Association between BMI Change, Transaminases, and Other Metabolic Parameters in Children with Nonalcoholic Fatty Liver Disease.

Background: Weight loss and lifestyle interventions are the mainstay of treatment in pediatric NAFLD. There are gaps in the literature on the objective improvement in BMI to meaningfully impact NAFLD in children. Aim: To determine the decrease in BMI associated with a significant decline in ALT and other metabolic parameters. Methods: Retrospective chart review of pediatric patients with the diagnosis of NAFLD. Data were collected at the baseline and 6 and 12 months. A linear regression model was used to assess the percent change in BMI predictive of change in ALT and other metabolic parameters. Results: 281 charts were included. 71% of patients who had up to a 2.5% loss in BMI at 6 months had a decrease in ALT of up to 10 U/L compared to 43% patients who did not have a decrease in BMI up to 2.5% loss at the same time period (P=0.01). The linear regression model showed that 6-month and 12-month percent changes in BMI are predictive of 6-month and 12-month ALT changes (P=0.01 and 0.02), respectively. ALT normalization was achieved on 12% of patients with a ≥2.5% decrease in BMI at 6 months compared to 1% of patients that had no decrease of ≥2.5% decrease in BMI at 6 months (P=0.01). The mean BMI Z-score decline was 0.18 (P=0.001) in the group with a ≥2.5% decrease in BMI at 6 months. Conclusions: BMI loss of up to 2.5% and the mean BMI Z-score 0.18 are associated with a significant decrease in ALT of up to 10 U/L. BMI percent change at 6 months and 12 months is predictive of changes in ALT. These results should help guide providers in clinical practice set objective goals for the management of children with NAFLD resulting from obesity.

Unpredictable tunneling in a retarded bistable potential.

We have studied the rich dynamics of a damped particle inside an external double-well potential under the influence of state-dependent time-delayed feedback. In certain regions of the parameter space, we observe multistability with the existence of two different attractors (limit cycle or strange attractor) with well separated mean Lyapunov energies forming a two-level system. Bifurcation analysis reveals that, as the effects of the time-delay feedback are enhanced, chaotic transitions emerge between the two wells of the double-well potential for the attractor corresponding to the fundamental energy level. By computing the residence time distributions and the scaling laws near the onset of chaotic transitions, we rationalize this apparent tunneling-like effect in terms of the crisis-induced intermittency phenomenon. Further, we investigate the first passage times in this regime and observe the appearance of a Cantor-like fractal set in the initial history space, a characteristic feature of hyperbolic chaotic scattering. The non-integer value of the uncertainty dimension indicates that the residence time inside each well is unpredictable. Finally, we demonstrate the robustness of this tunneling intermittency as a function of the memory parameter by calculating the largest Lyapunov exponent.

Recurrent Gastrointestinal Bleed Due to Small Bowel Vascular Malformation in a Patient with Turner Syndrome Diagnosed with Surgically Assisted Push Enteroscopy.

BACKGROUND Obscure gastrointestinal bleeding accounts for approximately 5% of all cases of gastrointestinal bleeding and the most frequent site is the small bowel. Turner syndrome (TS) is a genetic disorder of the second X chromosome in females. The association between gastrointestinal vascular malformations and Turner syndrome has been described in some case reports. Vascular malformation in Turner's syndrome can vary from asymptomatic to severe recurrent GI bleeds, but data on diagnosis and management of these patients are lacking. CASE REPORT A 14-year-old girl with TS presented with recurrent symptomatic melena. The initial work-up included a negative upper endoscopy, negative bidirectional endoscopies, and a video capsule endoscopy (VCE) that demonstrated large amount of blood and small erythematous lesion in the small bowel without active bleeding, and a negative Meckel scan. CT angiography was remarkable for prominent left lower mesenteric blood vessels, and a single-balloon enteroscopy demonstrated prominent vasculature throughout the small bowel. A a clip was placed at the site of a questionable bleed. The patient underwent a surgically assisted push enteroscopy due to recurrent bleeding; findings were consistent with diffuse vascular malformations. She was started on tranexamic acid and later transitioned to estrogen therapy without further reports of GI bleeding, anemia, or adverse effects from treatment 6 months after initial presentation. CONCLUSIONS Small bowel bleeding can be life-threating, and evidence-based guidelines in children are needed. Turner syndrome is associated with gastrointestinal vascular malformations, and suspicion for this diagnosis should be high for these patients when presenting with gastrointestinal bleeding. Estrogen might be an effective therapy in TS adolescent patients in the setting of diffuse vascular malformations (DVM).

Average conservative chaos in quantum dusty plasmas.

We consider a hydrodynamic model of a quantum dusty plasma. We prove mathematically that the resulting dust ion-acoustic plasma waves present the property of being conservative on average. Furthermore, we test this property numerically, confirming its validity. Using standard techniques from the study of dynamical systems, as, for example, the Lyapunov characteristic exponents, we investigate the chaotic dynamics of the plasma and show numerically its existence for a wide range of parameter values. Finally, we illustrate how chaotic dynamics organizes in the parameter space for fixed values of the initial conditions, as the Mach number and the quantum diffraction parameter are continuously varied.

The dose-dense principle in chemotherapy.

Chemotherapy is a cancer treatment modality that uses drugs to kill tumor cells. A typical chemotherapeutic protocol consists of several drugs delivered in cycles of three weeks. We present mathematical analyses demonstrating the existence of a maximum time between cycles of chemotherapy for a protocol to be effective. A mathematical equation is derived, which relates such a maximum time with the variables that govern the kinetics of the tumor and those characterizing the chemotherapeutic treatment. Our results suggest that there are compelling arguments supporting the use of dose-dense protocols. Finally, we discuss the limitations of these protocols and suggest an alternative.

Dynamics of the cell-mediated immune response to tumour growth.

Using a hybrid cellular automaton, we investigate the transient and asymptotic dynamics of the cell-mediated immune response to tumour growth. We analyse the correspondence between this dynamics and the three phases of the theory of immunoedition: elimination, equilibrium and escape. Our results demonstrate that the immune system can keep a tumour dormant for long periods of time, but that this dormancy is based on a frail equilibrium between the mechanisms that spur the immune response and the growth of the tumour. Thus, we question the capacity of the cell-mediated immune response to sustain long periods of dormancy, as those appearing in recurrent disease. We suggest that its role might be rather to synergize with other types of tumour dormancy.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.

Decay Dynamics of Tumors.

The fractional cell kill is a mathematical expression describing the rate at which a certain population of cells is reduced to a fraction of itself. We investigate the mathematical function that governs the rate at which a solid tumor is lysed by a cell population of cytotoxic lymphocytes. We do it in the context of enzyme kinetics, using geometrical and analytical arguments. We derive the equations governing the decay of a tumor in the limit in which it is plainly surrounded by immune cells. A cellular automaton is used to test such decay, confirming its validity. Finally, we introduce a modification in the fractional cell kill so that the expected dynamics is attained in the mentioned limit. We also discuss the potential of this new function for non-solid and solid tumors which are infiltrated with lymphocytes.

A validated mathematical model of tumor growth including tumor-host interaction, cell-mediated immune response and chemotherapy.

We consider a dynamical model of cancer growth including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. The tumor-immune and the tumor-host interactions are characterized to reproduce experimental results. A thorough dynamical analysis of the model is carried out, showing its capability to explain theoretical and empirical knowledge about tumor development. A chemotherapy treatment reproducing different experiments is also introduced. We believe that this simple model can serve as a foundation for the development of more complicated and specific cancer models.

Avoiding healthy cells extinction in a cancer model.

We consider a dynamical model of cancer growth including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. For certain parameter choice, the dynamical system displays chaotic motion and by decreasing the response of the immune system to the tumor cells, a boundary crisis leading to transient chaotic dynamics is observed. This means that the system behaves chaotically for a finite amount of time until the unavoidable extinction of the healthy and immune cell populations occurs. Our main goal here is to apply a control method to avoid extinction. For that purpose, we apply the partial control method, which aims to control transient chaotic dynamics in the presence of external disturbances. As a result, we have succeeded to avoid the uncontrolled growth of tumor cells and the extinction of healthy tissue. The possibility of using this method compared to the frequently used therapies is discussed.

Effective suppressibility of chaos.

Suppression of chaos is a relevant phenomenon that can take place in nonlinear dynamical systems when a parameter is varied. Here, we investigate the possibilities of effectively suppressing the chaotic motion of a dynamical system by a specific time independent variation of a parameter of our system. In realistic situations, we need to be very careful with the experimental conditions and the accuracy of the parameter measurements. We define the suppressibility, a new measure taking values in the parameter space, that allows us to detect which chaotic motions can be suppressed, what possible new choices of the parameter guarantee their suppression, and how small the parameter variations from the initial chaotic state to the final periodic one are. We apply this measure to a Duffing oscillator and a system consisting on ten globally coupled Hénon maps. We offer as our main result tool sets that can be used as guides to suppress chaotic dynamics.