  Augmented Reality (AR) has been used to facilitate surgical guidance during
External Ventricular Drain (EVD) surgery, reducing the risks of misplacement in
manual operations. During this procedure, the key challenge is accurately
estimating the spatial relationship between pre-operative images and actual
patient anatomy in AR environment. This research proposes a novel framework
utilizing Time of Flight (ToF) depth sensors integrated in commercially
available AR Head Mounted Devices (HMD) for precise EVD surgical guidance. As
previous studies have proven depth errors for ToF sensors, we first assessed
their properties on AR-HMDs. Subsequently, a depth error model and
patient-specific parameter identification method are introduced for accurate
surface information. A tracking pipeline combining retro-reflective markers and
point clouds is then proposed for accurate head tracking. The head surface is
reconstructed using depth data for spatial registration, avoiding fixing
tracking targets rigidly on the patient's skull. Firstly, $7.580\pm 1.488 mm$
depth value error was revealed on human skin, indicating the significance of
depth correction. Our results showed that the error was reduced by over $85\%$
using proposed depth correction method on head phantoms in different materials.
Meanwhile, the head surface reconstructed with corrected depth data achieved
sub-millimetre accuracy. An experiment on sheep head revealed $0.79 mm$
reconstruction error. Furthermore, a user study was conducted for the
performance in simulated EVD surgery, where five surgeons performed nine k-wire
injections on a head phantom with virtual guidance. Results of this study
revealed $2.09 \pm 0.16 mm$ translational accuracy and $2.97\pm 0.91$ degree
orientational accuracy.
