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1.  Is West Africa Approaching a Catastrophic Phase or is the 2014 Ebola Epidemic Slowing Down? Different Models Yield Different Answers for Liberia 
PLoS Currents  2014;6:ecurrents.outbreaks.b4690859d91684da963dc40e00f3da81.
An unprecedented epidemic of Zaire ebolavirus (EBOV) has affected West Africa since approximately December 2013, with intense transmission on-going in Guinea, Sierra Leone and Liberia and increasingly important international repercussions. Mathematical models are proving instrumental to forecast the expected number of infections and deaths and quantify the intensity of interventions required to control transmission; however, calibrating mechanistic transmission models to an on-going outbreak is a challenging task owing to limited availability of epidemiological data and rapidly changing interventions. Here we project the trajectory of the EBOV epidemic in Liberia by fitting logistic growth models to the cumulative number of cases. Our model predictions align well with the latest epidemiological reports available as of October 23, and indicates that the exponential growth phase is over in Liberia, with an expected final attack rate of ~0.1-0.12%. Our results indicate that simple phenomenological models can provide complementary insights into the dynamics of an outbreak and capture early signs of changes in population behavior and interventions. In particular, our results underscore the need to treat the effective size of the susceptible population as a dynamic variable rather than a fixed quantity, due to reactive changes in transmission throughout the outbreak. We show that predictions from the logistic model are more variable in the earlier stages of an epidemic (such as the EBOV epidemics in Sierra Leone and Guinea). More research is warranted to compare the performances of mechanistic and phenomenological approaches for disease forecasts, before such predictions can be fully used by public health authorities.
PMCID: PMC4318911
2.  Pre-existing hyperlipidaemia increased the risk of new-onset anxiety disorders after traumatic brain injury: a 14-year population-based study 
BMJ Open  2014;4(7):e005269.
Anxiety disorders (ADs) are common after traumatic brain injury (TBI). However, the risk factors of new-onset ADs remain unclear. This study was aimed at evaluating the incidence and risk factors for new-onset ADs, including pre-existing hyperlipidaemia and three major comorbidities (diabetes mellitus, hypertension and cardiovascular disease), in patients with TBI.
A matched cohort study was conducted using the Taiwan Longitudinal Health Insurance Database between January 1997 and December 2010.
A total of 3822 participants (1274 patients with TBI with hyperlipidaemia and 2548 age-matched and gender-matched patients with TBI without hyperlipidaemia).
Outcome measures
The incidence and HRs for the development of new-onset ADs after TBI were compared between the two groups.
The overall incidence rate of new-onset ADs for patients with TBI with hyperlipidaemia is 142.03/10 000 person-years (PYs). Patients with TBI with hyperlipidaemia have a 1.60-fold incidence rate ratio (p<0.0001) and increased HR of ADs (1.58, 95% CI 1.24 to 2.02) compared with those without hyperlipidaemia. The incidence rates of ADs for males and females with hyperlipidaemia, respectively, were 142.12 and 292.32/10 000 PYs, which were higher than those without hyperlipidaemia (93.03 and 171.68/10 000 PYs, respectively). Stratified by age group, hyperlipidaemia is a risk factor of ADs for patients with TBI aged 65 years or younger.
Pre-existing hyperlipidaemia is an independent predictor of new-onset ADs in patients with TBI, even when controlling for other demographic and clinical variables. Female patients with pre-existing hyperlipidaemia had significantly higher risk of new-onset ADs than males, especially between the ages of 35 and 65 years.
PMCID: PMC4120375  PMID: 25034630
3.  Improvement of optical transmittance and electrical properties for the Si quantum dot-embedded ZnO thin film 
Nanoscale Research Letters  2013;8(1):439.
A Si quantum dot (QD)-embedded ZnO thin film is successfully fabricated on a p-type Si substrate using a ZnO/Si multilayer structure. Its optical transmittance is largely improved when increasing the annealing temperature, owing to the phase transformation from amorphous to nanocrystalline Si QDs embedded in the ZnO matrix. The sample annealed at 700°C exhibits not only high optical transmittance in the long-wavelength range but also better electrical properties including low resistivity, small turn-on voltage, and high rectification ratio. By using ZnO as the QDs’ matrix, the carrier transport is dominated by the multistep tunneling mechanism, the same as in a n-ZnO/p-Si heterojunction diode, which clearly differs from that using the traditional matrix materials. Hence, the carriers transport mainly in the ZnO matrix, not through the Si QDs. The unusual transport mechanism using ZnO as matrix promises the great potential for optoelectronic devices integrating Si QDs.
PMCID: PMC3854540  PMID: 24148255
Si quantum dot; ZnO thin film; Transport mechanism
4.  Accurate state estimation from uncertain data and models: an application of data assimilation to mathematical models of human brain tumors 
Biology Direct  2011;6:64.
Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor.
We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise.
The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling.
This article was reviewed by Anthony Almudevar, Tomas Radivoyevitch, and Kristin Swanson (nominated by Georg Luebeck).
PMCID: PMC3340325  PMID: 22185645
State estimation; data assimiliation; mathematical models; glioblastoma multiforme
5.  Pharmacokinetics of p-Aminohippuric Acid and Inulin in Rabbits with Aristolochic Acid Nephropathy 
The characteristics of aristolochic acid nephropathy (AAN) are interstitial fibrosis and atrophy of the proximal tubules, but with no change in glomeruli. To investigate the effects of AA on renal functions and the pharmacokinetics (PKs) of p-aminohippuric acid (PAH) and inulin, New Zealand white rabbits were used in this study. The plasma concentrations of PAH and inulin were determined by validated HPLC methods. After a single intravenous administration of 0.5 mg/kg aristolochic acid sodium (AANa), rabbits exhibited mild to moderate nephrotoxicity on the 7th day. Significant tubulointerstitial damage to kidney specimens was found, but there were no remarkable glomerular changes. Clearance rates of PAH and inulin both significantly decreased in AANa-treated rabbits. In addition, there was a significant correlation among the degree of tubulointerstitial changes and PK parameters of PAH after AANa administration, but no correlation was noted with the PKs of inulin. With mild to moderate AAN in rabbits, the renal plasma flow significantly decreased by 55%, and the glomerular filtration rate also significantly decreased by 85%. In conclusion, major renal lesions were found on proximal tubules after AANa administration. The PKs of PAH and inulin significantly changed, and kidney functions, including the RPF and GFR, were reduced.
PMCID: PMC3124128  PMID: 21738526
6.  Enhanced modelling of the glucose–insulin system and its applications in insulin therapies 
It is well known that Michaelis–Menten kinetics is suitable for the response function in chemical reaction, when the reaction rate does not increase indefinitely when an excess of resource is available. However, the existing models for insulin therapies assume that the response function of insulin clearance is proportional to the insulin concentration. In this paper, we propose a new model for insulin therapy for both type 1 and type 2 diabetes mellitus, in which the insulin degradation rate assumes Michaelis–Menten kinetics. Our analysis shows that it is possible to mimic pancreatic insulin secretion by exogenous insulin infusions, and our numerical simulations provide clinical strategies for insulin–administration practices.
PMCID: PMC3032387  PMID: 21297886
diabetes; glucose–insulin regulator system; insulin therapy; time delay; periodic solution
Type 1 diabetics must inject exogenous insulin or insulin analogues one or more times daily. The timing and dosage of insulin administration have been a critical research area since the invention of insulin analogues. Several pharmacokinetical models have been proposed, and some are applied clinically in modeling various insulin therapies. However, their plasma insulin concentration must be computed separately from the models’ output. Furthermore, minimal analytical study was performed in these existing models. We propose two systemic and simplified ordinary differential equation models to model the subcutaneous injection of rapid-acting insulin analogues and long-acting insulin analogues, respectively. Our models explicitly model the plasma insulin and hence have the advantage of computing the plasma insulin directly. The profiles of plasma insulin concentrations obtained from these two models are in good agreement with the experimental data. We also study the dynamics of insulin analogues, plasma insulin concentrations, and, in particular, the shape of the dynamics of plasma insulin concentrations.
PMCID: PMC3030458  PMID: 19292507
insulin analogue; subcutaneous injection; hexamer; dimer; monomer; glucose
8.  Role of pirenoxine in the effects of catalin on in vitro ultraviolet-induced lens protein turbidity and selenite-induced cataractogenesis in vivo 
Molecular Vision  2011;17:1862-1870.
In this study, we investigated the biochemical pharmacology of pirenoxine (PRX) and catalin under in vitro selenite/calcium- and ultraviolet (UV)-induced lens protein turbidity challenges. The systemic effects of catalin were determined using a selenite-induced cataractogenesis rat model.
In vitro cataractogenesis assay systems (including UVB/C photo-oxidation of lens crystallins, calpain-induced proteolysis, and selenite/calcium-induced turbidity of lens crystallin solutions) were used to screen the activity of PRX and catalin eye drop solutions. Turbidity was identified as the optical density measured using spectroscopy at 405 nm. We also determined the in vivo effects of catalin on cataract severity in a selenite-induced cataract rat model. Sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS–PAGE) was applied to analyze the integrity of crystallin samples.
PRX at 1,000 μM significantly delayed UVC-induced turbidity formation compared to controls after 4 h of UVC exposure (p<0.05), but not in groups incubated with PRX concentrations of <1,000 μM. Results were further confirmed by SDS–PAGE. The absolute γ-crystallin turbidity induced by 4 h of UVC exposure was ameliorated in the presence of catalin equivalent to 1~100 μM PRX in a concentration-dependent manner. Samples with catalin-formulated vehicle only (CataV) and those containing PRX equivalent to 100 μM had a similar protective effect after 4 h of UVC exposure compared to the controls (p<0.05). PRX at 0.03, 0.1, and 0.3 μM significantly delayed 10 mM selenite- and calcium-induced turbidity formation compared to controls on days 0~4 (p<0.05). Catalin (equivalent to 32, 80, and 100 μM PRX) had an initial protective effect against selenite-induced lens protein turbidity on day 1 (p<0.05). Subcutaneous pretreatment with catalin (5 mg/kg) also statistically decreased the mean cataract scores in selenite-induced cataract rats on post-induction day 3 compared to the controls (1.3±0.2 versus 2.4±0.4; p<0.05). However, catalin (equivalent to up to 100 μM PRX) did not inhibit calpain-induced proteolysis activated by calcium, and neither did 100 μM PRX.
PRX at micromolar levels ameliorated selenite- and calcium-induced lens protein turbidity but required millimolar levels to protect against UVC irradiation. The observed inhibition of UVC-induced turbidity of lens crystallins by catalin at micromolar concentrations may have been a result of the catalin-formulated vehicle. Transient protection by catalin against selenite-induced turbidity of crystallin solutions in vitro was supported by the ameliorated cataract scores in the early stage of cataractogenesis in vivo by subcutaneously administered catalin. PRX could not inhibit calpain-induced proteolysis activated by calcium or catalin itself, and may be detrimental to crystallins under UVB exposure. Further studies on formulation modifications of catalin and recommended doses of PRX to optimize clinical efficacy by cataract type are warranted.
PMCID: PMC3144730  PMID: 21850160
9.  The evolutionary impact of androgen levels on prostate cancer in a multi-scale mathematical model 
Biology Direct  2010;5:24.
Androgens bind to the androgen receptor (AR) in prostate cells and are essential survival factors for healthy prostate epithelium. Most untreated prostate cancers retain some dependence upon the AR and respond, at least transiently, to androgen ablation therapy. However, the relationship between endogenous androgen levels and cancer etiology is unclear. High levels of androgens have traditionally been viewed as driving abnormal proliferation leading to cancer, but it has also been suggested that low levels of androgen could induce selective pressure for abnormal cells. We formulate a mathematical model of androgen regulated prostate growth to study the effects of abnormal androgen levels on selection for pre-malignant phenotypes in early prostate cancer development.
We find that cell turnover rate increases with decreasing androgen levels, which may increase the rate of mutation and malignant evolution. We model the evolution of a heterogeneous prostate cell population using a continuous state-transition model. Using this model we study selection for AR expression under different androgen levels and find that low androgen environments, caused either by low serum testosterone or by reduced 5α-reductase activity, select more strongly for elevated AR expression than do normal environments. High androgen actually slightly reduces selective pressure for AR upregulation. Moreover, our results suggest that an aberrant androgen environment may delay progression to a malignant phenotype, but result in a more dangerous cancer should one arise.
The model represents a useful initial framework for understanding the role of androgens in prostate cancer etiology, and it suggests that low androgen levels can increase selection for phenotypes resistant to hormonal therapy that may also be more aggressive. Moreover, clinical treatment with 5α-reductase inhibitors such as finasteride may increase the incidence of therapy resistant cancers.
This article was reviewed by Ariosto S. Silva (nominated by Marek Kimmel) and Marek Kimmel.
PMCID: PMC2885348  PMID: 20406442
10.  Tumor-Immune Interaction, Surgical Treatment, and Cancer Recurrence in a Mathematical Model of Melanoma 
PLoS Computational Biology  2009;5(4):e1000362.
Malignant melanoma is a cancer of the skin arising in the melanocytes. We present a mathematical model of melanoma invasion into healthy tissue with an immune response. We use this model as a framework with which to investigate primary tumor invasion and treatment by surgical excision. We observe that the presence of immune cells can destroy tumors, hold them to minimal expansion, or, through the production of angiogenic factors, induce tumorigenic expansion. We also find that the tumor–immune system dynamic is critically important in determining the likelihood and extent of tumor regrowth following resection. We find that small metastatic lesions distal to the primary tumor mass can be held to a minimal size via the immune interaction with the larger primary tumor. Numerical experiments further suggest that metastatic disease is optimally suppressed by immune activation when the primary tumor is moderately, rather than minimally, metastatic. Furthermore, satellite lesions can become aggressively tumorigenic upon removal of the primary tumor and its associated immune tissue. This can lead to recurrence where total cancer mass increases more quickly than in primary tumor invasion, representing a clinically more dangerous disease state. These results are in line with clinical case studies involving resection of a primary melanoma followed by recurrence in local metastases.
Author Summary
Melanoma is a deadly skin cancer that invades into the dermis and metastasizes into the surrounding tissue. In clinical cases, surgical excision of the primary tumor has led to widespread and accelerated growth in metastases. We develop a mathematical model describing the basic process of melanoma invasion, metastatic spread, and the anti-tumor immune response. This model is formulated using partial differential equations that describe the spatial and temporal evolution of a number of different cellular populations, and it uses a realistic skin geometry. Using simulations, we examine the importance of the immune response when a primary tumor is spawning satellite metastases. We find that local metastases can be suppressed by the immune response directed against the primary tumor, but grow aggressively following surgical treatment. We also find that moderately metastatic tumors optimally activate the local immune response against disseminated disease, and in this case tumor excision may have profound effects on metastatic growth. We conclude that surgical perturbation of the immune response controlling local metastases is one mechanism by which cancer can recur. This could have implications as to the appropriate clinical management of melanomas and other solid tumors.
PMCID: PMC2667258  PMID: 19390606

Results 1-10 (10)