Patent ID: 8862200

Claim:
A method for determining a position of a magnetic source coupled to a bone of a patient, the method comprising: (i) measuring a magnetic field generated by the magnetic source with a magnetic sensor array, the magnetic field being defined by a plurality of three-dimensional magnetic flux densities; (ii) generating first data indicative of components of the three-dimensional magnetic flux density of the magnetic source at a plurality of points in space based on the measuring step; (iii) determining an estimated position of the magnetic source; (iv) calculating second data indicative of a theoretical value of the components of the three-dimensional magnetic flux density of the magnetic source based on the estimated position; (v) calculating a difference between the first data and the second data; and (vi) repeating steps (iii)-(v) until the difference between the first data and the second data is less than a predetermined minimum threshold value, wherein calculating second data comprises calculating a theoretical value of an X-component of the three-dimensional magnetic flux density of the magnetic field using the following equation: B x = μ ⁢ ⁢ m [ 3 ⁢ x ⁡ ( x ⁢ ⁢ sin ⁡ ( Θ ) ⁢ cos ⁡ ( Φ ) + y ⁢ ⁢ sin ⁢ ( Θ ) ⁢ sin ⁡ ( Φ ) + z ⁢ ⁢ cos ⁡ ( Θ ) ) r 2 - sin ⁡ ( Θ ) ⁢ cos ⁡ ( Φ ) ] 4 ⁢ ⁢ π ⁢ ⁢ r 3 wherein B x is the theoretical value of the X-component, x is an X-coordinate value of the estimated position of a magnetic sensor of the magnetic sensor array with respect to the magnetic source, y is a Y-coordinate value of a magnetic sensor with respect to the magnetic source, z is a Z-coordinate value of the estimated position of the magnetic sensor with respect to the magnetic source, Θ is a rotational value about the X-axis of the estimated position of the magnetic source, Φ is a rotational value about the Y-axis of the estimated position of the magnetic source, μ is the permeability of free space, m is the magnetic strength of the magnetic source, and r=√{square root over (x 2 +y 2 +z 2 )}.