Quasi-Herglotz functions and convex optimization.

We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modelling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of Herglotz functions. It consists of differences of Herglotz functions and we show that several of the important properties and modelling perspectives are inherited by the new set of quasi-Herglotz functions. In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modelling of a non-passive gain medium formulated as a convex optimization problem, where the generating measure is modelled by using a finite expansion of B-splines and point masses.

Influence of bioactive glass on changes in alveolar process dimensions after exodontia.

BACKGROUND: Preservation of the alveolar process after tooth extraction is desirable because it facilitates placement of endosseous implants and minimizes adverse esthetic results associated with fixed partial dentures. The purpose of this study was to evaluate the clinical effectiveness of bioactive glass used as a graft material combined with calcium sulfate used in the form of a mechanical barrier in preserving alveolar ridges after tooth extraction. METHODS: Sixteen patients who required extraction of 2 anterior teeth or bicuspids participated in the study (split mouth design). After tooth extraction and elevation of a buccal full-thickness flap, experimental sockets were filled with bioactive glass, which in turn was covered with a layer of calcium sulfate. Control sites did not receive any graft or calcium sulfate. Titanium pins served as fixed reference points for measurements. No attempt was made to advance the flap to cover the socket areas on control or experimental sites (open socket approach). Reentry surgeries were performed at 6 months. RESULTS: Reentry surgeries showed that experimental sites presented with (1) significantly more internal socket bone fill (6.43 +/- 2.78 mm vs 4.00 +/- 2.33 mm on control sites), (2) less (although not statistically significantly less) resorption of alveolar bone height (0.38 +/- 3.18 mm vs 1.00 +/- 2. 25 mm on control sites), and (3) similar degree of horizontal resorption of the alveolar bony ridge as compared with controls (3. 48 +/- 2.68 mm vs 3.06 +/- 2.41 mm on control sites). CONCLUSIONS: This study suggests that treatment of extraction sockets with a combination of bioactive glass and calcium sulfate is of some benefit in preserving alveolar ridge dimensions after tooth extraction.

A comparison between enamel matrix proteins used alone or in combination with bovine porous bone mineral in the treatment of intrabony periodontal defects in humans.

BACKGROUND: It has been shown that clinical improvement of intrabony periodontal defects can be achieved with the use of enamel matrix proteins (EMPs) or by grafting with bovine porous bone mineral (BPBM). There is no report on the potential synergistic effect of EMPs and BPBM in periodontal regenerative therapy. The purpose of this study was to compare the clinical effectiveness of EMPs used alone or in combination with BPBM in the treatment of periodontal intrabony defects in humans. METHODS: Twenty-one paired intrabony defects were surgically treated using a split-mouth design. Intrabony defects were treated either with enamel matrix proteins (EMP group) or with enamel matrix proteins combined with bovine porous bone mineral (EMP/BPBM group). Re-entry surgeries were performed at 6 months. RESULTS: Preoperative probing depths, attachment levels, and transoperative bone measurements were similar for the EMP and EMP/BPBM groups. Postsurgical measurements taken at 6 months revealed a significantly greater reduction in probing depth in the EMP/BPBM group (3.43 +/- 1.32 mm on buccal sites and 3.36 +/- 1.35 mm on lingual sites) when compared to the EMP group (1.91 +/- 1.42 mm on buccal sites and 1.85 +/- 1.38 mm on lingual sites). The EMP/BPBM group also presented with significantly more attachment gain (3.13 +/- 1.41 mm on buccal sites and 3.11 +/- 1.39 mm on lingual sites) than the EMP group (1.72 +/- 1.33 mm on buccal sites and 1.75 +/- 1.37 mm on lingual sites). Surgical re-entry of the treated defects revealed a significantly greater amount of defect fill in favor of the EMP/BPBM group (3.82 +/- 1.43 mm on buccal sites and 3.74 +/- 1.38 mm on lingual sites) as compared to the EMP group (1.33 +/1.17 mm on buccal sites and 1.41 +/- 1.19 mm on lingual sites). CONCLUSIONS: The results of this study indicate that BPBM has the ability to augment the effects of EMPs in reducing probing depth, improving clinical attachment levels, and promoting defect fill when compared to presurgical levels.

A controlled re-entry study on the effectiveness of bovine porous bone mineral used in combination with a collagen membrane of porcine origin in the treatment of intrabony defects in humans.

AIM: The purpose of this study was to evaluate the clinical effectiveness of a bovine porous bone mineral used in combination with a porcine derived collagen membrane as a barrier in promoting periodontal regeneration in intrabony defects in humans. MATERIAL AND METHODS: The study employed a split-mouth design. 22 paired intrabony defects were treated and surgically re-entered 6 months after treatment. Experimental sites were grafted with bovine porous bone mineral and received a collagen membrane for guided tissue regeneration. Control sites were treated with an open flap debridement. RESULTS: Preoperative pocket depths, attachment levels and trans-operative bone measurements were similar for control and experimental sites. Post surgical measurements revealed a significantly greater reduction in pocket depth (differences of 1.89 +/- 0.31 mm on buccal 0.88 +/- 0.27 mm on lingual measurements) and more gain in clinical attachment (differences of 1.51 +/- 0.33 mm on buccal and 1.50 +/- 0.35 mm on lingual measurements) in experimental sites. Surgical reentry of the treated defects revealed a significantly greater amount of defect fill in favor of experimental sites (differences of 2.67 +/- 0.91 mm on buccal and 2.54 +/- 0.87 mm on lingual measurements). CONCLUSIONS: The results of this study indicate that clinical resolution of intrabony defects can be achieved using a combination of bovine porous bone mineral and an absorbable, porcine derived collagen membrane when employing a technique based on the principles of guided tissue regeneration. The nature of the attachment between the newly regenerated tissue and the root surfaces needs to be evaluated histologically to confirm the presence of new attachment.

The use of autogenous periosteal grafts as barriers for the treatment of intrabony defects in humans.

The purpose of this study was to evaluate the clinical effectiveness of a connective tissue graft including periosteum used as a barrier for guided periodontal tissue regeneration in interproximal bony defects. An open flap debridement of a comparable interproximal bony defect in the same patient was used as a control. This study was performed at 2 different clinical centers. Six paired defects were treated at one center, and 16 paired defects at the other. Reentry surgeries were performed at 6 months. Preoperative comparisons of control and experimental sites with respect to clinical parameters and osseous measurements were similar. Post-surgical experimental sites produced more gain in clinical attachment (1.25 mm on buccal and 1.25 mm on lingual sites at center A and 1.26 mm on buccal and 1.18 mm on lingual sites at center B) and osseous defect fill (1.84 mm on buccal and 2.00 mm on lingual sites at center A and 1.66 mm on buccal and 2.04 mm on lingual sites at center B) when compared to control sites. The results of this trial indicate that clinical resolution of interproximal periodontal defects can be obtained with periosteal grafts used as barriers.

Preservation of alveolar bone in extraction sockets using bioabsorbable membranes.

The purpose of this study was to evaluate the clinical effectiveness of a bioabsorbable membrane made of glycolide and lactide polymers in preserving alveolar ridges following tooth extraction using a surgical technique based on the principles of guided bone regeneration. Sixteen patients requiring extractions of 2 anterior teeth or bicuspids participated in the study (split-mouth design). Following elevation of buccal and lingual full-thickness flaps and extraction of teeth, experimental sites were covered with bioabsorbable membranes; control sites did not receive any membrane. Titanium pins served as fixed reference points for measurements. Flaps were advanced in order to achieve primary closure of the surgical wound. No membrane became exposed in the course of healing. Reentry surgeries were performed at 6 months. Results showed that experimental sites presented with significantly less loss of alveolar bone height, more internal socket bone fill, and less horizontal resorption of the alveolar bone ridge. This study suggests that treatment of extraction sockets with membranes made of glycolide and lactide polymers is valuable in preserving alveolar bone in extraction sockets and preventing alveolar ridge defects.

Evaluation of periosteal membranes and coronally positioned flaps in the treatment of Class II furcation defects: a comparative clinical study in humans.

The purpose of this study was to compare the clinical effectiveness of connective tissue grafts including periosteum used as a mechanical barrier for guided periodontal tissue regeneration and coronally positioned flaps in the treatment of Class II furcation defects. A total of 28 furcation defects were treated; 14 received a periosteal barrier and 14 received a coronally positioned flap. Reentry surgeries were performed at 6 months. No statistically significant differences were found preoperatively between the two treatment groups with respect to clinical parameters and osseous measurements. Postsurgically, both treatment modalities resulted in a significant decrease in probing depth and a significant gain in clinical attachment, but the differences observed were not statistically significant. The periosteal barrier group presented with a significantly better gain in vertical components of the alveolar bone (1.93 +/- 0.15 mm and 0.20 +/- 0.26 mm for periosteal barrier and coronally positioned flap groups, respectively; P < or = 0.001) and horizontal components of the alveolar bone (1.60 +/- 0.21 mm and 0.13 +/- 0.90 mm for periosteal barrier and coronally positioned flap groups, respectively; P < or = 0.001). The results of this trial indicate that similar clinical resolution of Class II furcation defects can be obtained with periosteal barriers and coronally positioned flaps. Periosteal barriers, however, are a better treatment alternative in achieving bone fill of the furcation area.

Histologic evaluation of guided tissue regeneration using 4 barrier membranes: a comparative furcation study in dogs.

This study evaluated and compared four different barrier membrane materials used to treat class II mandibular premolar and molar furcations in seven dogs with naturally occurring periodontitis. Five class II furcation defects in each animal were randomly assigned to one of four experimental groups or to a control group. Each defect was treated by surgical debridement, root planing, and barrier membrane coverage with one of the four test materials or no barrier membrane (control). Thus, each animal served as its own control. Following 6 months of healing, block sections were used to histologically measure the amount of regenerated tissue and stereometrically enumerate the inflammatory cell infiltration observed with each of the treatment modalities. The four barrier membrane materials (polycarbonate filter, silicone rubber, expanded polytetrafluoroethylene, and polycaprolactone) all provided a wound healing environment that promoted new cementum formation, with mean values ranging from 1.96 +/- 0.031 mm to 2.18 +/- 0.015 mm, and facilitated alveolar bone regeneration, with mean values ranging from 1.18 +/- 0.019 mm to 1.44 +/- 0.014 mm. Control-treated sites showed mean values of only 0.24 +/- 0.007 mm new cementum formation and 0.32 +/- 0.017 mm bone fill. Polycarbonate filter and polycaprolactone membrane barriers elicited a significantly greater chronic inflammatory cell response of lymphocyte and plasma cell infiltrates as compared to expanded polytetrafluoroethylene and silicone rubber, which were comparable to control-treated sites.

A bone regenerative approach to alveolar ridge maintenance following tooth extraction. Report of 10 cases.

TEN PATIENTS WHO REQUIRED two or more anterior teeth extractions were utilized in this study. Extraction procedures were carried out with a full thickness surgical flap approach. After flap reflection, teeth were removed with a minimum of trauma to the surrounding bone. Following extraction silicone-based impression techniques were used to produce a model of the alveolar process and small metal pins were placed in the alveolus to be used as fixed points to make measurements of ridge dimensions. One socket was covered with an expanded polytetrafluoroethylene (ePTFE) barrier membrane (experimental site); the other socket was a conventional control. The soft tissue flaps were then mobilized using periosteal releasing incision and the wound closed with ePTFE mattress sutures. Six months following extraction, patients were treated with flap surgery to expose both extractions sites to remove the ePTFE membranes and to measure ridge dimensions using the pins as fixed points. Clinical and model measurements have shown statistically significant better ridge dimensions at experimental sites than at control (P < or = 0.05). Three patients with exposed membranes had similar dimensional changes as controls. Results from this study suggested that this improved technique offers a predictable alveolar ridge maintenance enhancing the bone quality for dental implant procedures and esthetic restorative dentistry.