DIVIDING THE ABUTMENT PERIMETER INTO INFINITE IMAGINARY LINE SEGMENTS Instead of describing the TOC of an abutment as the angle of an ambiguous entity, the ��wall�� of an abutment, one can divide up the axial aspect of the abutment into infinite vertical line segments. selleck This way, one can describe TOC as the average angle of an infinite number of line segments emanating from specific points along the perimeter of the most apical extent of the axial aspect of the abutment (the ��abutment axial perimeter��). A dentist can imagine an ideal, cylinder abutment, where the perimeter of the cylinder base is the same as the abutment apical perimeter. If an imaginary plane is produced that is tangent to this imaginary, ideal cylinder abutment and intersects a point along the cylinder base perimeter, the intersection of the tangent plane and the cylinder forms a tangential line segment.

This tangential line segment originates at that point along the cylinder perimeter and continues vertically to the top of the cylinder. An infinite number of such tangent line segments can be produced, one for each point along the cylinder base perimeter. Since these infinite tangent line segments collectively form a cylinder, the angles of all of the tangent line segments produced from these tangent planes are the same, such that all of these individual tangent line segments are parallel with one another. Furthermore, with the actual abutment that has a frustum shape, if the axial aspect consists of a single plane reduction around the entire perimeter of the abutment, an imaginary tangent plane can be created that intersects the axial aspect of the abutment at a single point on the abutment apical perimeter.

This intersection forms a tangential line segment that continually contacts the surface of the abutment from that perimeter point to the occlusal aspect of the abutment. This tangential line segment formed on the actual abutment axial aspect forms an angle with the imaginary tangential line segment formed on the imaginary ideal cylinder form of the axial aspect of the abutment, where the apex of the two line segments is the point on the perimeter that they both originate from. The angle of these two line segments is the value of the convergence angle of the axial aspect of abutment at that point along the abutment apical perimeter.

The average angle of all of the tangential line segment pairs that can be formed for each point along the abutment apical Drug_discovery perimeter is essentially the TOC angle of the axial aspect of the abutment and is a measure of the extent to which the axial aspect of the actual abutment differs from an ideal, cylindrical abutment [Figure 1]. If the axial aspect of the abutment has a two-plane reduction, a tangential plane can be imagined that is tangent to an imaginary ��best fit approximation�� line that ��averages�� the angle formed by the two planes of reduction at that perimeter point [Figure 2].