An apparatus for determining a fractional flow reserve, comprising: an input interface, a processing unit, and a storage means; wherein the input interface is configured to obtain spectral CT volumetric image data representing a coronary tree of a human subject, wherein the spectral CT volumetric image data represents at least a section of a coronary tree of the human subject; wherein the storage means is configured to provide a parametric model for simulating a blood flow in a coronary tree; wherein the storage means is configured to provide a hyperemic boundary condition model representing at least one predefined hyperemic boundary condition parameter for the parametric model; wherein the processing unit is configured to extract at least one personalized feature from the spectral CT volumetric image data, wherein at least one personalized feature represents at least one morphological feature of the coronary tree, and wherein the morphological feature of the coronary tree represents plaque in the coronary tree and is at least one of the effective atomic number content of the plaque and the plaque appearance at different energy levels; wherein the processing unit is configured to adapt the hyperemic boundary condition model based on the at least one personalized feature resulting in a personalized hyperemic boundary condition model representing at least one personalized hyperemic boundary condition parameter for the parametric model; and wherein the processing unit is configured to determine a fractional flow reserve of a coronary vessel of the coronary tree of the human subject with the parametric model and the personalized hyperemic boundary condition model. an input interface, a processing unit, and a storage means; wherein the input interface is configured to obtain spectral CT volumetric image data representing a coronary tree of a human subject, wherein the spectral CT volumetric image data represents at least a section of a coronary tree of the human subject; wherein the storage means is configured to provide a parametric model for simulating a blood flow in a coronary tree; wherein the storage means is configured to provide a hyperemic boundary condition model representing at least one predefined hyperemic boundary condition parameter for the parametric model; wherein the processing unit is configured to extract at least one personalized feature from the spectral CT volumetric image data, wherein at least one personalized feature represents at least one morphological feature of the coronary tree, and wherein the morphological feature of the coronary tree represents plaque in the coronary tree and is at least one of the effective atomic number content of the plaque and the plaque appearance at different energy levels; wherein the processing unit is configured to adapt the hyperemic boundary condition model based on the at least one personalized feature resulting in a personalized hyperemic boundary condition model representing at least one personalized hyperemic boundary condition parameter for the parametric model; and wherein the processing unit is configured to determine a fractional flow reserve of a coronary vessel of the coronary tree of the human subject with the parametric model and the personalized hyperemic boundary condition model.