Design and optimization benefit from understanding the dependence of a quantity of interest (e.g., a design objective or constraint function) on the design variables. A low-dimensional active subspace, when present, identifies important directions in the space of design variables; perturbing a design along the active subspace associated with a particular quantity of interest changes that quantity more, on average, than perturbing the design orthogonally to the active subspace. This low-dimensional structure provides insights that characterize the dependence of quantities of interest on design variables. Airfoil design in a transonic flow field with a parameterized geometry is a popular test problem for design methodologies. We examine two particular airfoil shape parameterizations, PARSEC and CST, and study the active subspaces present in two common design quantities of interest, transonic lift and drag coefficients, under each shape parameterization. We mathematically relate the two parameterizations with a common polynomial series. The active subspaces enable low-dimensional approximations of lift and drag that relate to physical airfoil properties.In particular, we obtain and interpret a two-dimensional approximation of both transonic lift and drag, and we show how these approximation inform a multi-objective design problem.
BackgroundBone is a highly vascularized and resilient organ with innate healing abilities, however some bone injuries overwhelm these attributes and require intervention, such as bone tissue engineering strategies. Combining biomaterials and growth factors, such as bone morphogenetic protein 2 (BMP2), is one of the most commonly used tissue engineering strategies. However, use of BMP2 has been correlated with negative clinical outcomes including aberrant inflammatory response, poor quality bone, and ectopic bone.MethodsIn the present study, a novel poly-n-acetyl glucosamine (pGlcNAc, trade name Talymed) scaffold was utilized in addition to the commonly used acellular collagen sponge (ACS) BMP2 delivery system in a murine calvarial defect model to investigate whether the innate properties of Talymed can reduce the noted negative bone phenotypes associated with BMP2 treatment.ResultsComparison of murine calvarial defect healing between ACS with and without Talymed revealed that there was no measurable healing benefit for the combined treatment. Healing was most effective utilizing the traditional acellular collagen sponge with a reduced dose of BMP2.ConclusionsThe results of this investigation lead to the conclusion that excessive dosing of BMP2 may be responsible for the negative clinical side effects observed with this bone tissue engineering strategy. Rather than augmenting the currently used ACS BMP2 bone wound healing strategy with an additional anti-inflammatory scaffold, reducing the dose of BMP2 used in the traditional delivery system results in optimal healing without the published negative side effects of BMP2 treatment.
Many variables serve to alter the process of bone remodelling and diminish regeneration including the size and nature of the wound bed and health status of the individual. To overcome these inhibitory factors, tissue-engineered osteoconductive scaffolds paired with various growth factors have been utilized clinically. However, many limitations still remain, for example, bone morphogenetic protein 2 (BMP2) can lead to rampant inflammation, ectopic bone formation, and graft failure. Here, we studied the ability for a nanofiber scaffold (Talymed) to accelerate BMP2 growth factor-induced bone healing compared with the traditional absorbable collagen sponge (ACS) delivery system. One hundred fifty-five adult wild type mice were arranged in 16 groups by time, 4 and 8 weeks, and treatment, ACS or Talymed, loaded with control, low, medium, or high dosages of BMP2. Skulls were subjected to microCT, biomechanical, and histological analysis to assess bone regeneration. The use of Talymed within the defect site was found to decrease the bone volume, bone formation rate, and alkaline phosphatase activity compared with ACS/BMP2 combinations. Interestingly, though Talymed regenerated less bone, the regenerate was found to have a greater hardness value than that of bone within the ACS groups. However, the difference in bone hardness between scaffolds was not detectable by 8 weeks. Based on these results, we found that the nanofiber scaffold generated a better quality of bone regenerate at 4 weeks but, due to the lack of overall bone formation and the inhibition of normal remodelling processes, was not as efficacious as the current clinical standard ACS/BMP2 therapy.
Bone wound healing is a highly dynamic and precisely controlled process through which damaged bone undergoes repair and complete regeneration. External factors can alter this process, leading to delayed or failed bone wound healing. The findings of recent studies suggest that the use of selective serotonin reuptake inhibitors (SSRIs) can reduce bone mass, precipitate osteoporotic fractures and increase the rate of dental implant failure. With 10% of Americans prescribed antidepressants, the potential of SSRIs to impair bone healing may adversely affect millions of patients’ ability to heal after sustaining trauma. Here, we investigate the effect of the SSRI sertraline on bone healing through pre-treatment with (10 mg·kg-1 sertraline in drinking water, n = 26) or without (control, n = 30) SSRI followed by the creation of a 5-mm calvarial defect. Animals were randomized into three surgical groups: (a) empty/sham, (b) implanted with a DermaMatrix scaffold soak-loaded with sterile PBS or (c) DermaMatrix soak-loaded with 542.5 ng BMP2. SSRI exposure continued until sacrifice in the exposed groups at 4 weeks after surgery. Sertraline exposure resulted in decreased bone healing with significant decreases in trabecular thickness, trabecular number and osteoclast dysfunction while significantly increasing mature collagen fiber formation. These findings indicate that sertraline exposure can impair bone wound healing through disruption of bone repair and regeneration while promoting or defaulting to scar formation within the defect site.
Large craniofacial defects present a substantial clinical challenge that often requires the use of osteoconductive matrices and osteoinductive cues (i.e., bone morphogenetic proteins [BMP2]) to augment healing. While these methods have improved clinical outcomes, a better understanding of how the osteogenic fronts surrounding the defect, the underlying dura mater, and the cranial suture area contribute to healing may lead to more targeted therapies to enhance bone regeneration. We hypothesized that healing within a large bone defect will be precipitated from cells within the remaining or available suture mesenchyme abutting the edges of a murine critical sized defect. To investigate this hypothesis, 39 adult, wild-type mice were randomly arranged into groups (9 or 10 per group) by time (4 and 8 weeks) and treatment (control, acellular collagen sponge alone, or acellular collagen sponge loaded with a clinically relevant scaled dosage of BMP2). The skulls were then subjected to microcomputed tomography and histological analysis to assess bone regeneration in regions of interest within the defect area. A regional assessment of healing indicated that BMP2 drives greater healing than control and that healing emanates from the surgical margin, particularly from the margin associated with undisrupted suture mesenchyme. Though BMP2 treatment drove an increase in cell presence within the healing defect, there was no regional orientation of craniofacial stem cells or vascularity. Overall, these data reinforce that osteoconductive matrices in conjunction with osteoinductive peptides result in better healing of large calvarial defects. This healing is characterized as emanating from the surgical margin where there is an abundant supply of vasculature and progenitor cells.
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