A method of determining the shape of an artificial cement-less hip prosthesis stem, which is implanted into the deep hollow extending from the epiphysis of the femur to the diaphysis, so as to be gradually united with the femur by Bone-Growth, comprising;
- detecting the limitary thickness of the bony tissue of each part of the femur to have prosthesis, which is necessary for forming the wall of deep hollow, by applying threshold value of bone density to the three dimensional graphics data based on CT graphics data and MRI data obtained from the femur, calculating not only the shape of the imaginary three dimensional deep hollow extending to the medullary cavity, which is formed inside the bony tissue, but the coordinates of crotch side line and counter-crotch side line for regulating the shape of lateral section of the deep hollow, and the coordinates of anterior side line and posterior side line for regulating the shape of section perpendicular to the lateral section of the deep hollow;
- calculating not only the shape of the epiphysis opening of the imaginary three dimensional deep hollow and the position of the center of figure of the shape, from the position and the angle of the epiphysis opening determined on the basis of the reference line given beforehand so as to be parallel to the longitudinal direction of the femur, but the shape of the diaphysis opening of the imaginary three dimensional deep hollow and the position of the center of figure of the shape, from the length of the stem to be applied to the femur and the angle of the diaphysis opening;
- calculating the reference arc on the plane including the crotch-side line and counter crotch-side line which passes through the center of figure of the epiphysis opening mentioned above, the center of figure of the diaphysis opening, and the reference point in the lateral direction, which lies halfway between these two centers of figure, and from which the distance to said crotch side line is approximately equal to the distance to the counter-crotch side line;
- obtaining the pattern of the provisional deep hollow on the plane including the crotch and counter-crotch side lines, which is formed inside said imaginary three dimensional deep hollow surrounded by a small arc on the plane including the crotch and counter-crotch side lines which is concentric with the reference arc on the plane including the crotch and counter-crotch side lines and has a radius which is shorter than the radius of the reference arc and longer than the distance to the end point of epiphysis lying on said crotch side line, a large arc on the plane including the crotch and counter-crotch side lines which is concentric with said reference arc and has a radius which is longer than the radius of said reference arc and shorter than the distance to the end point of epiphysis lying on said counter-crotch side line, the crotch side line which is from the terminal point of the small arc where said small arc intersects the crotch side line to the end point of diaphysis lying on the crotch side line, and the counter-crotch side line which is from the terminal point of the large arc where said large arc intersects the counter-crotch side line to the end point of diaphysis lying on the counter-crotch side line;
- calculating the reference arc on the plane including the anterior and posterior side lines which passes through the center of figure of the epiphysis opening mentioned above, the center of figure of the diaphysis opening, and the reference point in the direction perpendicular to the lateral direction, which lies halfway between these two centers of the figure, and from which the distance to said anterior side line is approximately equal to the distance to the posterior side line,
- obtaining the pattern of the provisional deep hollow on the plane including the anterior and posterior side lines, which is formed inside said imaginary three dimensional deep hollow surrounded by a small arc on the plane including the anterior and posterior side lines which is concentric with the reference arc on the plane including the anterior and posterior side lines and has a radius which is shorter than the radius of the reference arc and longer than the distance to the end point of epiphysis lying on said anterior side line, a large arc on the plane including the anterior and posterior side lines which is concentric with said reference arc and has a radius which is longer than the radius of said reference arc and shorter than the distance to the end point of epiphysis lying on said posterior side line, the anterior side line which is from the terminal point of the small arc where said small arc intersects the anterior side line to the end point of diaphysis lying on the anterior side line, and the posterior side line which is from the terminal point of the large arc where said large arc intersects the posterior side line to the end point of diaphysis on the posterior side line;
- making the provisional tree dimensional reference stem containing the reference arc on the plane including the crotch and counter-crotch side lines and the reference arc on the plane including the anterior and posterior side lines, which consists of a body surrounded by four side planes formed by arranging said patterns of provisional deep hollow on the plane including the crotch and counter-crotch side lines on the anterior side line and the posterior side line respectively so as to face each other and said patterns of provisional deep hollow on the plane including the anterior and posterior side lines on the crotch side line and the counter-crotch side line respectively so as to face each other, and a quasi-circular cylinder having the same shape as said imaginary three dimensional deep hollow corresponding to the region from each terminal point of the small arc and the large arc of the body surrounded by four planes to the diaphysis opening;
- making the provisional three dimensional reference deep hollow which has the same shape as said provisional three dimensional reference stem, in order to calculate the position and the posture of the provisional three dimensional reference stem on each step that the stem is gradually pulled out of the deep hollow, obtaining the residual portion of provisional three dimensional reference deep hollow whose diaphysis portion is removed, where the deep hollow does not overlap the stem every step, with calculating the center of gravity and the principal axes of inertial thereof, and obtaining the residual portion of provisional three dimensional reference stem whose epiphysis portion is removed, where the stem does not overlap the deep hollow every step, with calculating the center of gravity and the principal axes of inertial thereof as well, shifting the center of gravity of the residual portion of provisional three dimensional reference stem to the principal axes of the residual portion of the deep hollow in the direction of pulling the stem on the condition that the posture of the stem is kept in the step, rotating the residual portion of provisional three dimensional reference stem around the center of gravity shifted in the last step so as to coincide the principal axes of inertial of the residual portion of provisional three dimensional reference stem in the direction of pulling the stem with the principal axes of inertial of the residual portion of provisional three dimensional reference deep hollow in the direction of pulling the stem, calculating the positions that the end points of diaphysis lying on the crotch side line and the anterior side line of the residual portion of provisional three dimensional reference stem, and the end points of diaphysis lying on the counter-crotch side line and the posterior side line occupy every step;
- making an imaginary three dimensional stem which has the same shape as said imaginary three dimensional deep hollow, moving the imaginary three dimensional stem in the imaginary three dimensional deep hollow by applying the transitional values of said occupied positions to the imaginary stem, calculating the interference portions where the imaginary three dimensional stem is disturbed to move in the imaginary three dimensional deep hollow while the stem is pulled out of the deep hollow and putting them in storage;
- calculating the outer surfaces of shape of the imaginary three dimensional stem whose interference portions are entirely removed on the basis of the data in storage, obtaining the reference stem whose final shape is inscribed to the supposed inner surface of shape for the purpose of smoothing the outer surface of shape of the imaginary three dimensional stem, taking an alternative reference point in the lateral direction on the region between a straight segment from the center of figure of the epiphysis opening to the center of figure of the diaphysis opening and said reference point in the lateral direction, taking an alternative reference point in the direction perpendicular to the lateral direction on the region between said straight segment and said reference point in the direction perpendicular to the lateral direction as well, regarding the alternative reference point in the lateral direction as the reference point in the lateral direction, and the alternative reference point in the direction perpendicular to the lateral direction as the reference point in the direction perpendicular to the lateral direction, obtaining the alternative provisional three dimensional reference stem having the alternative reference arc on the plane including the crotch and counter-crotch side lines whose curvature is different from that of the reference arc on the plane including the crotch and counter-crotch lines and the alternative reference arc on the plane including the anterior and posterior side lines whose curvature is different from that of the reference arc on the plane including the anterior and posterior side lines, calculating said occupied positions every step, obtaining the final shape of the alternative stem instead of said reference stem by following the procedure for calculating the interference portions of the stem where the imaginary three dimensional stem is disturbed to move in the imaginary three dimensional deep hollow by using the occupied position, and for putting the data in storage;
- and,
- computing the data on the positions and the postures of the reference stem and the alternative stem which have said final shape while putting these stems gradually into said imaginary three dimensional deep hollow, i.e., by taking the reverse steps of the series of steps mentioned above.