Mathematical Optimization of Blinatumomab Preparation Method Simplifies Dosing and Reduces Drug Waste

Introduction: Blinatumomab is a combination of two antibody fragments with different specificities; thus, it is a single-chain variable fragment with bispecific T-cell-engaging action. It damages target B cells via CD3-positive T-cell activation by transiently crosslinking patients' CD3-positive T cells with CD19-positive B cells. Blinatumomab-mediated T-cell activation involves temporary release of inflammatory cytokines, and it may cause specific adverse events, such as cytokine release syndrome, at the time of administration. Neurological events, such as cerebrovascular disorders, encephalopathy, convulsion seizures, confusion, and aphasia, may also appear. Furthermore, the infusion bag must be replaced within 96 hours for maintaining an aseptic condition (in case when no bacteriostatic agent is used). Due to such restrictions, the administration method is precisely set.

Methods: Based on the definition (recommended blinatumomab dosage), we show mathematically rigorous equality transformation. Reconstituted blinatumomab is obtained by dissolving one vial of blinatumomab with 3.0 mL of distilled water. The concentration of reconstituted blinatumomab is 12.5 μg/mL. Blinatumomab preparation solution is a solution in which blinatumomab dissolved in distilled water is added to normal saline, additional normal saline, and IVSS: 250 mL of normal saline, X mL of additional normal saline, and Y mL of intravenous solution stabilizer (IVSS), and Z mL of reconstituted blinatumomab to obtain a total volume of 250 + X + Y + Z mL of blinatumomab preparation solution. The blinatumomab preparation solution should be replaced within 96 hours of preparation even if there is residue.

For a weight ≥ 45 kg, the daily dose of blinatumomab is 28 μg/day. The reconstituted blinatumomab concentration is 12.5 μg/mL. Therefore, the daily dose of reconstituted blinatumomab is 28 ÷ 12.5 mL/day. On the other hand, the volume of blinatumomab preparation solution is 250 + X + Y + Z mL. The administration rate of blinatumomab preparation solution shall be V mL/h, the amount that can be administered in 24 hours is V × 24 mL. Therefore, the daily dose of reconstituted blinatumomab is Z × V × 24 ÷ (250 + X + Y + Z) mL/day. Therefore, the equation 28 ÷ 12.5 = Z × V × 24 ÷ (250 + X + Y + Z) holds true. Therefore, we get X + Y = (12.5 × Z × V × 24) ÷ 28 － 250 － Z. Substituting Z = 9 mL and V = 3.0 mL/h, we get X + Y = 30.28571429･･･ mL. According to product information, the ratio of normal saline to IVSS is 270 : 5.5. Therefore, IVSS is Y = (2750 + 11X + 11Y) ÷ 551 using the relationship of 270 : 5.5 = 250 + X : Y. Therefore, we get Y = 5.595540576･･･ mL, X = 24.69017371･･･ mL. For the first week of Cycle 1, the equation 9 ÷ 12.5 = Z × V × 24 ÷ (250 + X + Y + Z) holds true. By substitute Z = 3 mL, we get X + Y = (12.5 × 3 × V × 24) ÷ 9 － 250 － 3.

For a weight < 45 kg, the daily dose of blinatumomab is 15 μg/m²/day: body surface area(BSA)-based dose. The equation 15 × BSA ÷ 12.5 = Z × V × 24 ÷ (250 + X + Y + Z) holds true. Therefore, we get X + Y = (12.5 × Z × V × 24) ÷ (15 × BSA) － 250 － Z. For the first week of Cycle 1, the equation 5 × BSA ÷ 12.5 = Z × V × 24 ÷ (250 + X + Y + Z) holds true. By substitute Z = 3 mL, we get X + Y = (12.5 × 3 × V × 24) ÷ (5 × BSA) － 250 － 3. For a small BSA, by substitute Z = 2 mL, we get X + Y = (12.5 × 2 × V × 24) ÷ (5 × BSA) － 250 － 2. For a smaller BSA, by substitute Z = 1 mL, we get X + Y = (12.5 × 1 × V × 24) ÷ (5 × BSA) － 250 － 1.

Results: By performing enormous calculations (more than two thousand cases), we obtain the following results. For a weight ≥ 45 kg, administer at the pace of three vials in 96 hours; 21 vials of blinatumomab are required for a 28-day period. For a weight < 45 kg, for BSA 1.67 to 1.80, administer at the pace of three vials in 96 hours; 21 vials are required for a 28-day period. For BSA 1.26 to 1.66, administer at the pace of two vials in 72 hours; 19 vials are required for a 28-day period. For BSA 0.84 to 1.25, administer at the pace of two vials in 96 hours; 14 vials are required for a 28-day period. For BSA 0.84 to 1.25, administer at the pace of one vial in 48 hours; 14 vials are required for a 28-day period. For BSA 0.63 to 0.83, administer at the pace of one vial in 72 hours; 10 vials are required. For BSA 0.40 to 0.62, administer at the pace of one vial in 96 hours; 7 vials are required.

Conclusion: This mathematical proof provides a clear solution to blinatumomab preparation method. Dosing rate can be fixed at any integer value (mL/h). For a weight ≥ 45 kg, the number of blinatumomab vials used over a 28-day period can be reduced from 24 to 21 vials. For a weight < 45 kg, further reduced.

No relevant conflicts of interest to declare.