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Yan D, Wu X, Li J, Tang S. Statistical Analysis of Two-Compartment Pharmacokinetic Models with Drug Non-adherence. Bull Math Biol 2023; 85:65. [PMID: 37294520 DOI: 10.1007/s11538-023-01173-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2022] [Accepted: 05/29/2023] [Indexed: 06/10/2023]
Abstract
Poor drug adherence is considered one of major barriers to achieving the clinical and public health benefits of many pharmacotherapies. In the current paper, we aim to investigate the impact of dose omission on the plasma concentrations of two-compartment pharmacokinetic models with two typical routes of drug administration, namely the intravenous bolus and extravascular first-order absorption. First, we reformulate the classical two-compartment pharmacokinetic models with a new stochastic feature, where a binomial random model of dose intake is integrated. Then, we formalize the explicit expressions of expectation and variance for trough concentrations and limit concentrations, with the latter proved of the existence and uniqueness for steady-state distribution. Moreover, we mathematically demonstrate the strict stationarity and ergodicity of trough concentrations as a Markov chain. In addition, we numerically simulate the impact of drug non-adherence to different extents on the variability and regularity of drug concentration and compare the drug pharmacokinetic preference between one and two compartment pharmacokinetic models. The results of sensitivity analysis also suggest the drug non-adherence as one of the most sensitive model parameters to the expectation of limit concentration. Our modelling and analytical approach can be integrated into the chronic disease models to estimate or quantitatively predict the therapy efficacy with drug pharmacokinetics presumably affected by random dose omissions.
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Affiliation(s)
- Dingding Yan
- School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, 710119, People's Republic of China
| | - Xiaotian Wu
- School of Science, Shanghai Maritime University, Shanghai, 201306, People's Republic of China.
| | - Jun Li
- Faculté de pharmacie, Université de Montréal, Quebec, H3C3J7, Canada
- Centre de recherches mathématiques, Université de Montréal, Quebec, H3C3J7, Canada
| | - Sanyi Tang
- School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, 710119, People's Republic of China
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Ramos TI, Villacis-Aguirre CA, López-Aguilar KV, Santiago Padilla L, Altamirano C, Toledo JR, Santiago Vispo N. The Hitchhiker's Guide to Human Therapeutic Nanoparticle Development. Pharmaceutics 2022; 14:247. [PMID: 35213980 PMCID: PMC8879439 DOI: 10.3390/pharmaceutics14020247] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2021] [Revised: 01/04/2022] [Accepted: 01/13/2022] [Indexed: 02/06/2023] Open
Abstract
Nanomedicine plays an essential role in developing new therapies through novel drug delivery systems, diagnostic and imaging systems, vaccine development, antibacterial tools, and high-throughput screening. One of the most promising drug delivery systems are nanoparticles, which can be designed with various compositions, sizes, shapes, and surface modifications. These nanosystems have improved therapeutic profiles, increased bioavailability, and reduced the toxicity of the product they carry. However, the clinical translation of nanomedicines requires a thorough understanding of their properties to avoid problems with the most questioned aspect of nanosystems: safety. The particular physicochemical properties of nano-drugs lead to the need for additional safety, quality, and efficacy testing. Consequently, challenges arise during the physicochemical characterization, the production process, in vitro characterization, in vivo characterization, and the clinical stages of development of these biopharmaceuticals. The lack of a specific regulatory framework for nanoformulations has caused significant gaps in the requirements needed to be successful during their approval, especially with tests that demonstrate their safety and efficacy. Researchers face many difficulties in establishing evidence to extrapolate results from one level of development to another, for example, from an in vitro demonstration phase to an in vivo demonstration phase. Additional guidance is required to cover the particularities of this type of product, as some challenges in the regulatory framework do not allow for an accurate assessment of NPs with sufficient evidence of clinical success. This work aims to identify current regulatory issues during the implementation of nanoparticle assays and describe the major challenges that researchers have faced when exposing a new formulation. We further reflect on the current regulatory standards required for the approval of these biopharmaceuticals and the requirements demanded by the regulatory agencies. Our work will provide helpful information to improve the success of nanomedicines by compiling the challenges described in the literature that support the development of this novel encapsulation system. We propose a step-by-step approach through the different stages of the development of nanoformulations, from their design to the clinical stage, exemplifying the different challenges and the measures taken by the regulatory agencies to respond to these challenges.
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Affiliation(s)
- Thelvia I. Ramos
- Laboratorio de Biotecnología y Biofármacos, Departamento de Fisiopatología, Facultad de Ciencias Biológicas, Universidad de Concepción, Víctor Lamas 1290, Concepción 4070386, Chile; (T.I.R.); (C.A.V.-A.)
- Grupo de Investigación en Sanidad Animal y Humana (GISAH), Carrera Ingeniería en Biotecnología, Departamento de Ciencias de la Vida y la Agricultura, Universidad de las Fuerzas Armadas—ESPE, Sangolquí 171103, Ecuador
| | - Carlos A. Villacis-Aguirre
- Laboratorio de Biotecnología y Biofármacos, Departamento de Fisiopatología, Facultad de Ciencias Biológicas, Universidad de Concepción, Víctor Lamas 1290, Concepción 4070386, Chile; (T.I.R.); (C.A.V.-A.)
| | - Katherine V. López-Aguilar
- Carrera Ingeniería en Biotecnología, Departamento de Ciencias de la Vida y la Agricultura, Universidad de las Fuerzas Armadas—ESPE, Sangolquí 171103, Ecuador;
| | | | - Claudia Altamirano
- Escuela de Ingeniería Bioquímica, Facultad de Ingeniería, Pontificia Universidad Católica de Valparaíso, Av. Brasil 2085, Valparaíso 2362803, Chile;
- Centro Regional de Estudios en Alimentos Saludables, Av. Universidad 330, Placilla, Sector Curauma, Valparaíso 2340000, Chile
| | - Jorge R. Toledo
- Laboratorio de Biotecnología y Biofármacos, Departamento de Fisiopatología, Facultad de Ciencias Biológicas, Universidad de Concepción, Víctor Lamas 1290, Concepción 4070386, Chile; (T.I.R.); (C.A.V.-A.)
| | - Nelson Santiago Vispo
- School of Biological Sciences and Engineering, Yachay Tech University, Hda. San José s/n y Proyecto Yachay, Urcuquí 100119, Ecuador
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