Bifurcation analysis of a mathematical model of atopic dermatitis to determine patient-specific effects of treatments on dynamic phenotypes

AbstractBone remodeling identifies the process of permanent bone change with new bone formation and old bone resorption. Understanding this process is essential in many applications, such as optimizing the treatment of diseases like osteoporosis, maintaining bone density in long-term periods of disuse, or assessing the long-term evolution of the bone surrounding prostheses after implantation. A particular case of study is the bone remodeling process after dental implantation. Despite the overall success of this type of implants, the increasing life expectancy in developed countries has boosted the demand for dental implants in patients with osteoporosis. Although several studies demonstrate a high success rate of dental implants in osteoporotic patients, it is also known that the healing time and the failure rate increase, necessitating the adoption of pharmacological measures to improve bone quality in those patients. However, the general efficacy of these antiresorptive drugs for osteoporotic patients is still controversial, requiring more experimental and clinical studies. In this work, we investigate the effect of different doses of several drugs, used nowadays in osteoporotic patients, on the evolution of bone density after dental implantation. With this aim, we use a pharmacokinetic–pharmacodynamic (PK/PD) mathematical model that includes the effect of antiresorptive drugs on the RANK/RANK-L/OPG pathway, as well as the mechano-chemical coupling with external mechanical loads. This mechano-PK/PD model is then used to analyze the evolution of bone in normal and osteoporotic mandibles after dental implantation with different drug dosages. We show that using antiresorptive agents such as bisphosphonates or denosumab increases bone density and the associated mechanical properties, but at the same time, it also increases bone brittleness. We conclude that, despite the many limitations of these very complex models, the one presented here is capable of predicting qualitatively the evolution of some of the main biological and chemical variables associated with the process of bone remodeling in patients receiving drugs for osteoporosis, so it could be used to optimize dental implant design and coating for osteoporotic patients, as well as the drug dosage protocol for patient-specific treatments.

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Applying a patient-specific bio-mathematical model of glioma growth to develop virtual [18F]-FMISO-PET images

Mathematical Medicine and Biology A Journal of the IMA ◽

10.1093/imammb/dqr002 ◽

2011 ◽

Vol 29 (1) ◽

pp. 31-48 ◽

Cited By ~ 33

Author(s):

S. Gu ◽

G. Chakraborty ◽

K. Champley ◽

A. M. Alessio ◽

J. Claridge ◽

...

Keyword(s):

Mathematical Model ◽

Patient Specific ◽

Glioma Growth

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The mathematical stability study for the system of the CoO(OH) – overoxidized polypyrrole composite synthesis in the presence of fluor ions

Mongolian Journal of Chemistry ◽

10.5564/mjc.v16i0.663 ◽

2016 ◽

Vol 16 ◽

pp. 13-17

Author(s):

V. Tkach ◽

S.C. De Oliveira ◽

R. Ojani ◽

P.I. Yagodynets ◽

U. Páramo-García

Keyword(s):

Mathematical Model ◽

Steady State ◽

Bifurcation Analysis ◽

Stability Theory ◽

Stability Study ◽

Linear Stability Theory ◽

Monotonic Instability ◽

Overoxidized Polypyrrole ◽

Polypyrrole Composite ◽

Steady State Stability

The potentiostatic synthesis of CoO(OH) – Overoxidized polypyrrole composite in the presence of fluor ions has been investigated mathematically. The corresponding mathematical model was described and analyzed by means of linear stability theory and bifurcation analysis. The steady-state stability requirements, like also oscillatory and monotonic instability conditions are derived.Mongolian Journal of Chemistry 16 (42), 2015, 13-17

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Theoretical Description for Chlorantraniliprole Electrochemical Determination, Assisted by Squaraine Dye Nano Ag2O2 Composite

Biointerface Research in Applied Chemistry ◽

10.33263/briac112.92789284 ◽

2020 ◽

Vol 11 (2) ◽

pp. 9278-9284

Keyword(s):

Mathematical Model ◽

Reaction Mechanism ◽

Bifurcation Analysis ◽

Electrochemical Determination ◽

Theoretical Description ◽

The Other ◽

Linear Stability Theory ◽

Oxide Nanoparticles ◽

Monotonic Instability ◽

Squaraine Dye

The theoretical description for the chlorantraniliprole electrochemical determination, assisted by the hybrid composite of squaraine dye with Ag2O2 nanoparticles, has been described. The correspondent reaction mechanism has been proposed, and the correspondent mathematical model has been developed and analyzed by means of linear stability theory and bifurcation analysis. It has been shown that the chlorantraniliprole electrochemical anodic determination on high potential may be efficiently provided by silver (I, III) oxide nanoparticles, stabilized by the squaraine dye. On the other hand, the oscillatory and monotonic instability is also possible, being caused by DEL influences of the electrochemical stage.

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IDH–wild-type glioblastoma cell density and infiltration distribution influence on supramarginal resection and its impact on overall survival: a mathematical model

Journal of Neurosurgery ◽

10.3171/2021.6.jns21925 ◽

2021 ◽

pp. 1-9

Author(s):

Shashwat Tripathi ◽

Tito Vivas-Buitrago ◽

Ricardo A. Domingo ◽

Gaetano De Biase ◽

Desmond Brown ◽

...

Keyword(s):

Mathematical Model ◽

Overall Survival ◽

Cell Density ◽

Patient Specific ◽

Wild Type ◽

Tumor Invasiveness ◽

Postoperative Mri ◽

T1 Contrast ◽

Supramarginal Resection ◽

The Impact

OBJECTIVE Recent studies have proposed resection of the T2 FLAIR hyperintensity beyond the T1 contrast enhancement (supramarginal resection [SMR]) for IDH–wild-type glioblastoma (GBM) to further improve patients’ overall survival (OS). GBMs have significant variability in tumor cell density, distribution, and infiltration. Advanced mathematical models based on patient-specific radiographic features have provided new insights into GBM growth kinetics on two important parameters of tumor aggressiveness: proliferation rate (ρ) and diffusion rate (D). The aim of this study was to investigate OS of patients with IDH–wild-type GBM who underwent SMR based on a mathematical model of cell distribution and infiltration profile (tumor invasiveness profile). METHODS Volumetric measurements were obtained from the selected regions of interest from pre- and postoperative MRI studies of included patients. The tumor invasiveness profile (proliferation/diffusion [ρ/D] ratio) was calculated using the following formula: ρ/D ratio = (4π/3)2/3 × (6.106/[VT21/1 − VT11/1])2, where VT2 and VT1 are the preoperative FLAIR and contrast-enhancing volumes, respectively. Patients were split into subgroups based on their tumor invasiveness profiles. In this analysis, tumors were classified as nodular, moderately diffuse, or highly diffuse. RESULTS A total of 101 patients were included. Tumors were classified as nodular (n = 34), moderately diffuse (n = 34), and highly diffuse (n = 33). On multivariate analysis, increasing SMR had a significant positive correlation with OS for moderately and highly diffuse tumors (HR 0.99, 95% CI 0.98–0.99; p = 0.02; and HR 0.98, 95% CI 0.96–0.99; p = 0.04, respectively). On threshold analysis, OS benefit was seen with SMR from 10% to 29%, 10% to 59%, and 30% to 90%, for nodular, moderately diffuse, and highly diffuse, respectively. CONCLUSIONS The impact of SMR on OS for patients with IDH–wild-type GBM is influenced by the degree of tumor invasiveness. The authors’ results show that increasing SMR is associated with increased OS in patients with moderate and highly diffuse IDH–wild-type GBMs. When grouping SMR into 10% intervals, this benefit was seen for all tumor subgroups, although for nodular tumors, the maximum beneficial SMR percentage was considerably lower than in moderate and highly diffuse tumors.

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Bifurcation Analysis of a Model Accounting for the 14-3-3s Signalling Compartmentalisation

Quality Assurance in Healthcare Service Delivery, Nursing and Personalized Medicine ◽

10.4018/978-1-61350-120-7.ch004 ◽

2012 ◽

pp. 61-70

Author(s):

S. Nikolov ◽

J. Vera ◽

O. Wolkenhauer

Keyword(s):

Mathematical Model ◽

Cell Cycle ◽

Phase Portrait ◽

Bifurcation Analysis ◽

Subcellular Localisation ◽

Loss Of Stability ◽

Cycle Arrest ◽

Reversible Loss ◽

Analytical Tools

Bifurcation theory studies the qualitative changes in the phase portrait when we vary the parameters of the system. In this book chapter we adapt and extend a mathematical model accounting for the subcellular localisation of 14-3-3s, a protein involved in cell cycle arrest and the regulation of apoptosis. The model is analysed with analytical tools coming from Lyapunov-Andronov theory, and our analytical calculations predict that soft (reversible) loss of stability takes place.

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