Cleft lip nasal deformity has been challenging to plastic surgeons. A better understanding of the biomechanical aspect of the cleft nose would contribute to a better correction. In this study, finite element model of a normal nose was constructed and loaded with forces to recapitulate the unilateral cleft lip nasal deformity. Tether at the alar base was simulated by a laterally directed force at the lateral crus, and tether at the columella base by a posteriorly directed force at the medial crus. The equivalent von-Mises stress and the total deformation consequent to different patterns of loading were captured. In accordance with clinical observations, unilaterally loaded forces caused deformation on both sides of the nose. A correlation between the patterns of loading and different cleft lip nasal deformities was documented in detail. When set at the same force magnitude, tether at the columella base led to more extensive changes in the nasal morphology and higher level of stress than at the alar base. Clear identification of major pathological tethers in the nasolabial region might lead to more accurate and stable correction of cleft lip nasal deformities.

The factorization method provides a necessary and sufficient condition for characterizing the shape and position of an unknown scatterer by using far-field patterns of infinitely many time-harmonic plane waves at a fixed frequency (which are also called the multistatic data response matrix). This paper is concerned with the factorization method with a single far-field pattern to recover an arbitrary convex polygonal scatterer/source. Its one-wave version relies on the absence of analytical continuation of the scattered/radiated wave-fields in corner domains. It can be regarded as a domain-defined sampling method and does not require forward solvers. In this paper we provide a rigorous mathematical justification of the one-wave factorization method and present some preliminary numerical examples. In particular, the proposed method can be interpreted as a model-driven and data-driven imaging scheme, and it shows how to incorporate a priori knowledge about the unknown target into the test scatterers for the purpose of detecting obstacles/sources with specific features.

<p style='text-indent:20px;'>This paper is concerned with the factorization method with a single far-field pattern to recover an arbitrary convex polygonal scatterer/source in linear elasticity. The approach also applies to the compressional (resp. shear) part of the far-field pattern excited by a single compressional (resp. shear) plane wave. The one-wave factorization is based on the scattering data for a priori given testing scatterers. It can be regarded as a domain-defined sampling method and does not require forward solvers. We derive the spectral system of the far-field operator for rigid disks and show that, using testing disks, the one-wave factorization method can be justified independently of the classical factorization method.</p>