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**Clinical Application of Mathematical Long Bone Ratios to Calculate Appropriate Donor Limb Lengths in Bilateral Upper Limb Transplantations**
Justyn Lutfy, MD, CM

^{1}; Alexis Pietak, BSc Eng, BSc, PhD

^{2}; Shaun D. Mendenhall, MD

^{1}; Michael W. Neumeister, MD

^{1}^{1}Southern Illinois University School of Medicine, Springfield, IL; ^{2}Tufts University, Medford, MA
**Introduction:** Limited methods exist to aid in deciding the appropriate donor limb lengths in bilateral upper limb amputees qualifying for vascularized composite allotransplantation. To aid in this decision, our hypothesis was that mathematical equations could be created using long bone length ratios to approximate the patient's limb length prior to amputation.

**Methods:** A collection of thirty skeletons' unilateral upper limb long bones were measured using osteometric board and calipers to create a base data set. Anatomic segment ratios were calculated based on humerus length for males and females after multivariate linear regression analysis indicated a statistical difference. For clinical application testing, five minimally preserved cadavers underwent standardized upper limb x-rays. Radiographic bone lengths were measured along the long axis of the humerus, forearm, and third ray. These measured radiographic anatomic lengths were then compared to the predicted bone lengths, generated from the skeleton data set ratios, for each cadaver.

**Results:** The Chi Square Goodness of Fit test showed excellent fit (p<0.025 to p<0.001) between the predicted and radiographically measured lengths for the five cadavers. Depending on the cadaver, percent error in total limb length predicted to measured ranged from 0.1% to 5%. Table 1 shows the variables to multiply an individual humerus length to calculate a given anatomic segment. Inter-observer measurements showed no statistically significant difference using the Bland-Altman method.

**Conclusion:** If a bilateral upper limb amputee has one intact humerus, ratios to the humerus length can be reliably applied to calculate the pre-amputation limb length based on the patient's radiographic humerus length. These formulas are indicated for finding the appropriate limb lengths, and smaller anatomic segments, for donor-recipient matching in upper limb transplantation.

Table 1 Value to multiply the radiographically measured humerus to acquire the missing anatomic segment length based on sex. R/U: forearm, MC+C: 3rd metacarpal and carpus (i.e. palm height), MC: 3rd metacarpal, PP: proximal phalanx long finger, MP: middle phalanx long finger, DP: distal phalanx long finger

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