The work presented in this paper was motivated by the continuing need for a three-dimensional (3D) standard data set to test, validate and measure the accuracy of different image analysis procedures. Validation using data acquired in vivo is difficult since there is no direct information available for the imaged object to corroborate various analyses. Manual labeling is often used to determine truth indirectly in such cases, however intra- and inter-rater variability makes it sub-optimal as a gold standard. Without perfectly known reference data, absolute quantitative validation is not possible.
The use of in vivo MR or CT data confirmed by post-mortem images of macro- or microtomed histological sections is also of limited use, since tissue prepared for such imaging procedures may suffer from cytolysis, shrinkage, tearing and other gross deformations, making registration difficult and thus complicating direct comparison with the in vivo data. Using post-mortem data sets acquired soon after death is an option for validation (e.g, see  for multimodality registration). However the tissue's magnetic characteristics will be modified due to physical changes (such as decreasing temperature and oxygenation level) will affect the MR signal and consequently the tissue intensity contrasts on which post-processing procedures are dependent.
Physical phantoms have been used to address these problems since they allow control over the object shape and material properties. For example, geometrically simple phantoms for MR imaging made of agar gel with iron oxide particles have been used to test classification algorithms . More complex, anatomically realistic head phantoms such as the well known Hoffman Brain Phantom  have been used for anatomical simulation to create PET images , assessment of reconstruction accuracy of PET images , evaluation of SPECT imaging components , testing registration of SPECT and PET images  and testing modified filtered back projection algorithms to correct for head motion . While physical phantoms permit extensive testing in the real-world scanning environment, their strength is also their weakness in that their stability makes it difficult to change shape or material properties at will.
Digital phantoms have been proposed to address weaknesses associated with both post-mortem data and physical phantoms. The advantages of digital phantoms are many: they can be easily modified to model pathology or variations in normal anatomy. Simulating images from these phantoms allows complete control over factors that may affect an algorithm such as noise, contrast, slice thickness, pixel size, geometric distortion, and movement artefacts. By varying each of these possible sources of error, one can evaluate the procedure's robustness in a controlled fashion. Some uses of digital brain phantoms include evaluation of PET imaging characteristics [8,9], evaluation of partial volume effects (PVEs) in PET [10,11] and validation of registration algorithms . The principal weaknesses of simulated data are usually 1) the oversimplicity of the phantom geometry, 2) the improper treatment of edge-effects which leads to tissue mixing within imaged voxels and 3) improper modeling of the data acquisition and image formation stages. In this paper, we address the first two of these issues when generating a general purpose neuro-anatomical phantom for use with any tomographic imaging modality. The third issue is modality-specific and we give examples of simulated PET and MR images. More detailed treatment of the simulations concerned are given in related publications, cited below.
While testing with simulated data is necessary for algorithm validation, it is not sufficient. Additional testing with real data must also be completed to demonstrate that the algorithm actually works under real-world conditions where some unknown factors almost certainly remain. By definition, since they are unknown, algorithm behavior with respect to these factors will not have been simulated. While an in vivo study may be statistically weaker due to limited data and greater variability, results from such a study that behave in a manner consistent with and comparable to simulations make a strong argument for the validity of the method tested.
In this paper we describe the design, construction and application of a high resolution, volumetric, anthropomorphic, digital brain phantom that can be used to simulate medical image data. For example, realistic PET images can be generated using a simulator that accounts for acquisition geometry, attenuation, scatter, randoms and Poisson noise  as shown below in section III-A.2. Similarly, MR images can be simulated from physical principals by solving the Bloch equations  as described in section III-A.1. The important advantage of using this phantom are that the ``answer'' is known a priori and the phantom can be used to compute an objective measure of performance for a given image processing algorithm.