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PubMed2004

An efficient atomic orbital based second-order Møller-Plesset gradient program.

Based on the orbital-invariant atomic orbital formulation of the MP2 (Møller-Plesset second-order perturbation theory) energy and gradient [P. Pulay and S. Saebø, Theor. Chim. Acta 69, 357 (1986)], we have derived and programmed detailed working equations for closed-shell MP2 gradients. The orbital-invariant form avoids the difficulties of other formulations with frozen orbitals, and allows the use of arbitrary occupied orbitals, an important consideration for local correlation theories, although the present program uses canonical molecular orbitals. The atomic orbital formulation offers savings both in storage and computer time. Test calculations on systems containing up to approximately 100 atoms and approximately 1000 basis functions, performed on a single personal computer, are reported. Parallelization of the code is underway.

Journal Article↗

PubMed2006

Fast noniterative orbital localization for large molecules.

We use Cholesky decomposition of the density matrix in atomic orbital basis to define a new set of occupied molecular orbital coefficients. Analysis of the resulting orbitals ("Cholesky molecular orbitals") demonstrates their localized character inherited from the sparsity of the density matrix. Comparison with the results of traditional iterative localization schemes shows minor differences with respect to a number of suitable measures of locality, particularly the scaling with system size of orbital pair domains used in local correlation methods. The Cholesky procedure for generating orthonormal localized orbitals is noniterative and may be made linear scaling. Although our present implementation scales cubically, the algorithm is significantly faster than any of the conventional localization schemes. In addition, since this approach does not require starting orbitals, it will be useful in local correlation treatments on top of diagonalization-free Hartree-Fock optimization algorithms.

Journal Article↗

PubMed2006

Coupled-cluster with active space selected higher amplitudes: performance of seminatural orbitals for ground and excited state calculations.

The active space approach for coupled-cluster models is generalized using the general active space concept and implemented in a string-based general coupled-cluster code. Particular attention is devoted to the choice of orbitals on which the subspace division is based. Seminatural orbitals are proposed for that purpose. These orbitals are obtained by diagonalizing only the hole-hole and particle-particle block of the one-electron density of a lower-order method. The seminatural orbitals are shown to be a good replacement for complete active space self-consistent field orbitals and avoid the ambiguities with respect to the reference determinant introduced by the latter orbitals. The seminatural orbitals also perform well in excited state calculations, including excited states with strong double excitation contributions, which usually are difficult to describe with standard coupled-cluster methods. A set of vertical excitation energies is obtained and benchmarked against full configuration interaction calculations, and alternative hierarchies of active space coupled-cluster models are proposed. As a simple application the spectroscopic constants of the C(2) B (1)Delta(g) and B(') (1)Sigma(g) (+) states are calculated using active space coupled-cluster methods and basis sets up to quadruple-zeta quality in connection with extrapolation and additivity schemes.

Journal Article↗

PubMed1981

Circulant orbitals for atoms and molecules.

Circulant orbitals varphi(n) for a closed-shell system are the orbitals obtained when the N canonical orthonormal Hartree-Fock orbitals lambda([unk]) are subjected to a unitary transformation which is the discrete Fourier transformation: varphi(n) = 1/ radicalN Sigma([unk])lambda([unk])omega((n-1)([unk]-1)), where omega = exp(2pii/N). Electron densities associated with the orbitals varphi(n) are each close to the average total electron density. The Fock matrix, diagonal for canonical orbitals, for circulant orbitals is a Hermitian circulant matrix, epsilon(m, m+q) = 1/N Sigma([unk])epsilon([unk])omega(q([unk]-1)), where the epsilon([unk]) are the canonical orbital energies. The states ;Fvarphi(n) are uniformly distributed on the surface of a sphere in Hilbert space.

Journal Article↗

PubMed1998

Leukoregulin induction of protein expression in human orbital fibroblasts: evidence for anatomical site-restricted cytokine-target cell interactions.

The molecular basis for the profound inflammatory response and the accumulation of hyaluronan in orbital connective tissues seen in thyroid-associated ophthalmopathy is unknown. Moreover, the link between the orbital manifestations of Graves' disease and those in the pretibial skin, localized dermopathy, has yet to be established. We have reported recently that leukoregulin, an activated T lymphocyte-derived cytokine, dramatically induces hyaluronan synthesis and prostaglandin-endoperoxide H synthase 2 in human orbital fibroblasts in culture. In the current studies, utilizing giant two-dimensional gel electrophoresis, we find that orbital fibroblasts express constitutively a protein profile that distinguishes them from skin fibroblasts derived from the abdominal wall and from the pretibium. We further demonstrate that leukoregulin, when present in culture medium for 16 hr, up-regulates a set of orbital fibroblast proteins not present in untreated cultures or in fibroblasts from the abdominal wall. However, some of the same protein inductions are present in the pretibial fibroblasts. These leukoregulin-induced changes in protein expression are completely blocked by dexamethasone (10 nM). Our findings are the first to identify proteins that appear to be expressed and differentially regulated in an anatomical site-restricted manner in orbital and pretibial fibroblasts and seem to establish a molecular link between fibroblasts from the orbit and those in pretibial skin.

Binding Sites↗

PubMed2000

Balanced orbital decompression in Graves' orbitopathy: Upper eyelid crease incision for extended lateral wall decompression.

INTRODUCTION. This study reports on the results and complications detected in patients with Graves' orbitopathy who underwent balanced medial and lateral wall orbital decompression through concealed incisions. MATERIALS AND METHODS. The medial and lateral orbital walls of nine consecutive patients (14 eyes) were removed. A transnasal endoscopic spheno-ethmoidectomy was performed for the medial wall decompression. A lateral wall decompression was performed via an upper eyelid crease incision which was extended laterally in a relaxed skin tension line. The lateral aspect of the orbit was sculpted with a high-speed surgical drill from the inferior orbital fissure inferiorly and frontal bone of the lacrimal fossa superiorly to the orbital apex posteriorly, including the thick bone of the greater wing of the sphenoid. RESULTS. The decompression was performed for cosmetic purposes in seven patients (10 orbits) and for exposure keratopathy and restrictive myopathy in the remaining two patients (4 orbits). The average follow-up period was 13.6 months. The mean reduction of proptosis was 4.8 mm. The preoperative diplopia in two cases demonstrating restrictive myopathy worsened during the postoperative period. New onset diplopia was not detected in seven cases operated on for cosmetic purposes. All patients were satisfied with their eye status, visual rehabilitation and cosmetic appearance. CONCLUSIONS. The transnasal endoscopic approach for medial wall and extended lateral wall decompression with hidden eyelid crease incision provides a favorable cosmetic and physiologic outcome with proper retroplacement of the globe.

Journal Article↗

PubMed1999

Primary orbital rhabdomyosarcoma in an adult.

PURPOSE. Rhabdomyosarcoma is the most common primary orbital malignant tumor in children. Though rare above the age of twenty, the authors present a case of primary orbital rhabdomyosarcoma in an adult and review the literature. DESIGN. Clinico-pathologic case report. METHODS. A 34-year-old man presented with a recurrent orbital tumor four years after initial excision. This tumor was initially misdiagnosed elsewhere as Merkel cell tumor on the basis of spurious immunohistochemical studies. Excision biopsy of the recurrent orbital mass was performed. MAIN OUTCOME MEASURES. MRI of the orbit and brain was done as well as histopathologic examination and immunohistochemistry of the excised mass. RESULTS. Histopathologic study of the excised orbital tumor revealed rhabdomyosarcoma. CONCLUSION. Careful microscopic evaluation and immunohistochemical stains are important in confirming the diagnosis of atypical cases of orbital tumors.

Journal Article↗

PubMed1996

Stability of fronto-orbital advancement in nonsyndromic bilateral coronal synostosis: a quantitative three-dimensional computed tomographic study.

Fronto-orbital dysmorphology in nonsyndromic bilateral coronal synostosis includes frontal flattening, supraorbital recession, and ocular globe protrusion. Surgical advancement of the supraorbital region ("bandeau") is performed to correct these deformities. A retrospective analysis of 10 consecutive patients with nonsyndromic bilateral coronal synostosis was performed to assess the effect of two types of bandeau fixation at the nasion. The advanced bandeau was fixed medially at the nasion with a calvarial bone graft and polyglycolic acid sutures (bone graft/suture group, five patients) or with a microplate (plate group, five patients) and bilaterally at pterion with calvarial bone grafts and polyglycolic acid sutures (all patients). The cranio-orbital dysmorphology and the surgical results were studied using pre-, peri-, and post-operative three-dimensional computed tomographic (CT) data. Reformation, manipulation, editing, and quantitative measurements of the CT data were performed on a computer workstation and Analyze imaging program. Four measurements performed to evaluate the fronto-orbital morphology: the length:width ratio of anterior cranial fossa, ventral globe index, cornea position, and supraorbital rim lag. The ventral globe index assessed the degree of eyeball protrusion out of the orbit cavity. Measurements of the cornea position and supraorbital rim lag were performed on the longitudinal orbit projections of the CT data. Six normal skull CT scans were available for same measurement and comparison. Measurements of the preoperative fronto-orbital dysmorphology in bilateral coronal synostosis were significantly different from those of normal subjects. One year after the surgery, the length:width ratio of the anterior cranial fossa was normalized in both groups. The ventral globe index was improved but not normalized in both groups, whereas the cornea position and supraorbital rim lag were improved in the bone graft/suture group but were normalized in the plate group. Based on the quantitative data, the surgical outcomes in the plate group were significantly better than those in the bone graft/suture group. Major relapse of surgical advancement in the bone graft/suture group seemed to occur in perioperative period. In summary, at 1 year postoperatively, the bandeau advancement improved but did not entirely normalize the fronto-orbital dysmorphology of nonsyndromic bilateral coronal synostosis in either group. We conclude that plate rigid fixation at the nasion provides superior stability for bandeau advancement compared with bone graft/suture fixation.

Bone Plates↗

PubMed2003

Anthropometric study of synostotic frontal plagiocephaly: before and after fronto-orbital advancement with correction of nasal angulation.

Surgical correction of synostotic frontal plagiocephaly (unilateral coronal synostosis) focuses on the asymmetry of the forehead and orbits. However, there is controversy regarding whether nasal angulation should be addressed during primary fronto-orbital advancement in infancy. This prospective study was undertaken to answer that question. Preoperative and postoperative anthropometric measurements were obtained for 19 infants with nonsyndromic synostotic frontal plagiocephaly. The measurements included nasal angulation, nasion-to-endocanthion distance, nasion-to-exocanthion distance, and exocanthion-to-tragion distance. All patients underwent bilateral parallelogrammatic fronto-orbital correction. Closing wedge nasal ostectomy was performed for group I (n = 14) and was not performed for group II (n = 5). The average age at the time of follow-up assessments was 3 years 8 months (range, 1 to 14 years) in group I and 5 years 5 months (range, 2 to 15 years) in group II. A statistically significant change was observed for patients who underwent primary correction of nasal angulation; the change correlated with improved naso-orbital symmetry, as judged with nasion-to-endocanthion and nasion-to-exocanthion measurements (p < 0.01 and p < 0.05, respectively). Group I patients exhibited an average preoperative nasal angulation of 9.15 +/- 0.8 degrees that decreased to 3.1 +/- 0.6 degrees postoperatively (p < 0.01). Group II patients exhibited an average preoperative nasal angulation of 6.4 +/- 0.7 degrees that was unchanged postoperatively at 7.2 +/- 1 degrees. The improvement in nasal angulation in group I was particularly striking because the patients in group II exhibited, on average, a lesser degree of preoperative nasal deviation (p < 0.01). This prospective comparison of fronto-orbital correction of synostotic frontal plagiocephaly with and without nasal correction confirmed an earlier study and demonstrated that angulation of the nasal pyramid does not self-correct within 5 years after traditional bilateral fronto-orbital repair. Closing wedge nasal ostectomy results in improved nasal angulation and naso-orbital symmetry, without evidence of distortion or inhibition of nasal growth.

Anthropometry↗

PubMed2000

Optimal periodic orbits of continuous time chaotic systems

In previous work [B. R. Hunt and E. Ott, Phys. Rev. Lett. 76, 2254 (1996); Phys. Rev. E 54, 328, (1996)], based on numerical experiments and analysis, it was conjectured that the optimal orbit selected from all possible orbits on a chaotic attractor is "typically" a periodic orbit of low period. By an optimal orbit we mean the orbit that yields the largest value of a time average of a given smooth "performance" function of the system state. Thus optimality is defined with respect to the given performance function. (The study of optimal orbits is of interest in at least three contexts: controlling chaos, embedding of low-dimensional attractors of high-dimensional dynamical systems in low-dimensional measurement spaces, and bubbling bifurcations of synchronized chaotic systems.) Here we extend this previous work. In particular, the previous work was for discrete time dynamical systems, and here we shall consider continuous time systems (flows). An essential difference for flows is that chaotic attractors can have embedded within them, not only unstable periodic orbits, but also unstable steady states, and we find that optimality can often occur on steady states. We also shed further light on the sense in which optimality is "typically" achieved at low period. In particular, we find that, as a system parameter is tuned to be closer to a crisis of the chaotic attractor, optimality may occur at higher period.

Journal Article↗

PubMed2001

Ordered valence-bond states in symmetric two-dimensional spin-orbital systems.

We consider a superexchange Hamiltonian, H = -SUM ( )(2S(i) . S(j)-(1/2)) (2T(i) . T(j)-(1/2)), which describes systems with orbital degeneracy and strong electron-phonon coupling in the limit of large on-site repulsion. In an SU(4) Schwinger boson representation, a reduced spin-orbital interaction is derived exactly, and a mean field theory has been developed. In one dimension, a spin-orbital liquid state with a finite gap is obtained. On a two-dimensional square lattice a novel type of spin-orbital ferromagnetically ordered state appears, while spin and orbital are antiferromagnetic. An important relation has been found, relating the spin and orbital correlation functions to the combined spin-orbital ones.

Journal Article↗

PubMed2006

Injectable self inflating hydrogel pellet expanders for the treatment of orbital volume deficiency in congenital microphthalmos: preliminary results with a new therapeutic approach.

BACKGROUND/AIM: Children with congenital microphthalmos are usually able to wear an eye prosthesis but the cosmetic aspect is determined by the size of the orbital volume deficiency. Instead of using a ball shaped standard hydrogel expander or a regular orbital implant, which would necessitate enucleation of the microphthalmic eye, this study investigates the feasibility of volume augmentation with injectable pellet expanders, as formerly suggested for acquired anophthalmos in adults only. METHOD: The pellet expander is made from a self inflating hydrogel that takes up water by osmosis (dry state: length 8 mm, diameter 2 mm, volume 0.025 ml; in vitro hydrated state after around 1 day: length 15 mm, diameter 4 mm, volume 0.24 ml; swelling capacity: 9.6-fold). This report concerns six patients (two girls and four boys) aged between 4 months and 42 months with unilateral microphthalmos who were treated by injection of 4-14 pellet expanders into the retrobulbar orbital tissue. Volume augmentation was 1-3.5 ml. The pellets were injected using a customised trocar and placed behind the microphthalmos directed into the intraconal space. RESULTS: The increasing orbital volume was noticeable within 2 days and was confirmed by ultrasonography and magnetic resonance imaging. The final result can be anticipated by the volume augmentation effect produced by the amount of saline solution injected in the orbital apex region. All patients were fitted with an artificial eye, which was subsequently enlarged every 3-5 months. Anophthalmic enophthalmos was fully compensated with this technique. No complications have been encountered to date. CONCLUSIONS: Orbital volume augmentation with injectable self inflating hydrogel expander pellets is apparently a safe, quick, and minimally invasive technique for various indications in orbital reconstructive surgery-for example, to treat an enophthalmic appearance in microphthalmos and congenital or acquired anophthalmos.

Child, Preschool↗

PubMed1984

A specific IgG in Graves' ophthalmopathy and its relation to retro-orbital and thyroid autoimmunity.

An IgG (ophthalmopathic immunoglobulin) that binds to retro-orbital antigen was identified in serum from patients with active Graves' ophthalmopathy, and its nature and specificity were investigated. Dose related binding of this immunoglobulin to retro-orbital antigens prepared from guinea pig harderian gland or porcine eye muscle was found, which could be abolished by prior incubation with antigen. The immunoglobulin did not bind to thyroid membranes, thyroid microsomes, or thyroglobulin or interact with liver, skeletal muscle, or fat membranes. Serum with high activity of thyrotrophin binding inhibiting immunoglobulin did not react with retro-orbital antigen, and this activity was not affected by preincubation of the serum with retro-orbital antigen. Thyroid stimulating hormone was also without effect on retro-orbital antigen. It is concluded that Graves' ophthalmopathy is associated with a specific ophthalmopathic immunoglobulin that reacts with retro-orbital antigen as distinct from thyroid antigens, and that the autoimmune response is directed towards retro-orbital antigens. This suggests that the ophthalmopathy is an entity distinct from autoimmune thyroid disease.

Adult↗

PubMed2004

Myosin light chain 1 isoforms in slow fibers from global and orbital layers of canine rectus muscles.

PURPOSE: Initial results of an examination of the low molecular mass (< or =45 kDa) protein composition of canine rectus muscle homogenates, based on gel electrophoresis, revealed a distinct difference between the global and orbital layers in the myosin light chain (MLC)-1 region. The objectives of the present study were, therefore, to identify isoforms of MLC1 in homogenates of the global and orbital layers of adult canine rectus muscles and to determine the MLC1 isoform expression pattern among single muscle fibers isolated from both layers. METHODS: Muscle homogenates and single fibers from the global and orbital layers of canine rectus muscles were analyzed, using sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE). Matrix-assisted laser desorption/ionization-time-of-flight mass spectrometry (MALDI-TOF-MS) was used to identify a protein band in the orbital layer that comigrated with MLC1 in the adult canine atrium. RESULTS: Adult canine extraocular rectus muscles expressed embryonic skeletal/atrial MLC1 (MLC1(E/A)), in addition to the fast-type MLC1 (MLC1F) and slow-type MLC1 (MLC1S) isoforms expressed in limb skeletal muscles. MLC1(E/A) was detected in slow fibers of the orbital but not the global layer, and MLC1S was detected in slow fibers in only the global but not the orbital layer. Densitometric analysis of gel bands from homogenates supported these results, with significantly greater amounts of MLC1S in the global layer and of MLC1(E/A) in the orbital layer. CONCLUSIONS: MLC1(E/A) is expressed in rectus muscles of adult dogs. Furthermore, two types of slow fibers, distinguished on the basis of MLC1 isoform expression, exist in separate layers of canine rectus muscles.

Animals↗

PubMed2004

Accessibility, stabilizability, and feedback control of continuous orbital transfer.

This paper investigates the problem of low-thrust orbital transfer using orbital element feedback from a control-theoretic standpoint, concepts of controllability, feedback stabilizability, and their interaction. The Gauss variational equations (GVEs) are used to model the state-space dynamics. First, the notion of accessibility, a weaker form of controllability, is presented. It is then shown that the GVEs are globally accessible. Based on the accessibility result, a nonlinear feedback controller is derived that asymptotically steers a vehicle from an initial elliptic Keplerian orbit to any given elliptic Keplerian orbit. The performance of the new controller is illustrated by simulating an orbital transfer between two geosynchronous Earth orbits. It is shown that the low-thrust controller requires less fuel than an impulsive maneuver for the same transfer time. Closed-form, analytic expressions for the new orbital transfer controller are given. Finally, it is proved, based on a topological nonlinear stabilizability test, that there does not exist a continuous closed-loop controller that can transfer a spacecraft to a parabolic escape trajectory.

Journal Article↗

PubMed2004

Classification of periodic orbits in the four- and five-body problems.

The research described in this paper was motivated by the new types of periodic solutions that were recently discovered by Moore, Chenciner, Montgomery, and Simo in the three-body and the N-body problem (with large N). We attempt to classify the various types of periodic orbits, in the inertial frame, on the basis of an extensive numerical exploration. We have started an exploration of the four-body problem, where the classification of types of periodic orbits is more involved. We immediately found those orbits with symmetry with respect to the x-axis, the y-axis, or both. Complete quadruple interplay, or a triple system around a single mass is possible. Finally, what seems to be the most frequent, two binary systems in orbit around the general center of mass. However, the last group can be separated into several subgroups. We have, for instance, the case of two masses on one orbit and the two other masses on another orbit. This is again a partial choreography. We then have the case of double binary choreographies: two binary systems in which all four masses travel on one single curve. To realize this situation, a certain commensurability is needed between the overall period and the period of each binary system. The binary system makes an odd integer number, q, of revolutions during a general period. We computed many cases from q = 5 to 97. This indicates that we have a discrete infinity of choreographies. The choreography q = 5 is an especially remarkable star-shaped curve. Actually, we have two such infinite families, one with corotational and the other with contrarotational motions. We show that they can be justified by simple Keplerian approximations. Finally, we mention that our work depends heavily on the existence of symmetries. They simplify the algorithms for finding periodic orbits and they play an important role in the classification. In the four-body problem with equal masses, we have five different types of symmetries. In addition to the well-known collinear symmetry, we also found what we call double isosceles and trapezoidal symmetries. All our four-body choreographies satisfy these two symmetry conditions. In the five-body problem, we limit our work to two symmetry cases. We show that in Gerver's super-eight choreography, we are allowed to place a fifth mass at the center and we may speak about a larger sun with four smaller but equal planets that are in a choreography.

Journal Article↗

PubMed2005

Earth-to-Moon low energy transfers targeting L1 hyperbolic transit orbits.

In the frame of the lunar exploration, numerous future space missions will require maximization of payload mass, and simultaneously achieving reasonable transfer times. To fulfill this request, low energy non-Keplerian orbits could be used to reach the Moon instead of high energetic transfers. The low energy solutions can be separated into two main categories depending on the nature of the trajectory approaching the Moon: low energy transit orbits that approach the Moon from the interior equilibrium point L(1) and weak stability boundary transfers that reach the Moon after passing through L(2). This paper proposes an alternative way to exploit the opportunities offered by L(1) transit orbits for the design of Earth-Moon transfers. First, in a neighborhood of the L(1) point, the three-body dynamics is linearized and written in normal form; then the entire family of nonlinear transit orbits is obtained by selecting the appropriate nontrivial amplitudes associated with the hyperbolic part. The L(1)-Earth arc is close to a 5:2 resonant orbit with the Moon, whose perturbations cause the apogee to rise. In a second step, two selected low altitude parking orbits around the Earth and the Moon are linked with the transit orbit by means of two three-body Lambert arcs, solutions of two two-point boundary value problems. The resulting Earth-to-Moon trajectories prove to be very efficient in the Moon captured arc and save approximately 100 m/sec in Deltav cost when compared to the Hohmann transfer. Furthermore, such solutions demonstrate that Moon capture could be obtained in the frame of the Earth-Moon R3BP neglecting the presence of the Sun.

Journal Article↗

PubMed2000

Orbital sinus blood sampling in rats: effects upon selected behavioural variables.

The question addressed was whether the behaviour of rats is changed after orbital sinus blood sampling while they are under diethyl-ether anaesthesia. Twelve rats were subjected to sham anaesthesia, diethyl-ether anaesthesia and anaesthesia plus orbital puncture according to a Latin square. After each treatment, the behaviour of the rats was automatically monitored using the so-called LABORAS method, which discriminates between grooming, locomotion and inactivity. Treatment ended, and behaviour monitoring began, when the light period changed over to the dark period. The various behaviours were quantified as relative duration and frequency. Anaesthesia versus sham anaesthesia reduced the relative duration of grooming during the first 5 h after treatment. Anaesthesia plus orbital puncture versus anaesthesia alone did not significantly influence grooming, but orbital puncture did reduce the relative duration and the frequency of locomotion during the entire 20 h period, which was mainly due to a decrease in the dark period. After orbital puncture, the animals were also less frequently inactive. It is concluded that orbital puncture has an effect on behaviour superimposed on that of diethyl-ether anaesthesia. This observation may contribute new arguments to the debate on the acceptability of the orbital puncture technique.

Anesthesia↗