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PubMed2006

Mathematical modeling and simulation of drug release from microspheres: Implications to drug delivery systems.

This article aims to provide a comprehensive review of existing mathematical models and simulations of drug release from polymeric microspheres and of drug transport in adjacent tissues. In drug delivery systems, mathematical modeling plays an important role in elucidating the important drug release mechanisms, thus facilitating the development of new pharmaceutical products by a systematic, rather than trial-and-error, approach. The mathematical models correspond to the known release mechanisms, which are classified as diffusion-, swelling-, and erosion-controlled systems. Various practical applications of these models which explain experimental data are illustrated. The effect of gamma-irradiation sterilization on drug release mechanism from erosion-controlled systems will be discussed. The application of existing models to nanoscale drug delivery systems specifically for hydrophobic and hydrophilic molecules is evaluated. The current development of drug transport modeling in tissues utilizing computational fluid dynamics (CFD) will also be described.

Bone and Bones↗
PubMed2005

Mathematical modelling of the distribution of newly formed bone in bone tissue engineering.

New bone formation in bone substitutes is usually investigated by histomorphometric global analysis. This study provides a novel mathematical modelling approach of new bone formation in the use of osteoinductive and functionalized biomaterials for bone tissue engineering. We discuss here the repartition and the probability to get new bone formation inside Biphasic Calcium Phosphate (BCP) loaded with autologous osteogenic cells, functionalized with a cyclo RGD peptide, after implantation in rabbits for 2 and 4 weeks. This local analysis allowed us to complement classical global findings and to demonstrate that after 2 weeks of implantation, the probability of new bone formation was significantly higher in RGD-grafted BCP and that new formed bone was largely distributed from the edge to the centre of the implant. While no significant differences were obtained after 4 weeks of implantation between RGD-grafted and non-grafted materials, distribution of new bone formation inside RGD-grafted materials was significantly more homogeneous as demonstrated by our mathematical modelling approach. In conclusion, local analysis of new bone formation inside macroporous substitutes coupled with mathematical modelling constitutes a potential quantitative approach for the evaluation of the osteoconductive and osteoinductive characteristics of such biomaterials.

Algorithms↗
PubMed2004

Bulletin of mathematical biology-facts, figures and comparisons.

The Society for Mathematical Biology (SMB) owns the Bulletin of Mathematical Biology (BMB). This is an international journal devoted to the interface of mathematics and biology. At the 2003 SMB annual meeting in Dundee the Society asked the editor of the BMB to produce an analysis of impact factor, subject matter of papers, submission rates etc. Other members of the society were interested in the handling times of articles and wanted comparisons with other (appropriate) journals. In this article we present a brief history of the journal and report on how the journal impact factor has grown substantially in the last few years. We also present an analysis of subject areas of published papers over the past two years. We finally present data on times from receipt of paper to acceptance, acceptance to print (and to online publication) and compare these data with some other journals.

Biometry↗
PubMed2006

A mathematical model for simulating the bone remodeling process under mechanical stimulus.

OBJECTIVES: Among the current mathematical models for bone remodeling, few can consider bone resorption due to overload. The objective of this paper is to develop a new bone remodeling model which can simulate both underload and overload resorptions that often occur in dental implant treatments. METHODS: Based on the traditional model, a new mathematical equation relating the density change rate with mechanical stimulus has been developed. The new equation contains an additional quadratic term which can produce reduction in bone density at high load levels. In addition, to fully exploit the characteristics of this model, a range of different bone remodeling behaviors were studied under the load cases with both constant and varying stress magnitudes. Finally, the model was applied in conjunction with the finite element method to a practical case of dental implant treatment. RESULTS: The FE analysis results showed that bone resorption at the neck of the implant occurred due to occlusal overload but then resorption stopped after some time before reaching the coarse threads. Meanwhile, the density of the bone deeper into the mandible increased slightly due to the additional mechanical stimulus provided by the occlusal load. This phenomenon is observable in some clinical situations. SIGNIFICANCE: The new model can describe the bone overload resorption, a feature which is absent in most of the current models. And by simulating the dental implant treatment using FE method, the ability of the new mathematical model to simulate overload bone resorption has been clearly demonstrated.

Biomechanical Phenomena↗
PubMed2006

Diffusivity and distribution of vinblastine in three-dimensional tumour tissue: experimental and mathematical modelling.

The distribution of chemotherapeutics in solid tumours is poorly understood and the contribution it makes to treatment failure is unknown. Novel approaches are required to understand how the three-dimensional organisation of cancer cells in solid tumours affects drug availability. Since convective drug transport is limited by increased interstitial pressure in poorly vascularised cancers, the aim of this study was to measure the diffusive hindrance exerted by solid tumour tissue. Multicell layer tumour models comprising DLD1 colon cancer cells were characterised and fluxes were determined for [3H]-vinblastine and [14C]-sucrose. The mathematical models provided the diffusion coefficients for both compounds and predicted higher exposure of cells in the vicinity of vessels. The diffusion of vinblastine was three times slower than that of sucrose. Although slow diffusion delays vinblastine penetration into the avascular regions of tumours, the proliferating cells are generally in the marginal area of tumours. The mathematical model that we have developed enabled accurate quantification of drug pharmacokinetic behaviour, in particular, the diffusivity of vinblastine within solid tissue. This mathematical model may be adapted readily to incorporate the influence of factors mediating pharmacokinetic drug resistance.

ATP Binding Cassette Transporter, Subfamily B, Mem↗
PubMed2005

Estimation of the mtDNA mutation rate in aging mice by proteome analysis and mathematical modeling.

The accumulation of mitochondria containing mutated genomes was proposed to be an important factor involved in aging. Although the level of mutated mtDNA has shown to increase over time, it is currently not possible to directly measure the mtDNA mutation rate within living cells. The combination of mathematical modeling and controlled experiments is an alternative approach to obtain an estimate for the mutation rate in a well-defined system. In order to judge the relevance of mitochondrial mutations for the aging process, we used a mouse model to study age-related alterations of the mitochondrial proteins. Based on these experimental data we constructed a mathematical model of the mitochondrial population dynamics to estimate mtDNA mutation rates. Mitochondria were isolated from mouse brain and liver at six different ages (newborn to 24-months). A large-gel 2D-electrophoresis-based proteomics approach was used to analyze the mitochondrial proteins. The expression of two respiratory chain complex I subunits and one complex IV subunit decreased significantly with age. One subunit of complex III and one subunit of complex V increased in expression during aging. Together, these data indicate that complex I and IV deficiency in aged tissues might be accompanied by feedback regulation of other protein complexes in the respiratory chain. When we fitted our experimental data to the mathematical model, mtDNA mutation rate was estimated to be 2.7x10(-8) per mtDNA per day for brain and 3.2x10(-9) per mtDNA per day for liver. According to our model and in agreement with the mitochondrial theory of aging, mtDNA mutations could cause the detrimental changes seen in mitochondrial populations during the normal lifespan of mice, while at the same time ensure that the mitochondrial population remains functional during the developmental and reproductive period of mice.

Aging↗
PubMed2006

Mathematical model of phosphatidylinositol-4,5-bisphosphate hydrolysis mediated by epidermal growth factor receptor generating diacylglycerol.

Phosphatidylinositol-4,5-bisphosphate (PIP2) is hydrolyzed in response to the tyrosine phosphorylation of the epidermal growth factor receptor (EGFR) and plays an important role in regulating cell proliferation and differentiation through the generation of second messengers diacylglycerol (DAG) and trisphosphate inositol (IP3) which lead to the activation of protein kinase C (PKC) and increased levels of intracellular calcium, respectively. In the paper, a mathematical model was established to simulate the accumulation of DAG due to PIP2 hydrolysis mediated by EGFR. Molecular mechanisms between DAG, PIP2, EGFR and phosphatidylinositol transfer protein (PITP) were explained successfully, and positive cooperativity which existed between phospholipase C-gamma1 (PLC-gamma1) and PIP2 was also explained. In the model the effects of parameters on simulation of PIP2 hydrolysis were analyzed and the efficacies of some molecular intervention strategies were predicted. To test the coherence between the model and the biological response to epidermal growth factor (EGF) in cells, the levels of DAG and the tyrosine phosphorylation-EGFRs in NIH3T3 mouse embryonic fibroblast (MEF) were determined by biochemical experiments which showed that the accumulation of DAG was a sigmoidal function of phosphorylation-EGFR concentration, and the consistency between the mathematical model and experimental results was confirmed. In brief, this mathematical model provided a new idea for the further study of the dynamic change of biological characteristics in inositol phospholipid hydrolysis, predicting the efficacy of molecular intervention and the relationship between the metabolisms of inositol phospholipid and other signal transduction pathways.

Animals↗
PubMed2004

Mathematical modeling of granulocyte reconstitution after high-dose chemotherapy with stem cell support: effect of post-transplant G-CSF treatment.

Cancer patients treated with high-dose chemotherapy and autotransplanted with peripheral blood progenitor cells most often reconstitute neutrophils (> 0.5 x 10(9)c/l) 8-16 days after the initiation of treatment. By means of a mathematical model of human granulopoiesis, the present work assesses the effect of administering granulocyte colony stimulating factor (G-CSF) post-transplant to reduce engraftment time, and also assesses the effect of delaying initiation of G-CSF treatment relative to a general schedule. Hematopoietic progenitor cells from 21 breast cancer patients were mobilized by chemotherapy followed by G-CSF injections. Purified CD34+ cells taken from the mobilized blood were infused 3 days after termination of chemotherapy. Patients were given subcutaneous injections of G-CSF post-transplant (5 microg/kg every 12 h). Neutrophil counts calculated from a mathematical model were compared with data from individual patients. These results were also compared with data and modeling results from a group of 19 lymphoma patients given no post-transplant G-CSF therapy. The observed engraftment times were associated with the number of CFU-GM cells in the reinfused blood graft and the administration of post-transplant G-CSF. The latter finding was most predominant in patients given < 5.0 x 10(5) CFU-GM/kg bw. These tendencies were well captured by the model. Interestingly, the model showed no major differences in time to engraft neutrophils if the initiation of G-CSF was postponed for up to 5 days after transplantation. Our findings indicate that the present mathematical model of neutrophil recovery following high-dose therapy correlates with clinical observations and can potentially be used to predict time to neutrophil recovery.

Antineoplastic Agents↗
PubMed2005

Mathematical modelling of radiotherapy strategies for early breast cancer.

Targeted intraoperative radiotherapy (Targit) is a new concept of partial breast irradiation where single fraction radiotherapy is delivered directly to the tumour bed. Apart from logistic advantages, this strategy minimizes the risk of missing the tumour bed and avoids delay between surgery and radiotherapy. It is presently being compared with the standard fractionated external beam radiotherapy (EBRT) in randomized trials. In this paper we present a mathematical model for the growth and invasion of a solid tumour into a domain of tissue (in this case breast tissue), and then a model for surgery and radiation treatment of this tumour. We use the established linear-quadratic (LQ) model to compute the survival probabilities for both tumour cells and irradiated breast tissue and then simulate the effects of conventional EBRT and Targit. True local recurrence of the tumour could arise either from stray tumour cells, or the tumour bed that harbours morphologically normal cells having a predisposition to genetic changes, such as a loss of heterozygosity (LOH) in genes that are crucial for tumourigenesis, e.g. tumour suppressor genes (TSGs). Our mathematical model predicts that the single high dose of radiotherapy delivered by Targit would result in eliminating all these sources of recurrence, whereas the fractionated EBRT would eliminate stray tumour cells, but allow (by virtue of its very schedule) the cells with LOH in TSGs or cell-cycle checkpoint genes to pass on low-dose radiation-induced DNA damage and consequently mutations that may favour the development of a new tumour. The mathematical model presented here is an initial attempt to model a biologically complex phenomenon that has until now received little attention in the literature and provides a 'proof of principle' that it is possible to produce clinically testable hypotheses on the effects of different approaches of radiotherapy for breast cancer.

Brachytherapy↗
PubMed2004

A survey of mathematical models of competition with an inhibitor.

Mathematical models of the effect of inhibitors on microbial competition are surveyed. The term inhibitor is used in a broad sense and includes toxins, contaminants, allelopathic agents, etc. This includes both detoxification where the inhibitor is viewed as a pollutant and control where the inhibitor is viewed as an aid to controlling a bioreactor. The inhibitor may be supplied externally or may be created as an anti-competitor toxin. This includes plasmid-bearing, plasmid-free competition. The literature is spread across journals in different disciplines and with different notation. The survey attempts to present the mathematical models and the results of the corresponding analysis within a common framework and notation. Detailed mathematical proofs are not given but the methods of proof are indicated, references cited, and the results presented in tables. Open problems are indicated where there is a gap in the theory.

Bioreactors↗
PubMed2006

Word organization in coding DNA: a mathematical model.

This article deals with the relationship between vocabulary (total number of distinct oligomers or "words") and text-length (total number of oligomers or "words") for a coding DNA sequence (CDS). For natural human languages, Heaps established a mathematical formula known as Heaps' law, which relates vocabulary to text-length. Our analysis shows that Heaps' law fails to model this relationship for CDSs. Here we develop a mathematical model to establish the relationship between the number of type of words (vocabulary) and the number of words sampled (text-length) for CDSs, when non-overlapping nucleotide strings with the same length are treated as words. We use tangent-hyperbolic function, which captures the saturation property of vocabulary. Based on the parameters of the model, we formulate a mathematical equation, known as "equation of word organization", whose parameters essentially indicate that nucleotide organization of coding sequences are different from one another. We also compare the word organization of CDSs with the random word distribution and conclude that a CDS is neither similar to a natural human language nor to a random one. Moreover, these sequences have their unique nucleotide organization and it is completely structured for specific biological functioning.

Base Composition↗
PubMed2005

Intraperitoneal carboplatin infusion may be a pharmacologically more reasonable route than intravenous administration as a systemic chemotherapy. A comparative pharmacokinetic analysis of platinum using a new mathematical model after intraperitoneal vs. intravenous infusion of carboplatin--a Sankai Gynecology Study Group (SGSG) study.

OBJECTIVE: To clarify the pharmacological advantage of carboplatin-based intraperitoneal chemotherapy using the three-compartment mathematical model. METHODS: Eleven consecutive patients in one institution underwent intraperitoneal administration of carboplatin, and 11 consecutive patients in another institution received intravenous administration. Carboplatin (AUC=6 mg x min/ml) was diluted in 500 ml 5% glucose and administered either as an intraperitoneal bolus infusion or intravenous drip infusion during 1 h. Patients undergoing intravenous injection also received an infusion of 500 ml 5% glucose to obtain intraperitoneal samples. Intraperitoneal fluid and blood samples were obtained, immediately and 1, 2, 4, 8, 12, and 24 h after administration. The mathematical model consisting of a three-compartment model was applied to analyze the pharmacokinetics. The model was created with simultaneous differential equations and was solved by the Runge-Kutta method. RESULTS: The rate constants of platinum diffusion from the peritoneal cavity to serum, serum to peritoneal cavity, serum to peripheral space, peripheral space to serum, and elimination were 0.94+/-0.79 (mean+/-SD), 1.28+/-2.50, 16.50+/-9.26, 0.99+/-0.62, and 4.14+/-1.45 (h-1), respectively. When the theoretical pharmacological concentration of platinum was calculated using this mathematical model, 24-h platinum AUC in the serum was exactly the same regardless of intraperitoneal or intravenous administration of carboplatin. However, the 24-h platinum AUC in the peritoneal cavity was approximately 17 times higher when carboplatin was administered by the intraperitoneal route. CONCLUSION: The present pharmacological analysis suggests that intraperitoneal infusion of carboplatin is feasible not only as an intraperitoneal regional therapy but also as a more reasonable route for systemic chemotherapy.

Antineoplastic Combined Chemotherapy Protocols↗
PubMed1998

Human amniotic fluid mathematical model: determination and effect of intramembranous sodium flux.

OBJECTIVE: A recently described mathematical model of human amniotic fluid dynamics used known and estimated rates of fetal fluid production (lung liquid and urine) and composition (osmolality) to enable calculation of previously unmeasured routes of amniotic fluid resorption, including fetal swallowing and intramembranous (across the amnion) water flow. This "osmolar" model assumed that only free water resorption occurred across the intramembranous route. We hypothesized that intramembranous flow also may include solutes and electrolytes because significant concentration gradients exist between amniotic fluid and fetal plasma. We used mass balance analysis to determine the direction and magnitude of intramembranous sodium flux and to assess the ability of a newly described "sodium" model to predict changes in amniotic fluid volume in response to changes in intramembranous electrolyte flow. Mathematical modeling was used to predict changes in amniotic fluid volume in response to changes in intramembranous electrolyte flow. STUDY DESIGN: Model predictions were calculated using published values for human amniotic fluid and fetal urine composition and volume. Ovine studies were used to derive lung fluid volumes and composition. Fetal swallowing and intramembranous flow were independently determined using net amniotic fluid osmolar (osmolality model) and sodium (sodium model) balance. Differences between osmolality and sodium model predictions were normalized to calculate the net intramembranous sodium flux, assuming a net balance of intramembranous osmotic solute flow. RESULTS: Both sodium and osmolality models predicted swallowed volume to be greater than intramembranous flow until 28 to 32 weeks' gestation, after which the relationship reversed. However, the sodium model predicted greater intramembranous flow and lower swallowing rates compared with the osmolality model at all gestational ages. Osmolar mass balance required daily intramembranous sodium flux into the amniotic fluid, which increased with gestational age. Furthermore, assuming stable swallowing and intramembranous water flow, the model predicts that 5% increases or decreases in amniotic fluid solute concentrations caused by intramembranous flux result in polyhydramnios or oligohydramnios, respectively. CONCLUSION: Sodium and osmolality models demonstrate similarities in determinations of amniotic fluid dynamics. However, mass balance equations demonstrate a net intramembranous flow of sodium into the amniotic fluid under normal conditions. Mathematical modeling suggests that small alterations in daily intramembranous sodium flux may evoke large changes in amniotic fluid volume.

Amniotic Fluid↗
PubMed1962

The routine fitting of kinetic data to models: a mathematical formalism for digital computers.

A mathematical formalism is presented for use with digital computers to permit the routine fitting of data to physical and mathematical models. Given a set of data, the mathematical equations describing a model, initial conditions for an experiment, and initial estimates for the values of model parameters, the computer program automatically proceeds to obtain a least squares fit of the data by an iterative adjustment of the values of the parameters. When the experimental measures are linear combinations of functions, the linear coefficients for a least squares fit may also be calculated. The values of both the parameters of the model and the coefficients for the sum of functions may be unknown independent variables, unknown dependent variables, or known constants. In the case of dependence, only linear dependencies are provided for in routine use. The computer program includes a number of subroutines, each one of which performs a special task. This permits flexibility in choosing various types of solutions and procedures. One subroutine, for example, handles linear differential equations, another, special non-linear functions, etc. The use of analytic or numerical solutions of equations is possible.

Biophysical Phenomena↗
PubMed1997

Compartmentalized energy transfer in cardiomyocytes: use of mathematical modeling for analysis of in vivo regulation of respiration.

The mathematical model of the compartmentalized energy transfer system in cardiac myocytes presented includes mitochondrial synthesis of ATP by ATP synthase, phosphocreatine production in the coupled mitochondrial creatine kinase reaction, the myofibrillar and cytoplasmic creatine kinase reactions, ATP utilization by actomyosin ATPase during the contraction cycle, and diffusional exchange of metabolites between different compartments. The model was used to calculate the changes in metabolite profiles during the cardiac cycle, metabolite and energy fluxes in different cellular compartments at high workload (corresponding to the rate of oxygen consumption of 46 mu atoms of O.(g wet mass)-1.min-1) under varying conditions of restricted ADP diffusion across mitochondrial outer membrane and creatine kinase isoenzyme "switchoff." In the complete system, restricted diffusion of ADP across the outer mitochondrial membrane stabilizes phosphocreatine production in cardiac mitochondria and increases the role of the phosphocreatine shuttle in energy transport and respiration regulation. Selective inhibition of myoplasmic or mitochondrial creatine kinase (modeling the experiments with transgenic animals) results in "takeover" of their function by another, active creatine kinase isoenzyme. This mathematical modeling also shows that assumption of the creatine kinase equilibrium in the cell may only be a very rough approximation to the reality at increased workload. The mathematical model developed can be used as a basis for further quantitative analyses of energy fluxes in the cell and their regulation, particularly by adding modules for adenylate kinase, the glycolytic system, and other reactions of energy metabolism of the cell.

Adenosine Diphosphate↗
PubMed2002

A mathematical formula to calculate the theoretical range of motion for total hip replacement.

The reduced range of motion (ROM) resulting from total hip replacement (THR) leads to frequent prosthetic impingement, which may restrict activities of daily living and cause subluxation and dislocation. Therefore, to know the ROM of THR is very important in clinical situations and in the design of prostheses. THR involves a pure ball and socket joint. We created a mathematical formula to calculate the theoretical ROM of THR limited by the prosthetic impingement. The ROM of THR is governed by the following five factors, (1) The prosthetic ROM (oscillation angle: obtained from company data), (2) cup abduction (3) cup anterior opening, (4) the angle of the femoral neck component from the horizontal plane, and (5) the femoral neck anteversion. The last 4 factors are able to be obtained from anterior-posterior, axial X-rays and CT of the patient's THR. The objective was to create mathematical formulas that could accurately and quickly calculate the ROM of THR. By entering the five values into a computer programmed with the formulas, one could obtain the ROM for the THR. This reveals the effect on ROM of the oscillation angle and the interaction of ROM with cup abduction, anterior opening and neck anteversion. Furthermore this readily would enable a clinical evaluation of the possibility of postoperative dislocation and help in postoperative rehabilitation. The calculated numerical values of ROM by these mathematical formulas were successfully compared with the ROMs obtained from 3-dimensional computer graphics (3D-CG).

Biomechanical Phenomena↗
PubMed2003

Direct comparison of calculated hip joint contact forces with those measured using instrumented implants. An evaluation of a three-dimensional mathematical model of the lower limb.

Characterisation of hip joint contact forces is essential for the definition of hip joint prosthesis design requirements. In vivo hip joint contact force measurements have been made using instrumented hip joint prostheses. However, to allow determination of the range of values of joint contact force and their directions relative to anatomical structures in a range of subject groups sufficient to form an agreed data base it is necessary to adopt a different approach without the use of an implanted transducer. The use of mathematical models of the lower limb to examine the forces in soft tissues and at the joints has provided valuable insight into internal loading conditions. Several authors have proposed mathematical musculo-skeletal models. However, there have been only limited attempts at validation of these models. It is possible to use the results of in vivo force measurements from instrumented prostheses to validate the results calculated using the mathematical models. In this study two subjects with instrumented hip joint prostheses were studied. Forces at the hip joints were calculated using a three-dimensional model of the leg. Walking at slow, normal and fast speeds (0.97-2.01m/s), weight transfer from two to one leg and back again, and sit to stand were studied. Direct comparisons were made between the 'gold standard' measured hip joint contact forces and the calculated forces. There was general agreement between the calculated and measured forces in both pattern and magnitude. There were, however, discrepancies. Reasons for these differences in results are discussed and possible model developments suggested.

Computer Simulation↗
PubMed2003

Formulation of a mathematical model to predict solar water disinfection.

A mathematical model was formulated that will facilitate the prediction of solar disinfection by analyzing the effect of sunlight exposure (x(1)) and the load of bacterial contamination (x(2)), as predictor variables, on the efficiency of solar disinfection (y). Aliquots of 0.1 ml containing average numbers of E. coli, ranging between 1 and 5 x 10(3)cells/ml raw water, were introduced into each of the 96 wells of polystyrene microtitre plates. Plates, with the lid on, were exposed to sunlight for varying exposures ranging between 1.04 x 10(3) and 8.40 x 10(3)kJ m(-2). Double strength nutrient broth was then added. After 48 h incubation wells containing visible contamination were considered as containing one cell or more that survived the exposure. Data showed that disinfection is dependent both on the load of bacterial contamination and sunlight exposure. This relationship is characterized by curves having shoulders followed by a steep decline and then tailing off in an asymptotic fashion. The shoulder size increased with the increase of the contamination load, however, the slope remains the same. Statistical analysis indicates a positive correlation among the variables (R(2) = 0.893); the mathematical model, y=1-(1-e(-kx(1)))(x(2)), represents the relationship, with k being the solar inactivation constant. The exposure required to produce a given decontamination level can be predicted using the equation: x(1)=-1/kln[1-(1-y)(-1/x(2))]e(-micro/rho.m/A), where micro is the linear attenuation coefficient (m(-1)), rho is the density, m is the mass and A is the area of the exposed part of the sample. The predictor variables (x(1), x(2)) strongly influence the efficiency of solar disinfection, which can be predicted using the suggested mathematical model. The present data provides a means to predict the efficiency of solar disinfection as an approach to improve the quality of drinking water mainly in developing countries with adequate sunshine all year-round.

Disinfection↗