The introduction of Big Data Analytics (BDA) in healthcare will allow to use new technologies both in treatment of patients and health management. The paper aims at analyzing the possibilities of using Big Data Analytics in healthcare. The research is based on a critical analysis of the literature, as well as the presentation of selected results of direct research on the use of Big Data Analytics in medical facilities. The direct research was carried out based on research questionnaire and conducted on a sample of 217 medical facilities in Poland. Literature studies have shown that the use of Big Data Analytics can bring many benefits to medical facilities, while direct research has shown that medical facilities in Poland are moving towards data-based healthcare because they use structured and unstructured data, reach for analytics in the administrative, business and clinical area. The research positively confirmed that medical facilities are working on both structural data and unstructured data. The following kinds and sources of data can be distinguished: from databases, transaction data, unstructured content of emails and documents, data from devices and sensors. However, the use of data from social media is lower as in their activity they reach for analytics, not only in the administrative and business but also in the clinical area. It clearly shows that the decisions made in medical facilities are highly data-driven. The results of the study confirm what has been analyzed in the literature that medical facilities are moving towards data-based healthcare, together with its benefits.

Background: Any nation's health policy aims to properly care for its citizens and the society's quality of life. Since in the healthcare system, the population's health is the essential component of national wealth, health is treated as a public good and a social value. Therefore, in recent times, in addition to traditional instruments for promoting healthy lifestyles, health policy has increasingly turned to information instruments and digital technologies. Aims: The paper aims to recognize the role of Big Data Analytics (BDA) in developing Digital Social Innovation (DSI) in the healthcare field. The proposal of the author's Individual Health Plan Platform (IHPP) solution is presented as an example of Digital Social Innovation. Material and methods: The research is based on a critical analysis of the literature, followed by a Focus Group study aimed at determining the potential of Big Data Analytics, including especially analysis based on data from wearables, to help manage one's health and improve the society's well-being. The focus research also included verification of the research model presented in the article and evaluation of the proposed solution, the Individual Health Plan Platform, including the possibilities of its implementation as a solution to complement healthcare provided by medical facilities in Poland. Results: The results of the focus group interviews show that analysing data from wearables and the proposed IHPP could be helpful in managing one's own health and helping to level important problems in healthcare. Conclusion: One of the goals of this paper was to determine the role of BDAs in the development of social innovations in healthcare. From the analysis of the literature, results of the focus group study and discussion, it was concluded that Big Data Analytics has the potential to develop social innovation in healthcare.

The Kedem−Katchalsky equations in matrix version for homogeneous and nonhomogeneous solutions were applied for the interpretation of membrane transport. Coefficients L*_ij (for unstirred solutions), L_ij (for mechanically stirred solutions) (i ≠ j = 1, 2), and L*_ij/L_ij were calculated, on the basis of experimentally determined coefficients (L_p, σ, ω), for an aqueous glucose solution and configurations A and B of the membrane system, in which a cellulose membrane was mounted in a horizontal plane. In configuration A, the upper chamber contained aqueous glucose solution at concentration C_l, and the lower chamber contained aqueous glucose solution at concentration C_h. In configuration B, the position of solutions with concentrations C_l. and C_h. was reversed. From the calculations, it results that the values of coefficients L*₁₁ = L₁₁ are constant, but the values of coefficients L*₁₂, L₁₂, L₂₁, L*₂₁, and L₂₂ depend linearly on solution concentration in the membrane ( C). However, the value of coefficient L*₂₂ depends nonlinearly on C as well as on a membrane system configuration. A concentration Rayleigh number (R_C) was used in a thermodynamic model based on Kedem−Katchalsky equations for counting L*_ij/L_ij . It can be also stated that for R_C greater than threshold value ((R_C)_crit), conductance coefficients L*₁₂/L₁₂, L*₂₂/L₂₂, and det[L*]/det[L] depend on a configuration of the membrane system.

The Kedem-Katchalsky equations, modified by means of symmetric transformations of Peusner thermodynamic networks, were applied to interpret the membrane transport in concentration polarization conditions. The results from the study demonstrate that the resistance coefficients counted for membrane transport of aqueous solutions of glucose through Nephrophan membrane in horizontal plane are nonlinearly dependent on mean concentration of glucose in the membrane \({(\bar{C})}\) . It was also shown that the threshold value of concentration \({(\bar{C}_{cr})}\) existed, and for \({\bar{C} > \bar{C}_{cr}}\) , the resistance coefficients depend, while for \({\bar{C} < \bar{C}_{cr}}\) , they do not depend on the membrane system configuration. Increase of mean glucose concentration in the membrane (in the range \({\bar{C} > \bar{C}_{cr})}\) causes decrease of difference between resistance coefficients of the membrane system in homogeneous conditions (solutions mechanically stirred) and in conditions with hydrodynamic instabilities (configuration B). Besides increase of mean glucose concentration in the membrane (in the range \({\bar{C} > \bar{C}_{cr})}\) causes increase of the difference between resistance coefficients for membrane system with concentration polarization without hydrodynamic instabilities (configuration A) and membrane system in homogeneous conditions.

Estimation of thickness of concentration boundary layers by osmotic volume flux determination

Methods of Peusner’s network of thermodynamics enable the symmetric or hybrid transformation of classic Kedem–Katchalsky (K–K) equations into a network form. In the case of binary non-electrolyte solutions (homogenous and non-homogenous ones), two symmetric and two hybrid forms of the K–K equations may be obtained, containing relatively symmetric ( \(R_{ij}^{*},\,R_{ij},\,L_{ij}^{*}\) or \(L_{ij}),\) or hybrid ( \(P_{ij}^{*},\,P_{ij},\,H_{ij}^{*}\) or \(H_{ij})\) Peusner’s coefficients. In the following paper, the network form of the K–K equations was obtained, containing the Peusner’s coefficients \(P_{ij}^{*}\,(i,\, j\in \{1,\,2\}),\) and creating matrix of the second row of the Peusner’s coefficients \([P^{*}].\) The equations were used to study transport of aqueous glucose solutions through a Nephrophan membrane oriented horizontally as well as configurations A and B of a membrane system. The configuration A involves a solution with a higher concentration placed under the membrane, whereas a solution with a lower concentration is placed above the membrane. In the configuration B, the solutions are swapped with places. Dependences of the Peusner’s coefficients \(P_{ij}^{*}\) and \(P_{ij}\,(i,\, j \in \{1,\,2\})\) for non-homogenous ( \(P_{ij}^{*})\) and homogenous ( \(P_{ij})\) solutions upon the average concentration of glucose in the membrane ( \(\overline{{C}})\) were calculated. The transport properties of membrane are characterized by coefficients determined experimentally: the coefficient of reflection ( \(\sigma \) ), hydraulic permeability ( \(L_\mathrm{p})\) , and solution permeability ( \(\omega \) ) for aqueous glucose or ethanol solutions. The calculations show that values of coefficients \(P_{11}^{*},\,P_{12}^{*},\,P_{21}^{*}\) , and \(P_{22}^{*}\) depend non-linearly on both the membrane \(\overline{{C}}\) and the configuration of the membrane system. The values of the coefficients are different from the values of the coefficients \(P_{11},\,P_{12},\,P_{21}\) and \(P_{22}.\) Moreover, the coefficients \(P_{11},\,P_{12},\,P_{21}\) and \(P_{22}\) do not depend on the configuration of the membrane system. It was shown that there is a threshold value of concentration above which relations \(P_{11}^{*}/P_{11},\,P_{12}^{*}/P_{12}\) and \(P_{22}^{*}/P_{22}\) depend on the configuration of the membrane system.