Could you suggest me a trained CNN model which is trained on a larger dataset which supports input image size >400x400 pixels?
In my case I have very thin structures, if I rescale the images to the standard size e.g. 224x224 I will loose those structures.
Without your specific application it is hard to point you to appropriate pre-trained models. However, independent of your specific application I would suggest the following:
You do not necessarily need a pre-trained model supporting larger image sizes - depending on your application you need to re-train the last few layers (i.e. the fully-connected layers) anyway. However, the convolutional layers (as well as pooling layers, local response normalization layers, ReLU layers etc.) are independent of the image size. So you can take the convolutional layers form a pre-trained model (e.g. from the AlexNet or the reference BVLC model) and adapt the fully-connected layers to your need and re-train only those.
Nevertheless, here are some models with larger image sizes (you can find all of them in the Caffe Model Zoo). It may, however, depend on your application whether these models are of use. You can have a look at the prototxt files of these models to see the exact image size required.