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Allograft requests from clinical users always possess a big problem for the tissue bankers. Since the majority of clinical users of allografts are not tissue bankers, they roughly estimate allograft quantity before placing request. Hence they over request the grafts. Sometimes the user is also very far from the tissue bank and for safety reasons, he over-requests. As a result of this, a large amount of valuable allografts are requested and wasted after the surgery. Secondly even if the allografts are very carefully used in terms of sterilization precautions, there is no guarantee of the sterility once the packet is opened and re-packed. In the event of contamination, the allograft has to be re-sterilized and this has tremendous effect on the biomechanical properties. In the event there is no contamination, but a deep frozen allograft by the time it is opened, used, re-packed and brought back to the tissue bank, it is completely thawed from a temperature of -700 . Second time deep freezing from a thawed condition compensates with the biological as well as biomechanical properties of the allograft. As human tissue allografts are very valuable product in terms of monetary and ethically, the wastage is difficult to accept in moral terms. Unlike some tissue banks, where human tissue allografts are commercially sold, in Thailand it is still considered unethical to sell / trade in human tissue. Thus the responsibility of a tissue banker increases to concentrate that allografts are not wasted as wastage after the surgery.

The Bangkok Biomaterial Center, under the dynamic leadership of Prof. Yongyudh Vajaradul has come out with a solution. A bone allograft quantity estimation and calculation system. The so-called system has been named as “YV technique for bone quantity determination”.



The first step in the process is to study very carefully the x-ray of the defect side and also the intact side. The intact side x-ray is kept for reference and ocassionally comes in use. The defect for which the allograft is sought should be studied and the damage caused by the disease or deformity should be noted. A fair knowledge of the surgical procedure planned by the surgeon is essential. At this stage, the following items are essential:

1. Pencil - normal and colour

2. Eraser

3. Tracing Papers

4. Transparent plastic scale

5. Verniar and thickness callipers

Now we proceed with putting the x-ray on the illuminated x-ray view box. The transparent tracing paper is interposed on the x-ray film and the top, left and right sides of the paper is fixed with a plaster tape or ordinary tape. The lower part of the paper is kept free. Through the illumination, one can see the boundaries of the defect and adjacent bony structures. The tracing is made with the help of a normal pencil. In the event the boundaries are not very clear at some place, then the paper can be lifted from the lower part for physical examination of the boundaries on the x-ray box. Once the tracing is complete, it must be immediately photo-copied in multiple copies and a copy of the tracing must be affixed to the patient’s case report file. This is essential because the x-ray film of the recipient is not always accessible due to various constrains. A copy of the x-ray tracing will always be handy for use in the time of need.

The next step is to study the x-ray tracing and colour the defect areas. This will allow a clear visualization of the defect and one can arrive to the nearest geometric figure of the defect. It could be either a sphere, cube, rectangular block, cone or a cylinder. The shape must be studied carefully keeping the affected/defect part’s anatomy in mind. This is because many times a long bone is taken as a solid cylinder, whereas it is a hollow cylinder.

Now comes the stage to measure the dimensions. It must be noted that one should attempt to get atleast more than one measurement of any dimension viz length, height, diameter. This will allow to have the possibility of comming to an average and thereby reducing the chances of errors. An example is if a long bone is taken into consideration, it must be noted that no long bone in the human body is of the same diameter by default at its three points viz, proximal, mid shaft and distal. Hence it is important to have the diameters of proximal, mid-point and distal be taken and then divided by three to come to the diameter of the cylinder. By doing this we will arrive at the nearest concise value. Care must be taken while doing the calculations, that if the volume of graft required is for filling a defect by impaction, then the inner diameter of the cylinder(long bone) has to be substracted from the outer diameter of the cylinder (long bone).

Once the calculation has been done, we have to identify the type of bone allograft that shall be used to fill in the defect. We must keep in mind that if the affected area is a weight bearing area, then we must select cylinder or a ring of cortical bone. In the case of non-weight bearing areas, the graft can be freeze dried or morsellized deep frozen cancellous allografts. Size of the granules play an important role. In case the size of the granules are big, then two effects are noted during the graft insertion into the defect:

1. Initially the total quanity of allograft estimated before-hand and the quanitity used to fill up the defect will appear to have a difference. The used quantity will be more than the quantity estimated. This is due to the fact that some space is occupied by inter-granular areas.

2. Once impaction on the filled in allograft is done, more space will be created and more graft will be used. During the process of impaction, sometimes the granules will further break from their original size and thereby creating space for the need of more allografts. Hence in the case of filling in defects there should be an excess of 20 - 30% estimated in order to substantiate the loss of calculated amount due to compaction.



Long Bones: Diameter - Take proximal, distal and mid-point measurements. Divide by 3 to get the average/mean diameter.

Take inner and outer diameter measurements and divide them seperately to get the average/mean diameter.

Compacting Technique: If the stablization of the defect is by a intra-medullary nail or a long stem femoral prosthesis, then only inner diameter measurements are necessary in order to get the defect volume. This will give the volume of a solid cylinder. Since a IM Nail or the femoral stem of the prosthesis will be used in the medullary canal, the excess amount of graft will susbtantiate for the compacting. In this case extra quantity of the graft is not needed.

Cavity defect filling: Calculate the volume of the nearest geometric shape.

Acetabulum: Diameter - Take 3 different point measurements and divide them by 3 to get the average/mean value for the diameter.

Take care in differentiating the radius and diameter measurements.

Calculate the volume of a solid hemi-sphere

Take single point diameter measurement for acetabular cup (prosthesis)

Calculate the volume of a solid hemisphere for the acetabular cup ( prosthesis)

Reduce the volume of the acetabular cup (prosthesis) from the total vol ume of the acetabulum to arrive at the volume of the defect.

Long Bone Tumor- Take outer diameter at proximal and distal ends of the defect. This is essential to measure so as to avoid overhangs. Also in the case of a child tibia, it cannot be replaced with an adult femur or fibula but can be done with an adult humerus. Any cylinderical long bone replaced must be stuffed in the medullary canal with freeze dried or morsellized deep frozen cancellous bone allograft. We suggest the use of bone tablets in this place.

Interbody spinal fixation:     Diameter      -     AP/Lateral and midpoint from the x-ray film and arrive at average/mean diameter

                                         Height        -    Take 3 points at AP view

                                                                 Take 3 points at lateral view

Divide the 6 points to come to the average/mean height use cortical rings bone allograft

All freeze dried, morsellized deep frozen cancellous bone or bone tablet allografts used as a filler in the cavity defect should be soaked in the patient’s own blood before insertion into the cavity.

A case example for bone allograft quantity estimation using the YV formula is described. This is a case (Fig showing the tracing from X-ray ) from Hatyai Hospital, Songkla, Thailand. The request was for 8 deep frozen femoral heads to fill up bone defect in the acetabulum and proximal femur after a Revision Total Hip Arthroplasty. The calculations are as follows:



1 Amount of bone required for reconstruction of acetabular defect (ref. X-ray tracing).

Let BB' and CC' are diameters and AO radius of acetabular defect

Measurement of AO = 3.5cm (1r)

                              BB' = 4.7cm (2r)

                             CC' = 9.1cm (2r)

Total diameter of AO+BB'+CC' = 17.3cm

Average of radius (r)           = 17.3/5 = 3.46cm

Formula of a sphere             = 4/3Pr3

Total vol. of the acetabulam = {(4/3) x (22/7) x 3.463}/2 = 86.03 cc

Diameter of the acetabular cup (prosthesis) = 56mm

Radius of the acetabular cup (prosthesis) =  2.8 cm

Since the acetabular cup is a hemisphere, hence the volume of a hemisphere can be arrived at by the formula (4/3Pr3) /2.

Volume of the acetabular cup prosthesis = {(4/3) x (22/7) x (2.8)3}/2

                                                                       = 46 cc

Volume of acetabular defect = Total volume of acetabulam - Volume of acetabular cup (prosthesis)

                                                  = 86.03 - 46.00

                                                  = 40.03 cc


2 Amount of bone required for filling femoral shaft defect (ref. To x-ray tracing)

2.1 Volume of femoral shaft:

Let aa", bb' and cc' be the diameters of femoral shaft at three points.

Measurement of dia        aa' = 5.2cm

                                         bb' = 3.1cm

cc' = 2.0cm

     height h = 15.4c

Total diameter of aa'+bb'+cc' = 10.3cm

Average aa'+bb'+cc' = 10.3/3 = 3.4cm (diameter)

Average of radius (r) = 3.4cm/3 = 1.7cm

Formula for cylinder = Pr2h

Total vol. of femoral shaft = (22/7) x 1.72 x 15.4

Total vol. of femoral shaft = 139.7cc.


2.2 Volume of prosthesis:

Let a1a2, b1b2 and c1c2 be be the diameters of the prosthesis and h is the height, then;

Measurement of a1a2 = 2.5cm

                               b1b2= 1.7cm

                              c1c2= 1.0cm

                               h = 15.4cm

Total diameter of a1a2 + b1b2 + c1c2 = 5.2cm

Average a1a2 + b1b2 + c1c2 = 5.2/3 = 1.73cm (diameter)

Average of radius (r) = 1.73cm/2 = 0.86cm

Formula for cylinder = Pr2h

Total vol. of prosthesis = (22/7) x 0.862 x 15.4

Total vol. of prosthesis = 35.76cc.


2.3 Vol. of femoral defect = vol. of femoral shaft – vol. of prosthesis

                                          = 139.7cc. - 35.76cc.

Total vol. of femoral defect = 103.94cc.


3. Total volume of bone allograft required for Hadyai Hospital:

                       = Vol. of acetabular defect + total vol. of femoral defect

        = 40.03 cc. + 103.94cc.

        = 143.97cc

Each deep frozen femoral head vol. about 40cc,

the number of femoral head required by Hadyai Hospital = 143.97/40 = 3.59 femoral head.

By the above calculation/estimation, 4 deep frozen femoral head is sufficient for the above operation (Hadyai Hospital).



At the Bangkok Biomaterial Center, we have tried to use the YV formulas for various types of clinical conditions and tried to establish the validity of the formulas for various cases. A detailed paper on this work is expected to be read at the 8th International Conference of Asia Pacific Association of Surgical Tissue Banks to be held at Bali, Indonesia between 22nd - 26th October 2000. A complete text of this paper is also expected to be published in the 5th Volume of “Advances in Tissue Banking” editors G.O. Phillips, Von Versen, Publishers; World Scientific Concern, Singapore.

These formulas are an honest and sincere attempt to address the issue of bone allograft quanitity estimation and thereby saving valuable human bones. The Center and Prof. Yongyudh Vajaradul looks forward that these formulas are accepted by tissue banks and become a valuable assest for the science of tissue banking. It our humble request from valuable readers of this book to bring forth their queries and suggestions to help develop more formulas and to establish the existing formulas.


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Diagram showing the technique of calculation         AP view showing the interbody space


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Lateral view showing the anterior interbody space of vertebral column Diagram of the proximal femur indicating the area for consideration of bone loss measurement


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Prof. Yongyudh Vajaradul tracing from X-Ray  


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 Estimation of size from normal human bone       Calculation on paper with the help of Calipers