ability in the future,which lead to the stronger aspiration to accept the operation;Secondly,from the experience of children,it is not easy to hold the penis to pass urine,and these patients are afraid of being seen,the concealed penis can also cause different degree damage to the patients’ mental and physical health,even produce more serious psychological negative impact.It is beneficial to the majority of patients and their parents that the surgical treatment can improve the local health,psychological acceptance and beautify the image of the concealed penis.It is well known that the common treatment for concealed penis recently is surgical operation.The understanding of the disease by Urological Doctor has been improved in the recent years.However,there is not a unified model in the type of surgery for congenital concealed penis and a long-term effective evaluation.The surgical content mainly includes fixing the penis skin,releasing and covering the penile shaft.Nevertheless,it has been basically reached a consensus that using the inner prepuce wrapped on the penis could lead to a long time swelling postoperatively.So the penile shaft should be covered as far as possible by the outer prepuce.Since concealed penis have a conical appearance of the "top narrow bottom width",we conceive that the surface area of the outer prepuce of concealed penis can be calculated by the mathematical formula so that the penile shaft could be covered conveniently.Mathematics has permeated into each branch of medicine in the recent years.The application of mathematics is growing very widespread in the medical research.It is inseparable from the establishment of the mathematical model to the application,from the simple data analysis to the abundant data processing as well as the design of experiment.We refine the surface area computation of the outer prepuce in the concealed penis into mathematical concept.In this way,through the foundment of the mathematical model of cone,the measured data can be analyzed and applied to the plastic surgical process on the concealed penis repairing.This complete process is short for mathematical modeling in math.We have joined quantitative implementation concept into the plastic surgical process in the concealed penis foreskin repairing.This research carried through mathematical quantification calculation based on the three types of the different buried degree penis whose outer surface area and the area of degloving penis were all measured accurately.It was concluded that the proportion of the penile shaft could be covered by the outer prepuce in the three different type of concealed penis.It was verified for the feasibility of mathematical quantitative in the outer prepuce in plastic surgery.Meanwhile,its coverage ratio could be concluded according to the buried degree of concealed penis,which could guide and serve the clinical research and become a guidance to the other field of medicine.On the basis of improvement of Brisson operation,we designed a new method that the penis was degloved through the inverted "V" shape incision in the junction of the penis and the scrotum which combined with the mathematical quantitative tools.According to practices recently,it was concluded that the advantages of the operation were shown completely which compared with other methods such as Devine and Shiraki in the concealed penis repairing through comparative analysis.Because of the particularity of the tapered appearance in the children’s concealed penis,the area of the outer prepuce in concealed penis and the degloved penile shaft can be calculated through the establishment of the mathematical model.The penile shaft can be covered in the maximization by the outer prepuce of the concealed penis which is calculated under the help of mathematical modeling.Mathematical modeling and operation will be harmonious and brought out the best in each other at the same time.The mathematical quantification in the outer prepuce has an obvious advantage in the plastic surgical application in the children’s concealed penis through comparing with conventional surgical method.So the purpose of this research is to prove the advantage of the mathematical model in the process of the plastic surgery in concealed penis.2 Materials and Methods 2.1 Clinical Data 180 cases of all children’s concealed penis were selected from the Department of Urology in Zhengzhou Children’s Hospital in China from June 2012 to June 2015.They were distributed into two groups,according to admission time.There were 120 cases who came to hospital from June 2012 to June 2014 in group A,and group B was the other 60 cases from July 2014 to June 2015.They were all hospitalized,aged from 1 year and six months to 13 years old,the average age was 6.3 years old.The short appearance or the unusual phimosis was found firstly in the cardinal symptom after the patient was born in the earlier period.Physical examination showed that the penis present a little appearance,the side view of the penis was like a mouth of bird,and the glans was not exposed since the prepuce mouth was narrow that could not be turned on.These symptoms conformed to the diagnosis of congenital concealed penis.The buried penis caused by obesity was excluded in this study.Three types were divided according to the clinical manifestations: those whose glans and part of shaft of the penis in the cone prepuce could be seen in the natural state were named as type I(mild),those whose glans of the penis in the cone prepuce could be seen in the natural state besides visible percutaneous hill were named as type II(moderate),and those whose penis could not be seen in the natural state besides a cone pichel were named type III(serious).Group A had 120 cases including type I 35 cases,type II 46 cases,and type III 39 cases from June 2012 to June 2014,which were randomly employed three surgical types that were modified Brisson,Shiraki and Devine.Among them all the type I,35 cases whose parents had heavier psychological burden or the patients themselves paid a high attention to their genitals accepted surgical operation.6 cases of this group of children were obvious obesity,but the appearance features of the penis were all according with the congenital concealed penis,underwent surgical operation too.The surgical time lasted from the shortest 42 minutes to the longest 80 minutes,and average 62 minutes.The patients adopted the anesthesia in sacral canal blocking under the age of 7 years and under epidural block more than 7 years old.40 cases of children among 120 cases were randomly selected in addition,aged from 2 years 4 months to 12 years old,averaged 5.5 years.All of them were divided into two types named A1 and A2 according to the tapered appearance of the penis,respectively named as normal cone and slant cone.The cone was defined as normal cone belong to group A1 if the projection of the taper spire to the bottom circle was at the center,otherwise,as a slant cone belong to the group A2.It is concluded that the coverage rate could be calculated in all kinds of concealed penis whose penile shaft were covering by the outer prepuce through mathematical calculation.Group B including another 60 cases of concealed penis,were selected in the Department of Urology in Zhengzhou’s Children’s Hospital from July 2014 to June 2015,were divided randomly into two groups.50 cases among them were in normal weight and others were more than 20% of normal weight which were all completely according with the diagnostic criteria of concealed penis.This group of patients were all treated with operation,30 patients(group B1)were treated by the modified Brisson method,other 30 cases(group B2)were treated by the common method combined with mathematical model.2.2 Experimental Method 2.2.1 Mathematical Method For the group A1,A2 and B2 of children,we calculated the side area of the outer foreskin preoperatively in the flaccid state.As the concealed penis had a cone appearance,if the dorsal and ventral skin were symmetry,this was called normal cone,if not,called slant cone.The basal region of the penis was defined as the bottom of the cone,the distance of the longest bilateral points in the base of the concealed penis was defined as the diameter(D),and the distance from the base circle of the cone to the tip was defined as the generatrix(L)of the cone.The tapered side area of the outer foreskin in the concealed penis could be calculated according to the formula of the tapered side area: Sc1 = 1/2π·D·L.With the help of advanced mathematics,the side area of the slant cone Sc2 could be calculated.On account of dissymmetry between dorsal and ventral foreskin,the diameter(D)was as same as the normal cone,the vertical distance from the tip of the cone to bottom was recorded as height(h),the side area of the slant cone could be calculated through calculus.It was convenient that a software "Excel " was installed in one mobile phone so that the measuring data was input and result could be calculated whenever and wherever possible.The appearance of the penile shaft was like a cylinder,the diameter(d2)of the penile body after degloving the penis could be measured and the length defined as the height(h2)of the column from the base of the penis to the coronary ditch.The lateral area of the penile shaft was calculated according to the formula of the cylinder side area: Scy = π· d2· h2 and the difference(Sin= Scy-Sc)between Sc and Scy was the area needed to be covered by the inner,the reserved length(χ)of the inner foreskin could be calculated by the formula: χ = Sin /π· d2.This mass of data was measured in the penile natural state(flaccid)preoperatively and intraoperatively.2.2.2 Surgical Methods 2.2.2.1 Method of Modified Brisson At first,a longitudinal incision was made dorsally through median raphe in order to drag the penis out,then a circumferential incision was made,forming a mucosal collar 15 mm proximal to the coronal ditch.The abnormal ligament between the tunica dartos and Buck’s fascia was completely dissected.Secondly,an inverse " V " shape incision was adopted between the scrotal and penile shaft,and the penis was pulled out and degloved completely from the incision.To prevent penile retraction,the tunica albuginea of the penile shaft was fixed to the prepubic fascia at 10 and 2 o’clock,the angles between pubic penis and penis scrotum were formed,and the mucosal collar was circumferentially sutured to the shaft skin with 6-0 interrupted chromic sutures.At last,the inverse " V " shape incision was closed to the appearance of " Y " or " Z " shape.A compression dressing was applied and a Foley catheter was inserted.2.2.2.2 Method of Modified Brisson combined with mathematical model.We measured the distance of the longest bilateral points in the base of the buried penis called the diameter " D ",and the distance from the base of the cone to the tip of the foreskin called the generatrix " L ",according to the cone was normal or slant conical appearance,we could calculated the tapered side area on the basis of the formula that was mentioned above.Because all concealed penis had the appearance of phimosis,a longitudinal incision was made dorsally through median raphe firstly,in order to drag the penis out,and a circumferential incision was made,forming a mucosal collar 15 mm proximal to the coronal sulcus.The abnormal ligament between the tunica dartos and Buck’s fascia were completely dissected.We measured the length(h2)from the bottom of the penis to the coronary ditch and the diameter(d2)of the penile shaft by this time,the lateral area of the penile shaft was calculated according to Scy = π· d2· h2.Then the difference(Sin= Scy-Sc)between Scy and Sc could be calculated and the length χ of the remaining inner prepuce resulted.If the data of χ was shorter than 15 mm,the spare inner prepuce should be excised.An inverse " V " shape incision was made between the scrotal and penile shaft ventrally.The penis was pulled out from the incision and degloved completely.Extra attention was paid to prevent the damage of the dorsal neurovascular tract.To prevent penile retraction,the tunica albuginea of the penile shaft was fixed to the prepubic fascia at 10 and 2 o’clock,and the mucosal collar was circumferentially sutured to the shaft skin.The inverse " V " shape incision was closed to the appearance of " Y " shape.A compression dressing was applied and a Foley catheter was inserted.The operative duration was 62(range 45–85)minutes.2.2.2.3 Devine A longitudinal incision was made dorsally through median raphe firstly in order to separate the adhesion between the prepuce and the glans,then expand the narrow portion in the forepart of the prepuce.Since the expanding of penile shaft,the vertical incision had become a horizontal one,along which the inner foreskin was cut circularly.The penis was degloved completely while the abnormal ligament between the tunica dartos and Buck’s fascoa was freed and dissected.The penile body was fully extended and fixed on the root in order to prevent penis from retracting.After reseting the prepuce and removing the redundant,the annular incisions were sutured discontinuously.A compression dressing was applied around the penis and a Foley catheter was inserted.2.2.2.4 Shiraki At first,2 millimeters prepuce on the junction of the inner and outer prepuce was resected,then separated the inner and outer prepuce along the penile superficial fascia.The outer prepuce was proceeded three longitudinal incision located in the " 2,6,10 " pionts.The penis was degloved to the root and the abnormal ligament was freed and dissected between the tunica dartos and Buck’s fascoa.Meanwhile,the penis was lengthened completely.Three 15 millimeters longitudinal incisions were proceeded along the inner prepuce in the " 4,8,12 " pionts,after the penile root was fixed,the corresponding inner and outer prepuce flaps were respectively cross sutured together.A compression dressing was applied and a Foley catheter was inserted.3 Results 3.1 The method of modified Brisson have a superior effect than the other surgical methods.120 patients in group A had follow-up of 0.5 years to 2 years.In terms of the penis exposure,group Brisson had 38 good effect cases and effective rate was 84.4%,higher than other groups.Group Devine had 26 good effect cases and effective rate was 65.0%,and Shiraki had 23 cases,effective rate was 65.7%.The effectiveness of penile exposure in group Brisson had a significant difference by the multigroup variable rank-sum test,and the efficiency of the group Brisson was obviously higher than the other two groups.1 case had incision split at the middle of the inverted " Y " incision,while given suture cured under only local anesthesia.Respectively compared various complications to three groups each other,group Shiraki had a significant difference by the data comparison in stubborn edema in the prepuce and other complications.3.2 It was possibly calculated for the area of the concealed penile outer prepuce by establishing a mathematical model,which could be applied cover the penile shaft intraoperatively.The outer prepuce of the concealed penis could be maximized to cover the penile shaft after it was calculated by mathematical method.The outer prepuce could cover 90% area of the penile shaft for type I after which was degloved and need a small amount of inner prepuce to be complemented,for type Ⅱ,80% area could be covered,for type Ⅲ,70% could be covered.In the process of covering the penile shaft,the inner prepuce and the scrotal flap could be used for supplementary coverage.With the deepening of the concealed level,the coverage rate of the penile shaft decreased accordingly.3.3 The mathematical model of concealed penis could be applied to plastic surgery,guiding the inner prepuce retained at least,shortening the time of postoperative obstinate edema in the foreskin,and improving the valid extending rate.It is helpful for the application of the cone mathematical model on the penis foreskin covering in the preoperative and intraoperative specific calculation.The whole process of the operation can be done at specific quantitative implementation.Because the inner foreskin is easy to arise intractable edema,the outer foreskin should be remained at the maximum and the inner foreskin remained at the minimum.Between the comparison of the results,the extending rate of the concealed penis was increased and the swelling time was shorter in the using mathematical model group than the group that was not alongwith the mathematical model.4 Conclusions The method of reformed Brisson had a superior effect than other surgical methods,the complications were fewer.The outer prepuce of the concealed penis could be maximized to cover the penile shaft after it was calculated by mathematical method.Applied mathematics could be applied to clinical work and play a directive role in the process of quantitative implementation.With the deepening of the concealed level,the coverage rate of the penile shaft decreased accordingly.The inner prepuce needed to be remained to cover the penile shaft.It was effective for the modified Brisson method combined with mathematical model to treat the concealed penis,which improved the valid extending rate.The method could make the inner prepuce remained at least,shorten the time of postoperative stubborn edema in the inner prepuce. |
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