Variational analysis of inextensible elastic curves

We minimize elastic energies on framed curves which penalize both curvature and torsion. We also discuss critical points using the infinite dimensional version of the Lagrange multipliers’ method. Finally, some examples arising from the applications are discussed and also numerical experiments are presented.

Solution of the Kirchhoff-Plateau Problem

The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. We establish the existence of an equilibrium shape that minimizes the total energy of the system under the physical constraint of noninterpenetration of matter, but allowing for points on the surface of the bounding loop to come into contact. In our treatment, the bounding loop retains a finite cross-sectional thickness and a nonvanishing volume, while the liquid film is represented by a set with finite two-dimensional Hausdorff measure. Moreover, the region where the liquid film touches the surface of the bounding loop is not prescribed a priori. Our mathematical results substantiate the physical relevance of the chosen model. Indeed, no matter how strong is the competition between surface tension and the elastic response of the filament, the system is always able to adjust to achieve a configuration that complies with the physical constraints encountered in experiments.

Successful coaxial double-vein graft for infrarenal aortic pseudoaneurysm due to Salmonella infection associated with hepatic resection for hepatocarcinoma

This is a case of aortic pseudoaneurysm due to Salmonella aortitis successfully treated by coaxial double-vein graft replacement (femoral vein and internal jugular vein) associated with hepatic resection for hepatocarcinoma. The aim of the technique is to improve the solidness of the vascular anastomosis and the tensile strength of the autologous vein graft, thus preventing long-term degeneration. Simultaneous hepatic resection did not affect clinical outcome. At 5-year follow-up, neither morphological alteration of the double-vein graft nor neoplastic relapse of the hepatocellular carcinoma was observed. This surgical technique could potentially improve long-term outcome and could therefore be considered a useful modification of the classic femoral vein graft for substitution of the septic infrarenal aorta when an extension to the iliac or femoral artery is not necessary.

Limb salvage in lower-extremity sarcomas and technical details about vascular reconstruction

Vascular surgery may allow limb salvage when a sarcoma of the lower limb involves the main vascular bundle. We present our experience and describe the techniques which have been employed for such surgery. From October 1995 to April 1999, vascular surgery procedures were employed in seven patients with sarcomas of the thigh: two complete subadventitia dissections of the main vascular trunks, four artery replacements (two polytetrafluoroethylene [PTFE] grafts and two autologous saphenous grafts), and five venous reconstructions (all with autogenous saphenous graft: three substitutions; two distal transpositions with one external rigid support at the anastomosis). Clinical and instrumental (sonogram, computed tomography [CT] scan, echodoppler) follow-up was carried out at 3, 6, and then every 12 months after surgery (mean, 25 months; range, 6-53 months). Operative mortality and morbidity were nil. All the grafts were patent (one arterial thrombosis was successfully treated on the first postoperative day). The functional result was good in six patients and fair in one. Two patients died, 24 and 13 months after surgery, with disseminated disease, but had no local recurrence. Five patients are alive and disease-free. Vascular techniques allow limb salvage with en-bloc resection of sarcomas of the thigh involving the main vessels. Venous reconstructions are indicated after removal of both the superficial and deep femoral veins. We suggest limiting the number of anastomoses (two transpositions in our series) and using external rigid support in those patients with a small saphenous vein graft (one patient in our series).

Suprarenal aortic cross-clamping in elective abdominal aortic aneurysm surgery

INTRODUCTION

this retrospective study was undertaken to evaluate whether suprarenal aortic cross-clamping increased the perioperative mortality and morbidity as compared to infrarenal clamping, in order to create the rationale for a more extensive application of this apparently more traumatic manoeuvre.

MATERIALS AND METHODS

in a series of 734 elective aortic substitutions for abdominal aneurysm (AA), performed consecutively from January 1992 to June 1999, aortic cross-clamping was performed at a suprarenal level in 56 juxtarenal aneurysms, i.e. aneurysms extending to the lower edge of the renal arteries (8%, Group 1), and at an infrarenal level in 634 subrenal aneurysms (92%, Group 2). When analysing preoperative data, the diameter of aneurysms was larger in Group 1 than in Group 2 (p<0. 005). No significant differences were found between the two groups as regards age, sex, postinfarction cardiomyopathy, chronic obstructive pulmonary disease, chronic renal insufficiency and ASA classification of operative risks.

RESULTS

the average time of renal exclusion in the juxtarenal aneurysms was 20 min (range 12-35 min). There is no difference between the two groups as regards the time of aortic clamping (mean 50 vs. 60 min) or the need for homologous blood transfusion (7% vs. 11% of patients). Perioperative (30 days) mortality did not differ: 3.6% vs. 1.9% (n.s.); nor did the incidence of acute myocardial infarction (3.6% vs. 2.3%). Renal function deteriorated in 8 (14%) vs. 0 (0%) (p<0.001) and 1 patient (2%) required permanent dialysis, as compared to 0% in Group 2. The incidence of ischaemic colitis was also significantly higher in Group 1 (7%) than in Group 2 (2%, p<0.01).

CONCLUSION

this data shows that suprarenal clamping, which is necessary for the radical treatment of juxtarenal aortic aneurysms, can be performed with a low risk.