Biomechanical Informational Effect of Innovative Double or Triple Dental Abutment-implant: Case-series

Conception and design of the Double Abutment (DA) and Triple Abutment (TA): Scientific Rationality Traditional abutments are generally cylindrical nowadays, having two curved edges at the base and an edge that connects the two vertices on the side face (total of 3 edges) considering its strength as a unit, while the new DA and TA features a paraboloid geometric design along its entire length.

The paraboloid is a mathematical equation that generates quadric surfaces of two types: elliptic and hyperbolic. The elliptic paraboloid is shaped like an oval-shaped cup and can have a maximum or minimum point. In an appropriate coordinate system, with the three axes x, y and z, it can be represented by the equation: z/c=x2 /a2 + y2 /b2, where a and b are constants that determine the degree of curvature in the x-z and y-z planes, respectively (an elliptic paraboloid opens upwards). The hyperbolic paraboloid, or hypar, is a doubly ruled surface (composed of multiple lines, whose union forms the surface itself), usually saddle-shaped. Its coordinated system is also based on three axes, manifested in the equation: z/c = y2/b2 - x2/a2. For c>0, i.e., a hyperbolic paraboloid that opens downward along the x-axis and along the y-axis (i.e., the parabola in the x=0 plane is open upward and the parabola in the y=0 plane opens downward).

The design of DA (elliptical paraboloid) and TA (hyperbolic paraboloid) allows high stiffness with reduced bending stresses and equalization of forces. Additionally, TA hyperbolic paraboloid structures are the most complex and possess a unique combination of structural and architectural properties, resultant from its double curvature, concave convex and suited to carry the in-plane shear forces and transmit uniform eccentric axial forces to the other members of the system. Vectorial loads are minimized, preventing the traditional axis of transverse coordinates that imply early bone loss in the implant abutment connection area. These designs represent the interaction that exists between all biological phenomena and mathematics.

The new abutments are multiple mechanical load organizers, and support 2 (DA) or 3 (TA) crowns on each abutment, with an innovative geometric design that is totally passive (no welds), resulting from mathematical and physical conformations coupled in geometric vector models.

DA and TA are protected by the following patents: "Pilar geminado sobre implante osseointegrado e corretivo extensor compensatório de inclinações" [Double abutment on osseointegrated implant and compensating inclination extensor corrector (PI BR 0505827-9)]; "Splint abutment over osseointegrated implant and compensatory slanted coping" (United States Patent 9039416 and Canadian Patent No. 2,630,592); "System of triple abutments with connect (United States Patent 11,701,206); "Sistema de pilares trigeminados e múltiplos sobre implantes osseointegrados e guias direcionadores" [Triple and multiple abutments on osseointegrated implants and guide directors (PI BR 0800298-3, Brazil)]. All patents belong to the Institute of Technology and Research (Instituto de Tecnologia e Pesquisa -, Belo Horizonte, Minas Gerais, Brazil).