Bone Graft Substitutes in Maxillofacial Reconstruction - Structural and Biomechanical Perspectives

Reconstruction of a maxillofacial skeletal defect in the recent past has witnessed a paradigm shift in the process of treatment planning. It has now become a collaboration between the surgeon and the bioengineer to provide a customised stable reconstruction. Understanding maxillofacial skeleton from an architectural and biomechanical perspective would not only guide the surgeon in planning a reconstruction but also the bioengineer to select the biomaterial and design an ideal reconstruction. This paper intended to provide an insight into scientific concepts which needed to be considered during the designing of biomaterials for reconstruction of maxillofacial skeletal defects. Any object in the world, from a mechanical perspective is seen only as a material of varying physical and chemical (organic / inorganic) properties dwelling in a dynamic three-dimensional environment. Bone continuously has been re-modelling by adapting to the dynamic loading environment through an established force distribution pattern of equilibrium. 1 Hence, for a patient requiring reconstruction of defects of varying dimensions within the craniomaxillofacial skeleton, its architectural complexity should be seen from both the surgeon’s and bioengineer’s perspective. Such multidisciplinary approach would provide a customized comprehensive reconstructive and rehabilitative solution.

Sampling the Flow of a Bandlimited Function

We analyze the problem of reconstruction of a bandlimited function f from the space–time samples of its states $$f_t=\phi _t*f$$ f t = ϕ t ∗ f resulting from the convolution with a kernel $$\phi _t$$ ϕ t . It is well-known that, in natural phenomena, uniform space–time samples of f are not sufficient to reconstruct f in a stable way. To enable stable reconstruction, a space–time sampling with periodic nonuniformly spaced samples must be used as was shown by Lu and Vetterli. We show that the stability of reconstruction, as measured by a condition number, controls the maximal gap between the spacial samples. We provide a quantitative statement of this result. In addition, instead of irregular space–time samples, we show that uniform dynamical samples at sub-Nyquist spatial rate allow one to stably reconstruct the function $$\widehat{f}$$ f ^ away from certain, explicitly described blind spots. We also consider several classes of finite dimensional subsets of bandlimited functions in which the stable reconstruction is possible, even inside the blind spots. We obtain quantitative estimates for it using Remez-Turán type inequalities. En route, we obtain Remez-Turán inequality for prolate spheroidal wave functions. To illustrate our results, we present some numerics and explicit estimates for the heat flow problem.

Small defects reconstruction in waveguides from multifrequency one-side scattering data

<p style='text-indent:20px;'>Localization and reconstruction of small defects in acoustic or electromagnetic waveguides is of crucial interest in nondestructive evaluation of structures. The aim of this work is to present a new multi-frequency inversion method to reconstruct small defects in a 2D waveguide. Given one-side multi-frequency wave field measurements of propagating modes, we use a Born approximation to provide a <inline-formula><tex-math id="M1">\begin{document}$ \text{L}^2 $\end{document}</tex-math></inline-formula>-stable reconstruction of three types of defects: a local perturbation inside the waveguide, a bending of the waveguide, and a localized defect in the geometry of the waveguide. This method is based on a mode-by-mode spacial Fourier inversion from the available partial data in the Fourier domain. Indeed, in the available data, some high and low spatial frequency information on the defect are missing. We overcome this issue using both a compact support hypothesis and a minimal smoothness hypothesis on the defects. We also provide a suitable numerical method for efficient reconstruction of such defects and we discuss its applications and limits.</p>

Reconstruction of the right-hand part of a distributed differential equation using a positional controlled model

In this paper, we consider the stable reconstruction problem of the unknown input of a distributed system of second order by results of inaccurate measurements of its solution. The content of the problem considered is as follows. We consider a distributed equation of second order. The solution of the equation depends on the input varying in the time. The input, as well as the solution, is not given in advance. At discrete times the solution of the equation is measured. These measurements are not accurate in general. It is required to design an algorithm for approximate reconstruction of the input that has dynamical and stability properties. The dynamical property means that the current values of approximations of the input are produced on-line, and the stability property means that the approximations are arbitrarily accurate for a sufficient accuracy of measurements. The problem refers to the class of inverse problems. The algorithm presented in the paper is based on the constructions of a stable dynamical inversion and on the combination of the methods of ill-posed problems and positional control theory.

A new fluoroscopic view for evaluation of anteromedial cortex reduction quality during cephalomedullary nailing for intertrochanteric femur fractures: the 30° oblique tangential projection

Background Anteromedial cortex-to-cortex reduction is a key parameter for stable reconstruction of the fracture fragments during the intertrochanteric fracture fixation. This paper introduces the oblique fluoroscopic projection as a novel method to evaluate the quality of anteromedial cortical apposition. Methods Three proximal femur specimens were marked with steel wires along five anatomic landmarks: Greater trochanter, Lesser trochanter, Intertrochanteric line, Anterolateral tubercle and the Anteromedial cortical line. After obtaining the standard femoral neck AP and lateral fluoroscopic images, the C-arm was rotated by every 5°increments until a clear tangential view of the antero-medial-inferior corner cortex was observed. 98 cases of intertrochanteric hip fractures were enrolled from April 2018 to October 2019. After fixation with the nails, the intra-operative anteromedial cortex reduction quality was evaluated from the AP, the true lateral, and the new anteromedial oblique fluoroscopic images. The fluoroscopic results were compared with the post-operative 3D-CT reconstruction images. Results The specimen study showed that internal rotation of the C-arm to approximately 30 ° can remove all the obscure shadows and clearly display the antero-medial-inferior cortical tangent line. Clinically,the positive, neutral and negative apposition of different cortices via intra-operative fluoroscopic images showed79, 19 and 0 cases of medial cortical apposition in AP views; 2, 68 and 28 cases of anterior cortices in lateral views;and 22, 51 and 25cases of anteromedial cortical apposition in oblique views respectively. The post-operative 3D-CT reconstruction images revealed that the final anteromedial cortical contact was noted in 62 cases (63.3%), and lost in 36 cases (36.7%). The overall coincidence rate between intra-operative fluoroscopy and post-operative 3D-CT was 63.3% (62/98) in AP view,79.6% (78/98) in lateral view, and 86.7% (85/98) in oblique view(p < 0.001). Negative cortical apposition in oblique view was highly predictive of a final loss of cortical support on 3D CT (24/25 cases, 96%).And non-negative cortical apposition in oblique view was highly associated with true cortical support on 3D CT images (61/73 cases, 83.6%) (p < 0.001). Conclusions Besides the AP and lateral projections, an anteromedial oblique view of 30° certifies to be a very useful means for evaluation of the fracture reduction quality of anteromedial cortical apposition.