With disuse, say bed-rest, casting or micro-gravity, within what time-frame would phenotype muscle atrophy occur that is measurable ? Measured by anthropometry or some imaging technique. Limited to humans only,
The answer will depend on the muscle group you're interested in. Chronically-active muscles (e.g., lower-body muscles) are more susceptible to disuse.
Assuming you're interested in such muscles, the loss of lower-body lean mass appears to be around 100-200 g/wk during bed-rest (See some references below.) With this number, you can estimate the necessary duration of bed-rest if you know the resolution of the instrument you are using to assess atrophy.
Paddon-Jones D, Sheffield-Moore M, Urban RJ, et al. Essential amino acid and carbohydrate supplementation ameliorates muscle protein loss in humans during 28 days bedrest. J Clin Endocrinol Metab. 2004;89:4351–4358.
LeBlanc AD, Schneider VS, Evans HJ, et al. Regional changes in muscle mass following 17 weeks of bed rest. J Appl Physiol. 1992;73:2172–2178.
While completely agreeing with what Gordon suggested (especially regarding which muscle group we are taking into consideration), I just add few other publications you may be interested in.
Time course of muscular, neural and tendinous adaptations to 23 day unilateral lower-limb suspension in young men.J Physiol. 2007 Sep 15;583(Pt 3):1079-91. Epub 2007 Jul 26. de Boer MD1, Maganaris CN, Seynnes OR, Rennie MJ, Narici MV.
Effect of 5 weeks horizontal bed rest on human muscle thickness and architecture of weight bearing and non-weight bearing muscles. de Boer MD1, Seynnes OR, di Prampero PE, Pisot R, Mekjavić IB, Biolo G, Narici MV.
In human bed rest the soleus and vastus lateralis do not show histological atrophy (reduced crosssectional area) even after two weeks fully immobilisation, though molecular atrophy markers may be measured earlier e.g. within 1 wk following bed rest. Even if used in many clinical studies and in human bed rest studies, MRI of whole muscle (reduced muscle cross-sectional area) is probably not a tool to analyse atrophy due to a number of bias (fluid shift, edema, blood flow, fat, connective tissue infiltrations) and due to the differences seen at the histology level e.g. in individual muscle fibers. 4-6 weeks may be sufficient to see structural atrophy in bed rest, for example. At the gene and protein level atrophy genes /proteins are expressed much earlier, say within 24-48h post Immobilisation (were you cannot measure structural atrophy at all).