  The K\"arger model and its derivatives have been widely used to incorporate
transcytolemmal water exchange rate, an essential characteristic of living
cells, into analyses of diffusion MRI (dMRI) signals from tissues. The K\"arger
model consists of two homogeneous exchanging components coupled by an exchange
rate constant and assumes measurements are made with sufficiently long
diffusion time and slow water exchange. Despite successful applications, it
remains unclear whether these assumptions are generally valid for practical
dMRI sequences and biological tissues. In particular, barrier-induced
restrictions to diffusion produce inhomogeneous magnetization distributions in
relatively large-sized compartments such as cancer cells, violating the above
assumptions. The effects of this inhomogeneity are usually overlooked. We
performed computer simulations to quantify how restriction effects, which in
images produce edge enhancements at compartment boundaries, influence different
variants of the K\"arger-model. The results show that the edge enhancement
effect will produce larger, time-dependent estimates of exchange rates in e.g.,
tumors with relatively large cell sizes (>10 {\mu}m), resulting in
overestimations of water exchange as previously reported. Moreover, stronger
diffusion gradients, longer diffusion gradient durations, and larger cell
sizes, all cause more pronounced edge enhancement effects. This helps us to
better understand the feasibility of the K\"arger model in estimating water
exchange in different tissue types and provides useful guidance on signal
acquisition methods that may mitigate the edge enhancement effect. This work
also indicates the need to correct the overestimated transcytolemmal water
exchange rates obtained assuming the K\"arger-model.
