A MATHEMATICAL MODEL DESCRIBING CATCH-UP GROWTH IN CELIAC DISEASE

Abstract

The phenomenon of catch-up growth (CUG) is well known, but still poorly understood. One of the best examples of CUG is the growth pattern after the institution of a glutenfree diet in children with celiac disease (CD). Treatment leads in almost all cases to complete catch-up growth within 2 years. Therefore, the pattern of CUG during adequate treatment of CD may be considered as a model for optimal catch-up growth in children treated with any form of therapy for any growth disturbance. In order to describe this pattern mathematically, we analysed growth data of 17 CD patients who showed growth retardation before therapy and completed CUG before the start of puberty. Two subgroups were formed on the basis of the initial height standard deviation score (HSDSI). Nonlinear regression analysis of the individual growth data expressed as HSDS (corrected for parental height SDS) was carried out using a monomolecular growth function. For each subgroup an equation was found from which the expected HSDS at any given moment(HSDSI) can be calculated:Graphical representation of these equations shows that group 1 undergoes a relatively quick CUG which stabilizes at −0.5 SDS after two years of therapy. Group 2 catches up at a lower rate and stabilizes one year later, but reaches a higher endpoint at +0.4 SDS. These equations provide the clinician with a reference instrument for assessing the efficacy of a growth promoting therapy.