Temperature excursion: difference between revisions
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| Revision 35 — 01:33, 7 Sep 2025 CounterfeitCato (talk) restructure 14,260 bytes ±0 | Revision 36 — 10:35, 14 Sep 2025 SurpassSunniva (talk) fix unit 15,979 bytes +1,719 | ||
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| 89 | {{math|T_{MKT} = 10000 ÷ (33.8811 + 1.4164) = 10000 ÷ 35.2975 = 283.31 K = 10.2 °C}} | 89 | {{math|T_{MKT} = 10000 ÷ (33.8811 + 1.4164) = 10000 ÷ 35.2975 = 283.31 K = 10.2 °C}} |
| 90 | 90 | ||
| + | 91 | The mean kinetic temperature is 10.2 °C, above the 8 °C upper limit, while the arithmetic mean is 7.3 °C and comfortably inside it. The two statistics reach opposite conclusions about the same record. This is not an artefact: the arithmetic mean treats an hour at 22 °C as equivalent to an hour at 5 °C when for degradation purposes it is roughly eight times as costly.{{r|haynes1971}} | |
| + | 92 | ||
| 91 | === Why the two means diverge === | 93 | === Why the two means diverge === |
| 92 | The divergence is a direct consequence of convexity. Degradation rate is a convex function of temperature, so the average of the rates at two temperatures exceeds the rate at their average temperature. Mean kinetic temperature is defined as the temperature whose rate equals the average rate, and therefore always lies at or above the time-weighted arithmetic mean, with equality only for a constant profile. | 94 | The divergence is a direct consequence of convexity. Degradation rate is a convex function of temperature, so the average of the rates at two temperatures exceeds the rate at their average temperature. Mean kinetic temperature is defined as the temperature whose rate equals the average rate, and therefore always lies at or above the time-weighted arithmetic mean, with equality only for a constant profile. |
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| 101 | so approximately a threefold acceleration per 10 K. This is the origin of the informal expectation that degradation roughly triples for each 10 °C, and it is the reason a short warm interval can outweigh a long cold one.{{r|waterman2005}} | 103 | so approximately a threefold acceleration per 10 K. This is the origin of the informal expectation that degradation roughly triples for each 10 °C, and it is the reason a short warm interval can outweigh a long cold one.{{r|waterman2005}} |
| 102 | 104 | ||
| + | 105 | === Freezing and interfacial damage === | |
| + | 106 | Cooling a liquid formulation below its freezing point subjects the solute to several distinct stresses, none of which is described by the Arrhenius relationship. Ice formation concentrates the remaining solution — freeze concentration — raising solute and salt concentrations by as much as an order of magnitude and shifting pH where buffer components crystallise selectively. It creates a large ice-water interface at which peptides and proteins adsorb and may unfold. And it may bring the system through a temperature range in which cold denaturation occurs.{{r|bhatnagar2007}} | |
| + | 107 | ||
| + | 108 | The practical consequences are that a freezing excursion may cause more damage than a warming excursion of far greater apparent severity; that the damage is often physical rather than chemical, so a purity assay that resolves degradation products may not detect it while a size-exclusion or subvisible-particle method does; and that repeated freeze-thaw cycles are more damaging than a single freezing event of the same total duration, because each cycle regenerates the interface.{{r|bhatnagar2007,manning2010}} | |
| + | 109 | ||
| 103 | == References == | 110 | == References == |
| 104 | {{reflist}} | 111 | {{reflist}} |
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| 110 | <ref name="eugdp2013">European Commission. ''Guidelines of 5 November 2013 on Good Distribution Practice of medicinal products for human use'' (2013/C 343/01).</ref> | 117 | <ref name="eugdp2013">European Commission. ''Guidelines of 5 November 2013 on Good Distribution Practice of medicinal products for human use'' (2013/C 343/01).</ref> |
| 111 | <ref name="waterman2005">Waterman KC, Adami RC. "Accelerated aging: prediction of chemical stability of pharmaceuticals." ''International Journal of Pharmaceutics'' 293(1–2):101–125 (2005).</ref> | 118 | <ref name="waterman2005">Waterman KC, Adami RC. "Accelerated aging: prediction of chemical stability of pharmaceuticals." ''International Journal of Pharmaceutics'' 293(1–2):101–125 (2005).</ref> |
| + | 119 | <ref name="manning2010">Manning MC, Chou DK, Murphy BM, Payne RW, Katayama DS. "Stability of protein pharmaceuticals: an update." ''Pharmaceutical Research'' 27(4):544–575 (2010).</ref> | |
| 112 | <ref name="bhatnagar2007">Bhatnagar BS, Bogner RH, Pikal MJ. "Protein stability during freezing: separation of stresses and mechanisms of protein stabilization." ''Pharmaceutical Development and Technology'' 12(5):505–523 (2007).</ref> | 120 | <ref name="bhatnagar2007">Bhatnagar BS, Bogner RH, Pikal MJ. "Protein stability during freezing: separation of stresses and mechanisms of protein stabilization." ''Pharmaceutical Development and Technology'' 12(5):505–523 (2007).</ref> |
| 113 | <ref name="matthias2007">Matthias DM, Robertson J, Garrison MM, Newland S, Nelson C. "Freezing temperatures in the vaccine cold chain: a systematic literature review." ''Vaccine'' 25(20):3980–3986 (2007).</ref> | 121 | <ref name="matthias2007">Matthias DM, Robertson J, Garrison MM, Newland S, Nelson C. "Freezing temperatures in the vaccine cold chain: a systematic literature review." ''Vaccine'' 25(20):3980–3986 (2007).</ref> |