A mathematical model to predict the requirement for multiple Z plasties

pedicle. In the immediate postoperative period, this is done with the help of adhesive plasters and sometimes with flap-positioning splints. Later, the patient and the relatives are instructed about the correct position. Whichever technique is used, it would be good to have a system whereby the position preferred by the surgeon is conveyed to the people who monitor the flap in the ward and at home in a simple and straightforward manner, which is easy to understand and replicate. We have found the following technique to be very useful over the last four years.


A mathematical model to predict the requirement for multiple Z plasties
Dear Sir, It is well known that in a 60° Z plasty, the contractural diagonal is placed perpendicular to the other diagonal of the parallelogram and the length of the contractural diagonal equals the limbs of the Z [1] plasty.
The contractural diagonal lengthens by 75% when the two Z plasty flaps are transposed. [2] The flaps transpose ONLY if there is adequate lax tissue in the areas adjacent to the contractural diagonal. Hence, in effect, the lengthening across the contractural diagonal is accompanied by shortening of the diagonal at right angles to it. In a clinical situation, this shortening may be limited by tissue rigidity causing limitation in the size of the Z plasty. One can assess the laxity of the tissues by pinching skin between the thumb and the fingers.
Below we describe a mathematical theorem to deduce the size of a Z plasty from the measurements of the laxity of the tissues adjacent to the Z plasty.
In Figure 1, XY represents the scar. Let the contractural diagonal marked over the scar XY, which is equal to the limbs, AX and YB of the designed Z plasty, be equal to C cm. AB represents the other diagonal of the parallelogram, which also represents the points adjacent to the scar where shortening happens after transposition of the flaps. Let AB be equal to T cm.
In Figure 2, incisions made along AX, XY and YB will result in two triangular flaps AX′Y and BY′X, which are ready to be transposed. Note: AX = AX′ = X′Y = XY′ = YB = Y′B = C cm. Figure 3 shows the transposed flaps in which inset sides Y′B, AX′ each equal to C cm lie side by side. Notice that the distance between the points AB, which was T cm before transposition of flaps is now C cm. Hence, the shortening, which may be designated as L for laxity is T − C cm.
Hence, L = T − C In Figure 1, if the intersection of the two diagonals is represented as I, then the triangle AIX is a right-angled triangle.
According to Pythagoras' theorem, (AX) 2 = (AI) 2 + (IX) 2 . AX = C. Since I is the center of AB, AI = T/2. Since I is the centre of XY, IX = C/2. Hence, We have deduced above that laxity, L = T − C Hence, L = C√3 -C (√3 = 1.73) To summarize, if the laxity can be assessed and estimated by the pinch test as L then L divided by 0.73 gives the size of the Z plasty that must be used.

Examples:
If Laxity, L = 2 cm, the size of Z plasty, C must be 2 divided by 0.73 = 2.74 cm or less.
If L = 1 cm, the size of Z plasty, C must be 1 divided by 0.73 = 1.34 cm or less.
If L = 3 cm, the size of Z plasty, C must be 3 divided by 0.73 = 4.11 cm or less. To conclude, irrespective of the length of the scar, the size of the Z plasty drawn should be based on the laxity available. If there is insufficient laxity, the contracture will require more than one Z plasty to lengthen the full length of the contracture. If the tissue laxity [L] is ≥ the length of the scar, a single Z plasty is required. By this method the surgeon can decide whether a single or multiple Z plasties are required.
However, the clinical decision whether to use single or multiple Z plasties is determined by two other factorswhether a single or multiple Z plasty is more aesthetic and whether there is a confounding immovable anatomical feature (e.g., scar revision around the nose). Further since the skin doesn't behave as a mathematical model, one needs to find a method to accurately measure the amount of laxity in the skin.

A simple method to maintain immobilization and elevation of the hand in infants and children
Dear Sir, Hand elevation and immobilization is an essential step following hand surgeries, hand trauma and in oedematous and inflammatory conditions of the hand. This is difficult to maintain in infants and young children (less than four years old) in whom hand elevation is required. The patients in this age group are restless and irritable in the postoperative period and are understandably uncooperative to the elevation and immobilization regimes at other times too. Usage of bandage slings and bolsters/pillows are common ways to immobilize the limb. In addition, the staff nurses and parents/attendants of the patients are advised to maintain a constant vigil in keeping the hand immobilized and elevated. Older children tend to be more cooperative and elevation and immobilization can be maintained by conventional methods.
We have devised a simple technique to overcome the aforementioned problems with the utilization of infusion bottles. Following the surgery and/or dressings, we routinely give an above-elbow slab with plaster of Paris, dorsally, maintaining the elbow at 90° flexion and the hand in a supine position. Two infusion bottles are placed on either side of the arm and wrapped with a bandage [ Figure 1].
The right-angled upper elbow slab has two advantages: first, it doesn't slide down the limb as seen in the lower elbow slabs of the hand and secondly, it helps in maintaining limb elevation. An infusion bottle (500 ml crystalloid solution) is inexpensive and easily available in wards and operating rooms. When they are fastened as bolsters to the arm, they stabilize the limb from falling sideways and the combined weight of the infusion bottles and the slab makes it heavy for the infants and younger children to lift. This ensures immobilization of the limb and prevents them from thrashing the limb around. When the child is to be breastfed or to be taken in the parent's lap or carried around, only the bandage is Figure 1: This is a postoperative image following a surgery of the hand in a child. An above-elbow slab was applied and two infusion bottles were fastened gently to the arm