Biological invasion with a porous medium type diffusion in a heterogeneous space.

The knowledge of traveling wave solutions is the main tool in the study of wave propagation. However, in a spatially heterogeneous environment, traveling wave solutions do not exist, and a different approach is needed. In this paper, we study the generation and the propagation of hyperbolic scale singular limits of a KPP-type reaction-diffusion equation when the carrying capacity is spatially heterogeneous and the diffusion is of a porous medium equation type. We show that the interface propagation speed varies according to the carrying capacity.

Nonlinear Diffusion for Bacterial Traveling Wave Phenomenon.

The bacterial traveling waves observed in experiments are of pulse type which is different from the monotone traveling waves of the Fisher-KPP equation. For this reason, the Keller-Segel equations are widely used for bacterial waves. Note that the Keller-Segel equations do not contain the population dynamics of bacteria, but the population of bacteria multiplies and plays a crucial role in wave propagation. In this paper, we consider the singular limits of a linear system with active and inactive cells together with bacterial population dynamics. Eventually, we see that if there are no chemotactic dynamics in the system, we only obtain a monotone traveling wave. This is evidence that chemotaxis dynamics are needed even if population growth is included in the system.

On the modelling of spatially heterogeneous nonlocal diffusion: deciding factors and preferential position of individuals.

We develop general heterogeneous nonlocal diffusion models and investigate their connection to local diffusion models by taking a singular limit of focusing kernels. We reveal the link between the two groups of diffusion equations which include both spatial heterogeneity and anisotropy. In particular, we introduce the notion of deciding factors which single out a nonlocal diffusion model and typically consist of the total jump rate and the average jump length. In this framework, we also discuss the dependence of the profile of the steady state solutions on these deciding factors, thus shedding light on the preferential position of individuals.

Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit.

We rigorously prove the passage from a Lotka-Volterra reaction-diffusion system towards a cross-diffusion system at the fast reaction limit. The system models a competition of two species, where one species has a more diverse diet than the other. The resulting limit gives a cross-diffusion system of a starvation driven type. We investigate the linear stability of homogeneous equilibria of those systems and rule out the possibility of cross-diffusion induced instability (Turing instability). Numerical simulations are included which are compatible with the theoretical results.

Dose-Dependent Cytotoxicity of Gold Nanoparticles on Human Neural Progenitor Cells and Rat Brain.

Gold nanoparticles (GNPs) are utilized as diagnostic and therapeutic tools to detect and treat human disease. Researchers in the field of nanotoxicity are working to determine the physicochemical properties of nanoparticles that lead to toxicity in an effort to establish safe design rules. In this study, we performed the MTT and terminal transferase dUTP nick end labeling (TUNEL) assays to verify the cytotoxicity of GNPs on rat brain tissue and human neural progenitor cells (NPCs). As results, we observed that GNPs induced apoptosis in NPCs. NPCs were markedly damaged following the administration of 200 µM and 2 mM GNPs, whereas 2 µM GNPs showed slightly increased damage relative to that of the control. In addition, TUNEL-positive cells were densely distributed at regions surrounding the GNP injection site in the brain 7 days after the GNPs injection. During long-term GNPs exposure, TUNEL-positive cells were rarely observed in the cerebral cortex. In this study, we observed that apoptosis increased in proportion to GNP concentrations in the brain and in cultivated NPCs. These result suggest that large GNPs (<100 nm) are toxic and that the cytotoxicity increased as the concentration of GNPs increased in NPCs or in the brain.

Predictive formula of ideal lumbar lordosis and lower lumbar lordosis determined by individual pelvic incidence in asymptomatic elderly population.

PURPOSE: This study aimed to obtain reference values of lumbar lordosis (LL) and lower LL (LLL) from normal asymptomatic groups, determine the relationship between them and pelvic incidence (PI), and establish the predictive formula for ideal LLL in the elderly Korean population. METHODS: Standing plain lateral radiographs of the whole spine, including the pelvis, were analyzed in asymptomatic adult male volunteers without back pain or prior surgery involving the spine or lower extremity. Volunteers with scoliosis, spondylolisthesis, segmental disk space narrowing, and/or compression fractures in the radiographs were excluded. The following parameters were measured: LL, LLL, and pelvic parameters including PI. The values of PI-LL and PI-LLL were calculated, and the formula using stepwise multiple regression analysis was made. A P value of < 0.05 was considered statistically significant. RESULTS: The study participants included 150 volunteers. All were male participants with an average age of 64.1 ± 6.4. The average value of height, weight, and body mass index was 167.0 ± 5.5 cm, 67.3 ± 9.8 kg, and 24.1 ± 3.1 kg/m2, respectively. The average LL was - 57.5° ± 9.0°, LLL was - 41.7° ± 7.0°, and PI was 48.6° ± 8.6°. The formula was established as follows: PI-LL = 0.38 × PI - 27.61 (R2 = 0.172), PI-LLL = 0.77 × PI - 28.69 (R2 = 0.516), ideal LL = 0.62 × PI + 27.61 (R2 = 0.348), and ideal LLL = 0.225 × PI + 28.63 (R2 = 0.083). CONCLUSIONS: The ideal values of PI-LL and PI-LLL were inconsistent, and they have a positive correlation with PI in asymptomatic elderly population. Our data would be helpful as a normal reference value of ideal LL and LLL according to PI. These slides can be retrieved under Electronic Supplementary Material.

Predator-prey equations with constant harvesting and planting.

We propose Lotka-Volterra type predator-prey equations which include small constant terms. Depending on its sign, the constant may model various things. To see the effect of the constants clearly we drop all other functional responses except the ones in the original Lotka-Volterra equations. We add a small negative constant for the harvesting or the Allee effect. A positive constant is added to model the planting or external influx. We find the predator-prey equations with constant terms produce most of dynamic and static patterns observed from other predator-prey models with various functional responses.

Dispersal towards food: the singular limit of an Allen-Cahn equation.

The effect of dispersal under heterogeneous environment is studied in terms of the singular limit of an Allen-Cahn equation. Since biological organisms often slow down their dispersal if food is abundant, a food metric diffusion is taken to include such a phenomenon. The migration effect of the problem is approximated by a mean curvature flow after taking the singular limit which now includes an advection term produced by the spatial heterogeneity of food distribution. It is shown that the interface moves towards a local maximum of the food distribution. In other words, the dispersal taken in the paper is not a trivialization process anymore, but an aggregation one towards food.

A Discrete Velocity Kinetic Model with Food Metric: Chemotaxis Traveling Waves.

We introduce a mesoscopic scale chemotaxis model for traveling wave phenomena which is induced by food metric. The organisms of this simplified kinetic model have two discrete velocity modes, [Formula: see text] and a constant tumbling rate. The main feature of the model is that the speed of organisms is constant [Formula: see text] with respect to the food metric, not the Euclidean metric. The uniqueness and the existence of the traveling wave solution of the model are obtained. Unlike the classical logarithmic model case there exist traveling waves under super-linear consumption rates and infinite population pulse-type traveling waves are obtained. Numerical simulations are also provided.

Halo-gravity traction in the treatment of severe spinal deformity: a systematic review and meta-analysis.

PURPOSE: Halo-gravity traction has been reported to successfully assist in managing severe spinal deformity. This is a systematic review of all studies on halo-gravity traction in the treatment of spinal deformity to provide information for clinical practice. METHODS: A comprehensive search was conducted for articles on halo-gravity traction in the treatment of spinal deformity according to the PRISMA guidelines. Appropriate studies would be included and analyzed. Preoperative correction rate of spinal deformity, change of pulmonary function and prevalence of complications were the main measurements. RESULTS: Sixteen studies, a total of 351 patients, were included in this review. Generally, the initial Cobb angle was 101.1° in the coronal plane and 80.5° in the sagittal plane, and it was corrected to 49.4° and 56.0° after final spinal fusion. The preoperative correction due to traction alone was 24.1 and 19.3%, respectively. With traction, the flexibility improved 6.1% but postoperatively the patients did not have better correction. Less aggressive procedures and improved pulmonary function were observed in patients with traction. The prevalence of traction-related complications was 22% and three cases of neurologic complication related to traction were noted. The prevalence of total complications related to surgery was 32% and that of neurologic complications was 1%. CONCLUSION: Partial correction could be achieved preoperatively with halo-gravity traction, and it may help decrease aggressive procedures, improve preoperative pulmonary function, and reduce neurologic complications. However, traction could not increase preoperative flexibility or final correction. Traction-related complications, although usually not severe, were not rare.

Sagittal spinal alignment in asymptomatic patients over 30 years old in the Korean population.

BACKGROUND: We aim to provide sagittal and pelvic parameters according to different age groups in an asymptomatic population all over 30 years old and to investigate the possible causes of changes in these parameters. METHODS: Whole-spine, standing lateral radiographs were taken in 128 asymptomatic Korean people over 30 years old. The spinal parameters (the total thoracic kyphosis (TTK), maximal lumbar lordosis (MLL), total lumbar lordosis (TLL), lower lumbar lordosis (LLL), thoracolumbar junctional angle (TLJA), and lumbar inclination (LI)), pelvic parameters (pelvic incidence (PI), sacral slope (SS), and pelvic tilt (PT)), and spinal balance parameters (spinal balance, sacropelvic balance, and spinopelvic balance) were measured. The body mass index, body protein mass, waist line, skeletal muscle mass, and body fat mass were also measured for potential causes. RESULTS: TTK and TLJA were significantly increased in the group over 70 years of age compared to the other age groups (p = 0.0002, <0.001). TLL was significantly decreased in the group over 70 years of age (p = 0.002), whereas the PI values were similar to PI even in over 70-year age group. LLL did not differ in the group over 70 years of age (p = 0.29), gradually increasing with an increase in age. SS was significantly decreased and PT was significantly increased in the group over 70 years of age as compared to the other age groups (p = 0.049, 0.049, respectively). PI was similar in all age groups (p = 0.75). Spinal balance was significantly decreased in the group over 70 years of age (p = <0.0001). PT was significantly associated with body protein mass and skeletal muscle mass (p = 0.01, 0.001, respectively). Body protein mass and skeletal muscle mass were significantly lower in the group over 70 years of age (p = 0.02, 0.02) and were possible causes. CONCLUSIONS: Several sagittal and pelvic parameters are different in asymptomatic adults over 70 years of age. Decreased body protein mass and skeletal muscle mass are possible causes of these changes.

Evolution of Dispersal with Starvation Measure and Coexistence.

Many biological species increase their dispersal rate if starvation starts. To model such a behavior, we need to understand how organisms measure starvation and response to it. In this paper, we compare three different ways of measuring starvation by applying them to starvation-driven diffusion. The evolutional selection and coexistence of such starvation measures are studied within the context of Lotka-Volterra-type competition model of two species. We will see that, if species have different starvation measures and different motility functions, both the coexistence and selection are possible.

Posterior vertebral column resection in spinal deformity: a systematic review.

PURPOSE: This study aimed to assess the amount of correction and risk of complications of posterior vertebral column resection (PVCR) in the treatment of spinal deformity. METHODS: A comprehensive research was conducted in MEDLINE, EMBASE and Cochrane Database of Systematic Reviews for published articles about PVCR in spinal deformity. Data from these included studies were pooled with the help of the Review Manager software from the Cochrane Collaboration and the R software. The amount of correction of PVCR was indicated with change of coronal and sagittal Cobb angle after operation. Risk of complications was demonstrated with prevalence. RESULTS: 7 studies, a total of 390 patients, were included for analysis. The average operative time for PVCR was 430 min and the estimated blood loss was 2,639 ml. The mean amount of correction by PVCR was 64.1° in scoliosis and 58.9° in kyphosis, accounting a correction rate of 61.2 and 63.1 %, respectively. As to coronal and sagittal imbalance, data were limited. The overall prevalence of complications of PVCR was 32 % (95 % CI 12-54 %). The most common was neurologic complications, estimated to be 8 % (95 % CI 2-16 %). And risk of spinal cord injury was 2 % (95 % CI 0-3 %). The revision rate was 6 % (95 % CI 1-13 %). Incidence of infection was pooled to be 2 % (95 % CI 1-4 %). Complication rate related with implant was 2 % (95 % CI 0-6 %). CONCLUSION: PVCR is a powerful surgical procedure for severe spinal deformity. However, it has the risk of excessive blood loss and major complications. Decision of PVCR should be prudent and the procedure should be performed by an experienced surgical team.

Modified iliac screw fixation: technique and clinical application.

BACKGROUND: A conventional iliac bolt and the S2 alar iliac screw fixation technique (S2AI) are commonly used sacropelvic fixation techniques. However, conventional iliac bolt technique requires a lateral connector and commonly has prominent screw head problems. S2AI reportedly has a high instrument failure rate. We aim to introduce a modified iliac screw fixation technique and to investigate its clinical application in adult patients. METHODS: The entrance site of the modified iliac screw fixation technique was 1 cm medial and 1 cm caudal from the posterosuperior iliac spine. From 2009 to 2015, ten adult patients underwent sacropelvic fixation with the modified iliac screw fixation technique in our spine clinic. A minimum 12-month clinical and radiographic follow-up was adopted. The mean follow-up period was 30.7 months (12-74 months). Mean number of fixation levels was 7.7 segments (5-10 segments). RESULTS: Postoperatively, the C7 plumb line (SVA) was significantly decreased (P = 0.04). Upon the last X-ray, SVA did not differ between postoperative and the last X-ray (P = 0.1). There was no breakage during our follow-up period. There was no prominent screw head. There were no cases requiring implant removal. CONCLUSIONS: The modified iliac screw fixation technique does not cause prominence in the sacral region, and does not require a lateral connector, both of which are necessary when using the classical iliac bolt technique. This technique also avoids the acute angle between the screw head and the shaft of the screw commonly seen in S2AI. The modified iliac screw fixation technique can be an effective alternative for sacropelvic fixation.

Cytotoxicity of Gold Nanorods and Nanowires on Cultivated Neural Precursor Cells.

Given the emergence of nanotherapeutics and nanodiagnostics as key tools in today's medicine, it has become of critical importance to define the interactions of nanomaterials with biological systems. The biomedical applications of nanoparticles (NPs) in chemical sensing, biological imaging, drug delivery, photothermal therapy and cancer treatment have been demonstrated. Gold NPs as new biomedical tools are the focus of research due to their ease of synthesis, chemical stability and unique optical properties. Therefore, there is a need to establish the toxicity, side effects and safety of gold NPs for human applications. To study the in vitro cytotoxicity of gold NPs, we performed MTT assay using two types of gold NPs such as gold nanorods (GNRs) and gold nanowires (GNWs). The percentage cytotoxicity of damaged neural precursor cells (NPCs) that were treated with 100 mg GNRs was 97.5±3.9%; and proportion of damaged NPCs following the administration of the same dose of GNWs was 98.8±0.3%. The cytotoxicity of 10 mg GNRs in NPCs was 54.4±8.3%, whereas it was 98.7±0.6% for the same dose of GNWs. Then, to verify that gold NPs induced apoptotic cell death in NPCs, the LIVE/DEAD Viability/Cytotoxicity assay was performed. We observed that cell death of NPCs increased with an increase in quantity of both types of gold NPs. Cell viability assessed the overall dose-dependent toxicity of NPs in cultured cells. As the results suggest, this study demonstrated that treatment with gold NPs resulted in cellular toxicity in a dose-dependent manner in cultured NPCs.

Bacterial chemotaxis without gradient-sensing.

Chemotaxis models are based on spatial or temporal gradient measurements by individual organisms. The key contribution of Keller and Segel (J Theor Biol 30:225-234, 1971a; J Theor Biol 30:235-248, 1971b) is showing that erratic measurements of individuals may result in an accurate chemotaxis phenomenon as a group. In this paper we provide another option to understand chemotactic behavior when individuals do not sense the gradient of chemical concentration by any means. We show that, if individuals increase their dispersal rate to find food when there is not enough food, an accurate chemotactic behavior may be obtained without sensing the gradient. Such a dispersal has been suggested by Cho and Kim (Bull Math Biol 75:845-870, 2013) and was called starvation driven diffusion. This model is surprisingly similar to the original Keller-Segel model. A comprehensive picture of traveling bands and fronts is provided.

Proximal Junctional Kyphosis Following Spinal Deformity Surgery in the Pediatric Patient.

Proper understanding and restoration of sagittal balance is critical in spinal deformity surgery, including conditions such as adolescent idiopathic scoliosis and Scheuermann kyphosis. One potential complication following spinal reconstruction is proximal junctional kyphosis. The prevalence of proximal junctional kyphosis varies in the literature, and several patient- and surgery-related risk factors have been identified. To date, the development of proximal junctional kyphosis has not been shown to lead to a negative clinical outcome following spinal fusion for adolescent idiopathic scoliosis or Scheuermann kyphosis. Treatment options range from simple observation in asymptomatic cases to revision surgery with extension of the fusion proximally. Several techniques and technologies are emerging that seek to address and prevent proximal junctional kyphosis.

Numerical reconstruction of a full parallax holographic stereogram with radial distortion.

Successful commercialization of holographic printers based on holographic stereograms requires a tool for their numerical replaying and quality assessment before the time-consuming and expensive process of holographic recording. A holographic stereogram encodes 2D images of a 3D scene that are incoherently captured from multiple perspectives and rearranged before recording. This study presents a simulator which builds a full parallax and full color white light viewable holographic stereogram from the perspective images captured by a virtual recentering camera with its further numerical reconstruction for any viewer location. By tracking all steps from acquisition to recording, the simulator allows for analysis of radial distortions caused by the optical elements used at the recording stage. Numerical experiments conducted at increasing degree of pincushion distortion proved its insignificant influence on the reconstructed images in all practical cases by using a peak signal-to-noise ratio and the structural similarity as an image quality metrics.

Global asymptotic stability and the ideal free distribution in a starvation driven diffusion.

We study a logistic model with a nonlinear random diffusion in a Fokker-Planck type law, but not in Fick's law. In the model individuals are assumed to increase their motility if they starve. Any directional information to resource is not assumed in this starvation driven diffusion and individuals disperse in a random walk style strategy. However, the non-uniformity in the motility produces an advection toward surplus resource. Several basic properties of the model are obtained including the global asymptotic stability and the acquisition of the ideal free distribution.

Proximal junctional kyphosis following adult spinal deformity surgery.

PURPOSE: Proximal junctional kyphosis (PJK) is a common radiographic finding following long spinal fusions. Whether PJK leads to negative clinical outcome is currently debatable. A systematic review was performed to assess the prevalence, risk factors, and treatments of PJK. METHODS: Literature search was conducted on PubMed, EMBASE, and the Cochrane Central Register of Controlled Trials using the terms 'proximal junctional kyphosis' and 'proximal junctional failure'. Excluding reviews, commentaries, and case reports, we analyzed 33 studies that reported the prevalence rate, risk factors, and discussions on PJK following spinal deformity surgery. RESULTS: The prevalence rates varied widely from 6 to 61.7%. Numerous studies reported that clinical outcomes for patients with PJK were not significantly different from those without, except in one recent study in which adult patients with PJK experienced more pain. Risk factors for PJK included age at operation, low bone mineral density, shorter fusion constructs, upper instrumented vertebrae below L2, and inadequate restoration of global sagittal balance. CONCLUSIONS: Prevalence of PJK following long spinal fusion for adult spinal deformity was high but not clinically significant. Careful and detailed preoperative planning and surgical execution may reduce PJK in adult spinal deformity patients.