Very Long Baseline Interferometry (VLBI) measurements of the positions of extragalactic radio source have led to the most precise and stable celestial reference frame available to date. Generally, these radio sources exhibit spatially extended structures that are variable in both time and frequency on the milliarcsecond scale. Such radio-source structures set limits om possible improvements of the VLBI celestial reference frame and on its use for geodynamic and deep space navigation VLBI measurements. We present a study of the effects of radio-source structures in the delay and delay rate, which are the fundamental observables measured by VLBI for astrometric and geodetic applications. This study includes the theoretical formulation to model these effects, simulations for a simple two-component source, and analysis of real astrometric VLBI data acquired on the complex radio source NRAO140. For this source, the structure corrections have been calculated with maps produced by three different VLBI imaging techniques: the hybrid-CLEAN algorithm, the maximum entropy method, and model fitting. We compare the structure corrections calculated with the three brightness distributions to the actual data by forming the closure delays and delay rates. In this comparison, the measured closure delays and delay rates are from the same dataset as the amplitudes and closure phases used to map NRAO140. We conclude that the CLEAN map produces the most accurate structure corrections in this example.