Thermometry of bosonic mixtures in Optical Lattices via Demixing.

Motivated by recent experiments and theoretical investigations on binary mixtures, we investigate the miscible-immiscible transition at finite temperature by means of Quantum Monte Carlo. Based on the observation that the segregated phase is strongly affected by temperature, we propose to use the degree of demixing for thermometry of a binary bosonic mixture trapped in an optical lattice. We show that the proposed method is especially sensitive at low temperatures, of the order of the tunnelling amplitude, and therefore is particularly suitable in the regime where quantum magnetism is expected.

First-order phase transitions in optical lattices with tunable three-body onsite interaction.

We study the two-dimensional Bose-Hubbard model in the presence of a three-body interaction term, both at a mean-field level and via quantum Monte Carlo simulations. The three-body term is tuned by coupling the triply occupied states to a trapped universal trimer. We find that, for a sufficiently attractive three-body interaction, the n=2 Mott lobe disappears and the system displays first-order phase transitions separating the n=1 from the n=3 lobes and the n=1 and n=3 Mott insulator from the superfluid. We also analyze the effect of finite temperature and find that transitions are still of first order at temperatures T~J, where J is the hopping matrix element.

Quantum phases of cold polar molecules in 2D optical lattices.

We study the quantum phases of hard-core bosonic polar molecules on a two-dimensional square lattice interacting via repulsive dipole-dipole interactions. In the limit of small tunneling, we find evidence for a devil's staircase, where Mott solids appear at rational fillings of the lattice. For finite tunneling, we establish the existence of extended regions of parameters where the ground state is a supersolid, obtained by doping the solids either with particles or vacancies. We discuss the effects of finite temperature and finite-size confining potentials as relevant to experiments.

Expansion of a quantum gas released from an optical lattice.

We analyze the interference pattern produced by ultracold atoms released from an optical lattice, commonly interpreted as the momentum distributions of the trapped quantum gas. We show that for finite times of flight the resulting density distribution can, however, be significantly altered, similar to a near-field diffraction regime in optics. We illustrate our findings with a simple model and realistic quantum Monte Carlo simulations for bosonic atoms and compare the latter to experiments.

Inhibition of vascularization in tumor growth.

The transition to a vascular phase is a prerequisite for fast tumor growth. During the avascular phase, the neoplasm feeds only from the (relatively few) existing nearby blood vessels. During angiogenesis, the number of capillaries surrounding and infiltrating the tumor increases dramatically. A model which includes physical and biological mechanisms of the interactions between the tumor and vascular growth describes the avascular-vascular transition. Numerical results agree with clinical observations and predict the influence of therapies aiming to inhibit the transition.

Competition effects in the dynamics of tumor cords.

A general feature of cancer growth is the cellular competition for available nutrients. This is also the case for tumor cords, neoplasms forming cylindrical structures around blood vessels. Experimental data show that, in their avascular phase, cords grow up to a limit radius of about 100 microm, reaching a quasi-steady-state characterized by a necrotized area separating the tumor from the surrounding healthy tissue. Here we use a set of rules to formulate a model that describes how the dynamics of cord growth is controlled by the competition of tumor cells among themselves and with healthy cells for the acquisition of essential nutrients. The model takes into account the mechanical effects resulting from the interaction between the multiplying cancer cells and the surrounding tissue. We explore the influence of the relevant parameters on the tumor growth and on its final state. The model is also applied to investigate cord deformation in a region containing multiple nutrient sources and to predict the further complex growth of the tumor.

Diffusion with evolving sources and competing sinks: development of angiogenesis.

Tumors ensure their long-time growth by emitting molecular messengers that induce cellular modifications in neighboring capillaries. These modifications are conducive to the enlargement of the vascular system feeding the tumor. This phenomenon, termed angiogenesis, is controlled by the diffusion and competitive trapping of nutrients and molecular messengers by several cell species. The number, location, and properties of these traps change continuously. The angiogenic process also implies that nutrient sources are time dependent. Starting from assumptions at the cellular level, we formulate a mathematical model that predicts the evolution of angiogenesis and the increase in the blood flow to the tumor. The model also predicts the emergence of directed growth and the possibility of therapeutical synergy. Simulations permit a careful analysis of the influence of the main parameters.

Emergence of taxis and synergy in angiogenesis.

Angiogenesis, the expansion of the vascular system feeding a tumor, is crucial to both primary tumors long-time growth and for the successful implantation of metastases. We formulate a model that relates the energetic requirements of the cancer cells to the production and diffusion of an angiogenic factor and to the ensuing evolution of neighboring endothelial cells. The model yields predictions for the development of neovascularization and for the increase in the blood flow to the tumor. We show that the directed growth of the vascular net is an emergent property and that therapies targeting different stages of the angiogenic process might have a synergistic effect.

Effects of anatomical constraints on tumor growth.

Competition for available nutrients and the presence of anatomical barriers are major determinants of tumor growth in vivo. We extend a model recently proposed to simulate the growth of neoplasms in real tissues to include geometrical constraints mimicking pressure effects on the tumor surface induced by the presence of rigid or semirigid structures. Different tissues have different diffusivities for nutrients and cells. Despite the simplicity of the approach, based on a few inherently local mechanisms, the numerical results agree qualitatively with clinical data (computed tomography scans of neoplasms) for the larynx and the oral cavity.

Local interaction simulation approach for the response of the vascular system to metabolic changes of cell behavior.

The self-regulatory interactions between cells and the vascular system are mediated by signals propagating at a finite speed. In order to build up a physical model of these processes, several features, such as storing of internal energy, nonclassical nonlinear behavior, and delay and threshold effects, have to be taken into account. Considering cells as particles in different metabolic states according to their internal energy, we have developed a model based on the local interaction simulation approach. Several numerical results, in qualitative agreement with biological observations, illustrate the applicability of the model and the method to implement it.

A mathematical model for light dosimetry in photodynamic destruction of human endometrium.

We are involved in the development of photodynamic therapy (PDT) as a minimally invasive method for treating dysfunctional uterine bleeding, one of the primary clinical indications for hysterectomy. In this paper, we analyse light propagation through the uterus in order to specify the requirements for a light delivery system capable of effectively performing endometrial PDT. Our approach involves developing an analytical model based on diffusion theory to predict optical fluence rate distributions when cylindrical and spherical optical applicators are placed in the uterine cavity. We apply the results of our model calculations to estimate the thermal effects of optical irradiation and the effective photodynamic optical dose. Theoretical fluence rate calculations are compared to fluence rate measurements made in fresh, surgically removed human uteri. Our results show that a trifurcated cylindrical optical applicator inserted into the human uterus can provide a light dose that is sufficient to cause photodynamic destruction of the entire endometrium. When the optical power per unit length of each cylindrical applicator is 100 mW cm-1 (at 630 nm), a fluence rate of 40 mW cm-2 is delivered to the boundary layer between the endometrium and the myometrium (a depth of about 4-6 mm). The optical fluence delivered to the boundary layer after 20 min of exposure is 50 J cm-2, a level that is generally accepted to cause tissue damage throughout the endometrium in most patients.

A multicenter study of laparoscopic management of selected cystic adnexal masses in postmenopausal women.

BACKGROUND: The objective of this study was to determine the ability to predict benign adnexal masses in postmenopausal women and to evaluate the effectiveness of laparoscopic management in selected patients. STUDY DESIGN: Postmenopausal women found to have an adnexal mass were prospectively evaluated with clinical examination, sonography, and serum CA-125 levels. Women with cystic masses greater than 3 cm but less than 10 cm, with distinct borders, without solid parts or septations greater than 2 mm, without ascites or matted bowel, and with serum CA-125 levels less than 35 IU per mL were operated upon by laparoscopy. RESULTS: Sixty-one women gave consent for the study. Cyst size ranged from 3 to 10 cm. All masses were accurately predicted to be benign. Fifty-eight (95 percent) women were successfully managed by operative laparoscopy and three required laparotomy. For the patients managed by laparoscopy, the mean operative time was 63 minutes, the mean postoperative hospitalization period was 12 hours, and the mean return to normal activity was 5.6 days. CONCLUSIONS: The combination of clinical examination, sonographic appearance and serum CA-125 levels can accurately predict benign masses in postmenopausal women. Operative laparoscopy is acceptable for these patients and provides for a short period of hospitalization and a rapid recovery.

Management of Selected Adnexal Masses in Postmenopausal Women by Operative Laparoscopy-A Multicentered Study

With careful preoperative assessment we have selected postmenopausal women who were believed to have benign adnexal masses and who were candidates for removal of these masses via operative laparoscopy. Criteria for inclusion were: postmenopausal status; cystic adnexal mass less than 10 cm. with distinct borders and without irregular solid parts or thick septa; CA 125<35 U/ml; and no contraindications for surgery. Sixty-one women were entered into the study. All of the masses were benign, including 27 serous cysts, 15 serous cystadenomas, 1 mucinous cystadenoma, 5 serous cystadenofibromas, 6 paratubal cysts, 3 retroperitoneal cysts, and 4 chronic hydrosalpinges. Fifty-eight patients had successful pelviscopic removal of their adnexal mass. Three patients (5%) required laparotomy. For patients managed by operative laparoscopy, mean operating time was 63 minutes, mean postoperative stay was 12 hours, and mean time to return to normal activity was 5.6 days. We conclude that the combination of CA 125 values and pelvic ultrasound can successfully predict benign masses in postmenopausal women, and removal of these masses by operative laparoscopy is acceptable in carefully selected women.