scholarly journals A mathematical model of drug dynamics in an electroporated tissue

2021 ◽  
Vol 18 (6) ◽  
pp. 8641-8660
Author(s):  
Nilay Mondal ◽  
◽  
Koyel Chakravarty ◽  
D. C. Dalal ◽  
Keyword(s):  
Mathematical Model ◽  
Drug Delivery ◽  
Electric Field ◽  
Mathematical Formulation ◽  
Drug Uptake ◽  
Model Parameters ◽  
Pulse Period ◽  
Electric Pulses ◽  
Drug Concentrations ◽  
Clinical Experiments

<abstract><p>In order to overcome the obstruction of cell membranes in the path of drug delivery to diseased cells, the applications of electric pulses of adequate potency are designated as electroporation. In the present study, a mathematical model of drug delivery into the electroporated tissue is advocated, which deals with both reversibly and irreversibly electroporated cells. This mathematical formulation is manifested through a set of differential equations, which are solved analytically, and numerically, according to the complexity, with a pertinent set of initial and boundary conditions. The time-dependent mass transfer coefficient in terms of pores is used to find the drug concentrations through reversibly and irreversibly electroporated cells as well as extracellular space. The effects of permeability of drug, electric field and pulse period on drug concentrations in extracellular and intracellular regions are discussed. The threshold value of an electric field ($ E &gt; 100 $ V cm$ ^{-1} $) to initiate drug uptake is identified in this study. Special emphasis is also put on two cases of electroporation, drug dynamics during ongoing electroporation and drug dynamics after the electric pulse period is over. Furthermore, all the simulated results and graphical portrayals are discussed in detail to have a transparent vision in comprehending the underlying physical and physiological phenomena. This model could be useful to various clinical experiments for drug delivery in the targeted tissue by controlling the model parameters depending on the tissue condition.</p></abstract>

scholarly journals Inverse mechanistic modeling of transdermal drug delivery for fast identification of optimal model parameters

2020 ◽  
Author(s):  
Thijs Defraeye ◽  
Flora Bahrami ◽  
Rene M Rossi
Keyword(s):  
Drug Delivery ◽  
Inverse Modeling ◽  
Transdermal Drug Delivery ◽  
Drug Transport ◽  
Mechanistic Model ◽  
Mechanistic Modeling ◽  
Drug Uptake ◽  
Added Value ◽  
Model Parameters ◽  
Transdermal Drug Delivery Systems

Transdermal drug delivery systems are a key technology to administer drugs with a high first-pass effect in a non-invasive and controlled way. Physics-based modeling and simulation are on their way to become a cornerstone in the engineering of these healthcare devices since it provides a unique complementarity to experimental data and insights. Simulations enable to virtually probe the drug transport inside the skin at each point in time and space. However, the tedious experimental or numerical determination of material properties currently forms a bottleneck in the modeling workflow. We show that multiparameter inverse modeling to determine the drug diffusion and partition coefficients is a fast and reliable alternative. We demonstrate this strategy for transdermal delivery of fentanyl. We found that inverse modeling reduced the normalized root mean square deviation of the measured drug uptake flux from 26 to 9%, when compared to the experimental measurement of all skin properties. We found that this improved agreement with experiments was only possible if the diffusion in the reservoir holding the drug was smaller than the experimentally-measured diffusion coefficients suggested. For indirect inverse modeling, which systematically explores the entire parametric space, 30 000 simulations were required. By relying on direct inverse modeling, we reduced the number of simulations to be performed to only 300, so a factor 100 difference. The modeling approach's added value is that it can be calibrated once in-silico for all model parameters simultaneously by solely relying on a single measurement of the drug uptake flux evolution over time. We showed that this calibrated model could accurately be used to simulate transdermal patches with other drug doses. We showed that inverse modeling is a fast way to build up an accurate mechanistic model for drug delivery. This strategy opens the door to clinically-ready therapy that is tailored to patients.

Studying Dynamic Behaviour of Flexible Rotors With an Analytic Model That Includes Non-Linear Supports, Non-Stiff Support Structure and Torsion Flexibility

2007 ◽  
Author(s):  
Heller G. Sa´nchez A. ◽  
Jesu´s M. Pintor B.
Keyword(s):  
Mathematical Model ◽  
Dynamic Analysis ◽  
Dynamic Behaviour ◽  
Mathematical Formulation ◽  
Model Parameters ◽  
Analytic Model ◽  
Support Structure ◽  
Stationary Response ◽  
Rigid Structure ◽  
Flexible Rotors

This article presents a mathematical formulation based on FEM for the dynamic analysis of flexible rotors that are not grounded necessary to a rigid structure. Furthermore, it uses the component synthesis in order to introduce the behavior of the structure where the rotor is grounded. The developed mathematical model calculates the model parameters stationary response.

Pharmacokinetics of Drug Distribution

Drug Delivery ◽  
2001 ◽  
Author(s):  
W. Mark Saltzman
Keyword(s):  
Time Course ◽  
Molecular Mechanisms ◽  
Drug Distribution ◽  
The Body ◽  
Drug Uptake ◽  
Pharmacokinetic Analysis ◽  
Model Parameters ◽  
Drug Concentrations ◽  
Uptake Rates ◽  
Tissue Compartments

Pharmacology, the study of agents and their actions, can be divided into two branches. Pharmacodynamics is concerned with the effects of a drug on the body and, therefore, encompasses dose–response relationships as well as the molecular mechanisms of drug activity. Pharmacokinetics, on the other hand, is concerned with the effect of the body on the drug. Drug metabolism, transport, absorption, and elimination are components of pharmacokinetic analysis. Physiology influences the distribution of drugs within the body; overall distribution depends on rates of drug uptake, rates of distribution between tissue compartments, and rates of drug elimination or biotransformation. Each of these phenomena potentially involves aspects of drug diffusion, permeation through membranes, and fluid movement that were introduced in the previous sections. The goal of pharmacokinetics is synthesis of these isolated basic mechanisms into a functional unit; this goal is most often achieved by development of a mathematical model that incorporates descriptions of the uptake, distribution, and elimination of a drug in humans or animals. This model can then be used to predict the outcome of different dosage regimens on the time course of drug concentrations in tissues. The development of a complete pharmacokinetic model for any given drug is a substantial undertaking, since the fate of any compound introduced into a whole organism is influenced by a variety of factors, and is usually complicated—in ways that are difficult to predict—by the presence of disease. In this section, pharamacokinetics will be introduced by first considering the simplest situation: an agent is introduced into a single body compartment from which it is also eliminated. While quite sophisticated compartmental models can be developed from this basic construct, it is frequently difficult to relate model parameters (such as the volume of specific compartments or the rate of transfer between compartments) to physiological or anatomical parameters. To avoid this difficulty, physiological pharmacokinetic models are frequently employed; in these models, the kinetics of drug uptake, distribution, and elimination from local tissue sites are predicted by constructing anatomically and biochemically accurate models of the tissue environment.

Research on the Microfluidics Control Method Based on the EOF Technology

2006 ◽  
Vol 532-533 ◽  
pp. 65-68
Author(s):  
Hong Yuan Jiang ◽  
Hu Kun Yang ◽  
Yang Wang ◽  
Tao Jiang
Keyword(s):  
Mathematical Model ◽  
Drug Delivery ◽  
Zeta Potential ◽  
Electric Field ◽  
Drug Delivery Systems ◽  
Control Method ◽  
Novel Technology ◽  
Micro Total Analysis Systems ◽  
Total Analysis ◽  
The Relationship

Electroosmoticflow (EOF) applied in micropump is a novel technology, which will be widely applied in micro total analysis systems (μTAS) and drug delivery systems. EOF velocity in microchannel depends on the zeta potential (ζ), the electric field (E) parallel to the microchannel and so on. Electric field can be decreased if ζ can be increased, which can reduce the disadvantage caused by the high electric field voltage. This paper discusses the relationship between EOF velocity and ζ, E, to realize this concept. Through building mathematical model, this paper analyzes the effects of changing ζ and E on EOF velocity, which provides the microfluidics control theory basis to design EOF micropump and presents a new subject of manufacturing micropump process.

scholarly journals Inverse Mechanistic Modeling of Transdermal Drug Delivery for Fast Identification of Optimal Model Parameters

2021 ◽  
Vol 12 ◽  
Author(s):  
Thijs Defraeye ◽  
Flora Bahrami ◽  
René M. Rossi
Keyword(s):  
Drug Delivery ◽  
Inverse Modeling ◽  
Transdermal Drug Delivery ◽  
Drug Transport ◽  
Mechanistic Model ◽  
Mechanistic Modeling ◽  
Drug Uptake ◽  
Added Value ◽  
Model Parameters ◽  
Transdermal Drug Delivery Systems

Transdermal drug delivery systems are a key technology to administer drugs with a high first-pass effect in a non-invasive and controlled way. Physics-based modeling and simulation are on their way to become a cornerstone in the engineering of these healthcare devices since it provides a unique complementarity to experimental data and additional insights. Simulations enable to virtually probe the drug transport inside the skin at each point in time and space. However, the tedious experimental or numerical determination of material properties currently forms a bottleneck in the modeling workflow. We show that multiparameter inverse modeling to determine the drug diffusion and partition coefficients is a fast and reliable alternative. We demonstrate this strategy for transdermal delivery of fentanyl. We found that inverse modeling reduced the normalized root mean square deviation of the measured drug uptake flux from 26 to 9%, when compared to the experimental measurement of all skin properties. We found that this improved agreement with experiments was only possible if the diffusion in the reservoir holding the drug was smaller than the experimentally measured diffusion coefficients suggested. For indirect inverse modeling, which systematically explores the entire parametric space, 30,000 simulations were required. By relying on direct inverse modeling, we reduced the number of simulations to be performed to only 300, so a factor 100 difference. The modeling approach’s added value is that it can be calibrated once in-silico for all model parameters simultaneously by solely relying on a single measurement of the drug uptake flux evolution over time. We showed that this calibrated model could accurately be used to simulate transdermal patches with other drug doses. We showed that inverse modeling is a fast way to build up an accurate mechanistic model for drug delivery. This strategy opens the door to clinically ready therapy that is tailored to patients.

Mathematical model to predict the characteristics of polarization in dielectric materials: The concept of piezoelectrcity and electrostriction

2019 ◽  
Author(s):  
Chem Int
Keyword(s):  
Mathematical Model ◽  
Electric Field ◽  
Lead Zirconate Titanate ◽  
Dielectric Material ◽  
Strain Curve ◽  
Dielectric Materials ◽  
Lead Zirconate ◽  
Simulation Software ◽  
Constitutive Law ◽  
Basic Material

Model was developed for the prediction of polarization characteristics in a dielectric material exhibiting piezoelectricity and electrostriction based on mathematical equations and MATLAB computer simulation software. The model was developed based on equations of polarization and piezoelectric constitutive law and the functional coefficient of Lead Zirconate Titanate (PZT) crystal material used was 2.3×10-6 m (thickness), the model further allows the input of basic material and calculation of parameters of applied voltage levels, applied stress, pressure, dielectric material properties and so on, to generate the polarization curve, strain curve and the expected deformation change in the material length charts. The mathematical model revealed that an application of 5 volts across the terminals of a 2.3×10-6 m thick dielectric material (PZT) predicted a 1.95×10-9 m change in length of the material, which indicates piezoelectric properties. Both polarization and electric field curve as well as strain and voltage curve were also generated and the result revealed a linear proportionality of the compared parameters, indicating a resultant increase in the electric field yields higher polarization of the dielectric materials atmosphere.

scholarly journals Drug Delivery by Ultrasound-Responsive Nanocarriers for Cancer Treatment

Pharmaceutics ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1135
Author(s):  
Kristin Entzian ◽  
Achim Aigner
Keyword(s):  
Drug Delivery ◽  
Biological Effects ◽  
Invasive Technique ◽  
Stimuli Responsive ◽  
Comprehensive Overview ◽  
Drug Concentrations ◽  
Therapeutic Outcomes ◽  
Cost Efficient ◽  
Safety Considerations

Conventional cancer chemotherapies often exhibit insufficient therapeutic outcomes and dose-limiting toxicity. Therefore, there is a need for novel therapeutics and formulations with higher efficacy, improved safety, and more favorable toxicological profiles. This has promoted the development of nanomedicines, including systems for drug delivery, but also for imaging and diagnostics. Nanoparticles loaded with drugs can be designed to overcome several biological barriers to improving efficiency and reducing toxicity. In addition, stimuli-responsive nanocarriers are able to release their payload on demand at the tumor tissue site, preventing premature drug loss. This review focuses on ultrasound-triggered drug delivery by nanocarriers as a versatile, cost-efficient, non-invasive technique for improving tissue specificity and tissue penetration, and for achieving high drug concentrations at their intended site of action. It highlights aspects relevant for ultrasound-mediated drug delivery, including ultrasound parameters and resulting biological effects. Then, concepts in ultrasound-mediated drug delivery are introduced and a comprehensive overview of several types of nanoparticles used for this purpose is given. This includes an in-depth compilation of the literature on the various in vivo ultrasound-responsive drug delivery systems. Finally, toxicological and safety considerations regarding ultrasound-mediated drug delivery with nanocarriers are discussed.

scholarly journals Implantable Polymeric Drug Delivery Devices: Classification, Manufacture, Materials, and Clinical Applications

Polymers ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 1379 ◽  
Author(s):  
Sarah Stewart ◽  
Juan Domínguez-Robles ◽  
Ryan Donnelly ◽  
Eneko Larrañeta
Keyword(s):  
Drug Delivery ◽  
Side Effects ◽  
Patient Compliance ◽  
Oral Delivery ◽  
Oral Route ◽  
Clinical Applications ◽  
Drug Concentrations ◽  
Effective Delivery ◽  
Materials Used ◽  
Drug Delivery Devices

The oral route is a popular and convenient means of drug delivery. However, despite its advantages, it also has challenges. Many drugs are not suitable for oral delivery due to: first pass metabolism; less than ideal properties; and side-effects of treatment. Additionally, oral delivery relies heavily on patient compliance. Implantable drug delivery devices are an alternative system that can achieve effective delivery with lower drug concentrations, and as a result, minimise side-effects whilst increasing patient compliance. This article gives an overview of classification of these drug delivery devices; the mechanism of drug release; the materials used for manufacture; the various methods of manufacture; and examples of clinical applications of implantable drug delivery devices.

Pharmaceutical Calculations — A Basic Review

2002 ◽  
Vol 18 (5) ◽  
pp. 257-259
Author(s):  
Nicole M Russo
Keyword(s):  
Drug Delivery ◽  
Pharmaceutical Preparation ◽  
Medication Administration ◽  
Patient Specific ◽  
Specific Drug ◽  
Mathematical Concepts ◽  
Data Synthesis ◽  
Drug Concentrations ◽  
Data Source ◽  
Stock Solutions

Objective: To review mathematical topics used in pharmaceutical preparation, specifically ratios and proportions, percentage concentrations, and stock solutions. Data Source: Online pharmaceutics sources and current pharmaceutics textbooks were consulted. Data Synthesis: Ratios and proportions are basic tools for adjusting drug concentrations. Using proportions, medications can be provided in any concentration desired. By extending this technique to percentage concentrations, prescriptions can be interpreted and calculated. In the same manner, the ability to dilute stock solutions provides patient-specific drug delivery. Conclusions: The mathematical concepts of ratios and proportions, percentage concentrations, and stock dilutions are essential for correct medication administration in any setting.

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