Biexponential Equation Research Articles

Study of phosphate sorption on rendzina soil by heterogeneous isotopic exchange: a biexponential kinetic model

Phosphate sorption on rendzina soil was studied by P-32 heterogeneous isotopic exchange under a steady-state. There are two types of sorbed phosphate, namely strongly and weakly bonded phosphate, the latter being able to exchange with phosphate (H232PO4−) ions in the soil solution. The experimental kinetic data was not fitted by the one exponential kinetic model. Starting from this observation, a new kinetic model is established by assuming two types of weakly bonded phosphate, which take part in the two parallel exchange processes. A biexponential kinetic equation is obtained, which fits the experimental data much better than the one exponential equation.Graphical abstract

Histopathological graded liver lesions: what role does the IVIM analysis method have?

This study aims to investigate three different image processing methods on quantitative parameters of IVIM sequence, as well as apparent diffusion coefficients and simple perfusion fractions, for benign and malignant liver tumors. IVIM images with 8 b-values (0-1000s/mm2) and 1.5T MRI scanner in 16 patients and 3 healthy people were obtained. Next, the regions of interest were selected for malignant, benign, and healthy liver regions (50, 56, and 12, respectively). Then, the bi-exponential equation of the IVIM technique was fitted with two segmented fitting methods as well as one full fitting method (three methods in total). Using the segmented fitting method, diffusion coefficient (D) is fixed with a mono-exponential equation with b-values that are greater than 200s/mm2. The perfusion fraction (f) can then be calculated by extrapolating, as the first method, or fitting simultaneously with the pseudo-diffusion coefficient (D*) as the second method. In the full fitting method, as the third method, all IVIM parameters were obtained simultaneously. The mean values of parameters from different methods were compared in different grades of lesions. Our results indicate that the image processing method can change statistical comparisons between different groups for each parameter. The D value is the only quantity in this technique that does not depend on the fitting process and can be used as an indicator of comparison between studies (P < 0.05). The most effective method to distinguish liver lesions is the extrapolated f method (first method). This method created a significant difference (P < 0.05) between the perfusion parameters between benign and malignant lesions. Using extrapolated f is the most effective method of distinguishing liver lesions using IVIM parameters. The comparison between groups does not depend on the fitting method only for parameter D.

Molecular-Level Photo-Orientation Insights into Macroscopic Photo-Induced Motion in Azobenzene-Containing Polymer Complexes.

As part of continuing efforts to deepen the understanding of photo-induced mass transport in azo-containing polymers, we compared the diffraction efficiency (DE) during surface-relief grating (SRG) inscription, photo-induced molecular orientation (<P2>), and thermal stability in two sets of supramolecular azopolymer complexes, namely, hydrogen-bonded (H-bonded) and ionically bonded (i-bonded) complexes, both as a function of the polymer degree of polymerization (DP). To that end, poly(4-vinylpyridine) (P4VP) polymers with DPs of 41, 480, and 1900 were H-bonded at an equimolar ratio with 4-hydroxy-4'-dimethylaminoazobenzene (azoOH), and the fully quaternized derivatives of the three P4VPs (P4VPMe) were i-bonded via ion exchange to sodium 4-[(4-dimethylamino)-phenylazo]benzene sulfonate (azoSO3), also known as methyl orange, where the OH functionality of azoOH is replaced by a sulfonate group. The i-bonded complexes show much better DE performances and <P2> levels than those of H-bonded complexes, which we relate to the liquid crystal structure of the former complexes. Fitting the <P2> curves by a biexponential equation leads to two parameters associated with a fast trans-cis or angular hole burning (AHB) process and a slow angular redistribution (AR) process of the azo, respectively. It is found that AHB is predominant in the H-bonded complexes, whereas the AR contribution is much greater in the i-bonded complexes, assuring their superior SRG efficiency that is enabled by the anisotropic free volume created mainly by the AR process. In each set of complexes, the SRG efficiency is much better for the lowest DP complex, while the AR contribution is constant (and low) for the H-bonded complexes and increases roughly linearly with the decrease in DP for the i-bonded complexes. The latter difference might be related to the presence of entanglements in the complexes with DPs 480 and 1900, which slow down the macroscopic movement during SRG inscription but not the molecular-scale movement in photo-orientation.

Derivation of pesticide aged sorption parameters from laboratory incubation data

The results of the incubation laboratory experiment showed that the decomposition of cyantraniliprole is bi-phasic and the rapid decomposition in the period after the application of the pesticide is accompanied by a subsequent slowdown of this process. The use of the biexponential equation increased the accuracy of the description of the dynamics of decomposition of cyantraniliprole, as evidenced by the static indices. The bi-exponential equation coefficients were used to calculate the parameters of non-equilibrium sorption. The obtained parameters served as input data for the PEARL model. Modelling the migration of cyantraniliprole with considering aged sorption, showed a significant decrease in the predicted concentrations of the pesticide in percolate.

Fouling characterization during initial stage of cross-flow ultrafiltration

Ultrafiltration (UF) membrane is an attractive pretreatment technology used in desalination water system. However, the unavoidable membrane fouling over time is the key problem in the development of this technology. Fouling evaluation in the initial stage may provide relevant information about the fouling tendencies. In this work, the extent of fouling was investigated through a new method allows evaluating the fouling in cross-flow UF in the initial filtration stage. An empirical adjustment of flux decline data based on a bi-exponential equation with 4 coefficients is proposed for determining the Rcfi and RV − CF parameters. The first parameter Rcfi is defined as the initial cross-flow resistance. The second parameter RV − CF is defined as increasing resistance per specific volume of permeate in cross-flow. The measurement of the fouling parameters is evaluated in a laboratory facility with the following established conditions: (1) operation in cross-flow mode and (2) a flow measurement period limited to roughly 1 h. The procedure is intended to detect two different flow decline zones with different fouling processes at the initial stage of cross-flow filtration. The method applicability was tested with two cellulosic membranes of 10 kDa and 20 kDa and solutions of 4 kDa and 35 kDa polyethylene glycol (PEG) and alginate at different concentrations. In the case of the Rcfi parameter, the results show measurable values with high colloidal concentration of PEG. The RV − CF results shows a sensitive increase with foulant concentration, in different degree, depending on the type of solution and membrane used.

Effect of different application rates of metamitron as fruitlet chemical thinner on thinning efficacy and fluorescence inhibition in Gala and Fuji apple

Crop thinning is an important and difficult agricultural practice. Knowing the effect of the application dose of a product is a crucial element of any thinning program. The aims of this study were to investigate the effect of different metamitron doses on Gala and Fuji apples applied at fruit king diameters of between 8 and 10 mm and to determine fluorescence inhibition at the different application rates. Trials were conducted over two seasons from 2015 to 2016 in apple orchards in Lleida (Spain). Photosynthesis inhibition caused by metamitron was also analysed and measured, using chlorophyll fluorescence and biexponential pharmacokinetic models. Under the trial conditions, the application of metamitron reduced final fruit set, number of fruits per tree and crop load depending on the application rate. A dose effect was observed in all yield parameters. Moreover, when metamitron showed high efficacy, there was an improvement in fruit weight, coloration and diameter. The estimated parameters A, α and B using a biexponential equation were related with final fruit set, however the period of inhibition has to be finished before prediction can be made of metamitron efficacy in the year. The fluorescence analysis showed a dose effect, with metamitron dose increasing inhibition. Additionally, the same result was also observed in the area under curve analysis, with metamitron dose reducing the area and inhibition increasing. In all yield parameters, the fluorescence and area under curve analyses showed differences between cultivars, with the inhibition caused by metamitron higher in Gala than in Fuji. Moreover, differences between years were observed. 2015 was warmer than 2016, and the higher temperatures increased the thinning efficacy of metamitron.

Characterization of lower limb muscle activation patterns during walking and running with Intravoxel Incoherent Motion (IVIM) MR perfusion imaging

BackgroundThe distribution of energy use among different lower limb muscles during walking and running is not well understood. Local blood flow within skeletal muscle tissue depends on its metabolic activity during activation. The non-invasive magnetic resonance microvascular perfusion method Intravoxel Incoherent Motion (IVIM) is able to quantify muscle activation. PurposeTo non-invasively determine quantitative changes in local microvascular perfusion and blood flow via IVIM in order to characterize specific muscle activation of the lower limb at rest, during walking and during running. Methods3 T MR IVIM diffusion-weighted images of N = 16 lower extremities (bilateral imaging of n = 8 healthy volunteers; mean age 27.5 ± 5.7 years) were acquired at rest and immediately after walking and running for 15 min, respectively. A transverse monopolar pulsed gradient fat suppressed spin echo EPI sequence was used (9 b-values from 0 to 1000s/mm2, 3 orthogonal directions). Anatomical transverse T1-weighted turbo SE images were acquired at rest. Muscles at the pelvis, thigh and lower leg were segmented. IVIM perfusion parameters f, D* and fD* and the diffusion coefficient D were obtained after standard two-steps fitting of the IVIM bi-exponential signal equation. Descriptive statistics, t-tests, Pearson's correlations and Partial Spearman correlations were used for statistical analyses. ResultsThe microvascular blood flow (fD*) increased significantly and stepwise from rest (1.65 ± 0.83*10−3 mm2/s) to walking (1.99 ± 0.80*10−3 mm2/s, P < 0.001) and running (2.18 ± 0.98*10−3 mm2/s, P < 0.001). The perfusion increase was most pronounced for lower leg and feet muscles (P < 0.001). Hamstring muscles showed a higher microvascular perfusion increase than quadriceps muscles (P < 0.05). A higher increase of the heartrate from walking to running correlated significantly with a lower increase of fD* from walking to running (R = -0.16, P = 0.001). ConclusionIVIM MRI quantitatively measures local microvascular muscle perfusion to detect muscle activation patterns through walking and running. A redistribution of blood flow towards the lower leg was observed during running as compared to walking.

Brevis thinning efficacy at different fruit size and fluorescence on ‘Gala’ and ‘Fuji’ apples

Brevis thinning efficacy depends on climatic and cultivar conditions. The objective of this work was to evaluate the efficacy of one application of Brevis in ‘Gala’ and ‘Fuji’ apple applied at different fruit sizes (fruit king diameter ranging between 6.5 and 21.5 mm) and to determine which fruit diameters were most sensitive to Brevis application. Trials were conducted over two seasons from 2015 to 2016 in apple orchards in Lleida (Spain). Photosynthesis inhibition caused by Brevis was also analysed and measured, using chlorophyll fluorescence and biexponential pharmacokinetic models. In 2016, for all Brevis treatments and an untreated control, quantum yield (Qy) was measured in all leaves in different shoots, with photosynthesis inhibition and its evolution analysed in three sections (closest to branch, mid-shoot and vegetative section). Under the trial conditions, Brevis thinning effect was observed at king fruit diameters from 9 to 19 mm, with maximum efficacy observed in the 11.5–14 mm range. However, susceptibility to Brevis differed between varieties and years. The fluorescence analysis using a biexponential equation showed adequate fits and the calculated values correlated well with the measured Qy(%) values. The area under curve per day analysis showed that, at the same application dose, fluorescence inhibition decreased with increasing fruit diameter. The fluorescence analysis of shoot sections four days after Brevis application showed differences between varieties, with the inhibition caused by Brevis higher in ‘Gala’ than in ‘Fuji’. However, this analysis showed no significant differences in ‘Gala’, with all sections showing similar inhibition (27%–35%). By contrast, ‘Fuji’ showed different inhibition values in the different sections. The vegetative section showed the significantly highest inhibition, and the zone nearest the branch the lowest.

Co-encapsulation of acyclovir and curcumin into microparticles improves the physicochemical characteristics and potentiates in vitro antiviral action: Influence of the polymeric composition

The present study developed and characterized microparticles formulations containing acyclovir and curcumin co-encapsulated in order to overcome the biopharmaceutical limitations and increase the antiviral effect of both drugs. The microparticles were prepared by a spray drying methodology following the ratio 1:3 (drug:polymer), which were made by hydroxypropylmethylcellulose (HPMC) and/or Eudragit® RS100 (EUD). The MP-1 formulation was composed of HPMC and EUD (1:1), MP-2 formulation was composed only of HPMC and MP-3 formulation was composed only of EUD. All formulations showed yielding around 50% and acceptable powder flowability. Drug content determination around 82.1–96.8% and 81.8–87% for acyclovir and curcumin, respectively. The microparticles had spherical shape, size within 11.5–15.3 μm, unimodal distribution and no chemical interactions among the components of the formulations. Of particular importance, the polymeric composition considerably influenced on the release profile of the drugs. The in vitro release experiment demonstrated that the microencapsulation provided a sustained release of acyclovir as well as increased the solubility of curcumin. Besides, mathematical modeling indicated that the experimental fit biexponential equation. Importantly, drugs microencapsulation promoted superior antiviral effect against BoVH-1 virus in comparison to their free form, which could be attributed to the improvement in the aforementioned physicochemical parameters. Therefore, these formulations could be promising technological drug carriers for acyclovir and curcumin, which highlight the great offering a potential alternative treatment for viral herpes.

Temperature effect on electrical characteristics of negative DC corona charged polyimide films

The study of the effect of sample temperature on the electric properties of PI films has been investigated. Surface potential decay (SPD) measurements on PI (Kapton HN, thickness: 50 μm) films were measured, after negative corona discharge, as a function of sample temperature varying from 27 to 80 °C. The measurements showed significant increase in the SPD rate with increasing sample temperature. Surface potential profile, return potential appearing after charge neutralization and charging current characteristics have been experimentally recorded for different sample temperatures in order to interpret SPD evolution at high sample temperature. The SPD curves were analyzed by fitting a bi-exponential decay Equation according to the presence of two different decay mechanisms related to shallow and deep traps. The distributions of trapped charges are obtained for different sample temperatures.

Proton-Assisted Recoupling (PAR) in Peptides and Proteins.

Proton-assisted recoupling (PAR) is examined by exploring optimal experimental conditions and magnetization transfer rates in a variety of biologically relevant nuclear spin-systems, including simple amino acids, model peptides, and two proteins-nanocrystalline protein G (GB1), and importantly amyloid beta 1-42 (M0Aβ1-42) fibrils. A selective PAR protocol, SUBPAR (setting up better proton assisted recoupling), is described to observe magnetization transfer in one-dimensional spectra, which minimizes experiment time (in comparison to two-dimensional experiments) and thereby enables an efficient assessment of optimal PAR conditions for a desired magnetization transfer. In the case of the peptide spin systems, experimental and simulated PAR data sets are compared on a semiquantitative level, thereby elucidating the interactions influencing PAR magnetization transfer and their manifestations in different spin transfer networks. Using the optimum Rabi frequencies determined by SUBPAR, PAR magnetization transfer trajectories (or buildup curves) were recorded and compared to simulated results for short peptides. PAR buildup curves were also recorded for M0Aβ1-42 and examined conjointly with a recent structural model. The majority of salient cross-peak intensities observed in the M0Aβ1-42 PAR spectra are well-modeled with a simple biexponential equation, although the fitting parameters do not show any strong correlation to internuclear distances. Nevertheless, these parameters provide a wealth of invaluable semiquantitative structural constraints for the M0Aβ1-42. The results presented here offer a complete protocol for recording PAR 13C-13C correlation spectra with high-efficiency and using the resulting information in protein structural studies.

Magnetic resonance spin-spin relaxation time estimation in a rat model of fatty liver disease.

To compare mono- and bi-exponential relaxation model equations to discriminate between normal and fatty liver disease. Six rats on a choline deficient amino acid modified (CDAA) diet and six on normal chow were studied. Multiple spin echo images with increasing echo times (TEs) were collected at 9.4T. Pixel-wise T2 maps were generated using mono-exponential decay function to calculate T2M , and a bi-exponential to calculate, short T2 component (T2S ), long T2 component (T2L ), and fractions of these components (ρS , ρL ), respectively. Statistical F-tests and Akaike's information criterion (AIC) were used to assess the relative performance of the two models. F-test and AIC showed that in the CDAA group, T2 bi-exponential model described the signal of T2 weighted imaging of the liver better than the mono-exponential model. Controls were best described by the mono-exponential model. Mean values for T2M , T2L , T2S , ρS , ρL were 31.2 ± 0.7 ms, 72.8 ± 3.3 ms, 8.2 ± 0.6 ms,71.2 ± 2.1%, 30.4 ± 1.3%, respectively, in CDAA rats, compared with 18.8 ± 0.5 ms, 32.3 ± 0.7 ms, 9.2 ± 1.8 ms, 79 ± 2%, 21.0 ± 1.1% in controls. In the fatty liver of CDAA rats we have shown that T2 weighted images fit the bi-exponential model better than mono-exponential decays thus providing a better description of the data. 1 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2018;47:468-476.

Kozeny–Carman permeability relationship with disintegration process predicted from early dissolution profiles of immediate release tablets

This study was oriented toward the disintegration profiling of the diclofenac sodium (DS) immediate-release (IR) tablets and development of its relationship with medium permeability kperm based on Kozeny–Carman equation. Batches (L1–L9) of DS IR tablets with different porosities and specific surface area were prepared at different compression forces and evaluated for porosity, in vitro dissolution and particle-size analysis of the disintegrated mass. The kperm was calculated from porosities and specific surface area, and disintegration profiles were predicted from the dissolution profiles of IR tablets by stripping/residual method. The disintegration profiles were subjected to exponential regression to find out the respective disintegration equations and rate constants kd. Batches L1 and L2 showed the fastest disintegration rates as evident from their bi-exponential equations while the rest of the batches L3–L9 exhibited the first order or mono-exponential disintegration kinetics. The 95% confidence interval (CI95%) revealed significant differences between kd values of different batches except L4 and L6. Similar results were also spotted for dissolution profiles of IR tablets by similarity (f2) test. The final relationship between kd and kperm was found to be hyperbolic, signifying the initial effect of kperm on the disintegration rate. The results showed that disintegration profiling is possible because a relationship exists between kd and kperm. The later being relatable with porosity and specific surface area can be determined by nondestructive tests.

Highly aqueous soluble CaF2:Ce/Tb nanocrystals: effect of surface functionalization on structural, optical band gap, and photoluminescence properties.

The design of nanostructured materials with highly stable water-dispersion and luminescence efficiency is an important concern in nanotechnology and nanomedicine. In this paper, we described the synthesis and distinct surface modification on the morphological structure and optical (optical absorption, band gap energy, excitation, emission, decay time, etc.) properties of highly crystalline water-dispersible CaF2:Ce/Tb nanocrystals (core-nanocrystals). The epitaxial growth of inert CaF2 and silica shell, respectively, on their surface forming as CaF2:Ce/Tb@CaF2 (core/shell) and CaF2:Ce/Tb@CaF2@SiO2 (core/shell/SiO2) nanoarchitecture. X-ray diffraction and transmission electron microscope image shows that the nanocrystals were in irregular spherical phase, highly crystalline (~20 nm) with narrow size distribution. The core/shell nanocrystals confirm that the surface coating is responsible in the change of symmetrical nanostructure, which was determined from the band gap energy and luminescent properties. It was found that an inert inorganic shell formation effectively enhances the luminescence efficiency and silica shell makes the nanocrystals highly water-dispersible. In addition, Ce3+/Tb3+-co-doped CaF2 nanocrystals show efficient energy transfer from Ce3+ to Tb3+ ion and strong green luminescence of Tb3+ ion at 541 nm(5D4→7F5). Luminescence decay curves of core and core/shell nanocrystals were fitted using mono and biexponential equations, and R 2 regression coefficient criteria were used to discriminate the goodness of the fitted model. The lifetime values for the core/shell nanocrystals are higher than core-nanocrystals. Considering the high stable water-dispersion and intensive luminescence emission in the visible region, these luminescent core/shell nanocrystals could be potential candidates for luminescent bio-imaging, optical bio-probe, displays, staining, and multianalyte optical sensing. A newly designed CaF2:Ce/Tb nanoparticles via metal complex decomposition rout shows high dispersibility in aqueous solvents with enhanced photoluminescence. The epitaxial growth of inert CaF2 shell and further amorphous silica, respectively, enhanced their optical and luminescence properties, which is highly usable for luminescent biolabeling, and optical bioprobe etc.

A Simplified Model for Intravoxel Incoherent Motion Perfusion Imaging of the Brain.

Despite a recent resurgence, intravoxel incoherent motion MRI faces practical challenges, including limited SNR and demanding acquisition and postprocessing requirements. A simplified approach using linear fitting of a subset of higher b-values has seen success in other organ systems. We sought to validate this method for evaluation of brain pathology by comparing perfusion measurements using simplified linear fitting to conventional biexponential fitting. Forty-nine patients with gliomas and 17 with acute strokes underwent 3T MRI, including DWI with 16 b-values (range, 0-900 s/mm2). Conventional intravoxel incoherent motion was performed using nonlinear fitting of the standard biexponential equation. Simplified intravoxel incoherent motion was performed using linear fitting of the log-normalized signal curves for subsets of b-values >200 s/mm2. Comparisons between ROIs (tumors, strokes, contralateral brain) and between models (biexponential and simplified linear) were performed by using 2-way ANOVA. The root mean square error and coefficient of determination (R2) were computed for the simplified model, with biexponential fitting as the reference standard. Perfusion maps using simplified linear fitting were qualitatively similar to conventional biexponential fitting. The perfusion fraction was elevated in high-grade (n = 33) compared to low-grade (n = 16) gliomas and was reduced in strokes compared to the contralateral brain (P < .001 for both main effects). Decreasing the number of b-values used for linear fitting resulted in reduced accuracy (higher root mean square error and lower R2) compared with full biexponential fitting. Intravoxel incoherent motion perfusion imaging of common brain pathology can be performed by using simplified linear fitting, with preservation of clinically relevant perfusion information.

Cerebral perfusion measurement in brain death with intravoxel incoherent motion imaging

The assessment of brain death can be challenging in critically ill patients, and cerebral perfusion quantification might give information on the brain tissue viability. Intravoxel incoherent motion perfusion imaging is a magnetic resonance imaging technique, which extracts perfusion information from a diffusion-weighted sequence, and provides local, microvascular perfusion assessment without contrast media injection. Diffusion weighted images were acquired with 16 b-values (0–900 s/mm2) in the brain in two patients with cerebral death, confirmed by clinical assessment and evolution, as well as in two age-matched healthy subjects. The intravoxel incoherent motion perfusion fraction maps were obtained by fitting the bi-exponential signal equation model. 8 regions of interest were drawn blindly in the brain neocortex (in the frontal, temporal, parietal, and occipital lobes on both sides) and perfusion fractions were compared between patients with cerebral death and healthy control. Statistical significance was assessed using two-sided Wilcoxon signed rank test, and set to α < 0.05. Intravoxel incoherent motion (IVIM) perfusion fraction was vanishing in the brain of the two patients with cerebral brain death compared to the healthy controls. Mean (± standard deviation) cortex perfusion fraction was 0.016 ± 0.005 respectively 0.005 ± 0.008 in the cerebral death patients, compared to respectively 0.052 ± 0.021 (p = 0.02) and 0.071 ± 0.042 (p = 0.008) in the age-matched controls. Intravoxel incoherent motion perfusion imaging is a promising tool to assess local brain tissue viability in critically ill patients.

Measurement of the Radiation Dose Rates of Patients Receiving Treatment with I-131 Using Telescopic Radiation Survey Meter

Introduction In order to discharge the patients receiving treatment with large radiation doses of 131I for thyroid cancer, it is necessary to measure and evaluate the external dose rates of these patients. The aim of the study was to assess a new method of external dose rate measurement, and to analyze the obtained results as a function of time. Materials and Methods In this study, a telescopic radiation survey meter was utilized to measure the external dose rates of a sample population of 192 patients receiving treatment with high-dose 131I at one, 24, and 48 hours after dose administration. Results The proposed technique could reduce the occupational radiation exposure of the physicist by a factor of 1/16. Moreover, the external dose rates of both genders rapidly decreased with time according to bi-exponential equations, which could be attributed to the additional factors associated with iodine excretion, as well as the physiology of the body in terms of 131I uptake. Conclusion According to the results of this study, telescopic radiation survey meter could be used to measure the external dose rates of patients receiving treatment with 131I. Furthermore, the average difference in the radiation exposure between female and male patients was calculated to be less than 17%.

Viscosity–temperature relationship of lipid‐based excipients amenable for spray congealing: Derivation of a rheological parameter with good correlation to particle size

The objective of this paper was to investigate the viscosity‐temperature relationship of lipid‐based materials (fatty alcohol, fatty acid, fatty ester and glycerides) amenable for spray congealing. The flow properties and viscosity–temperature relationship of cetyl alcohol, stearic acid, myristyl myristate, glyceryl monostearate, glyceryl dibehenate, hydrogenated soybean oil, hydrogenated vegetable oil and hydrogenated cottonseed oil were investigated using continuous ramping and temperature ramping tests. The viscosity–temperature data obtained was fitted into two existing viscosity–temperature models as well as a series of mathematical functions. The peak melting points of the materials were established by differential scanning calorimetry. Morphology and size of the spray‐congealed microparticles were analysed by scanning electron microscopy and laser diffractometry. Correlation analyses were conducted to explore the relationship between viscosity and microparticle median size. When molten, all eight lipid‐based materials used were Newtonian liquids. Viscosity of these materials decreased in a biphasic manner with increasing temperature which fitted a simple biexponential equation. The viscosity–temperature curves showed distinct transition points, from which mathematical manipulations generated a new rheological parameter termed Tp. Compared to the conventionally used viscosity values at spraying temperature, the Tp values of materials showed a stronger correlation with the median size of spray‐congealed microparticles produced.Practical applications: From this work, a new temperature‐independent constant (Tp) unique to each lipid‐based material was derived and found to have good correlation with the resultant spray‐congealed microparticle median size. This work aims to introduce Tp as a viable parameter of the rheology of lipid‐based materials for optimisation of formulation in spray congealation. Besides spray congealing, the application of Tp may be extended to other melt processes, such as melt granulation, melt extrusion and hot melt coating.(A) A typical biexponential temperature ramping curve showing the location of the characteristic transition point (Tp). (B) Graph of median size (μm) of spray‐congealed microparticles against Tp values.

Mathematical approach for understanding deagglomeration behaviour of drug powder in formulations with coarse carrier

Deagglomeration of cohesive particles in combination with coarse carrier is a key requirement for inhaled formulations. The aim of the project was to propose a mathematical approach to understand aerosolization behaviour of micronized particles alone and in formulation with carriers. Salbutamol sulphate and salmeterol xinafoate were blended separately with fine lactose (ratio 1:4) and fine and coarse lactose (1:4:63.5). Laser diffraction was employed to characterize the powder median particle size. The deagglomeration of micronized materials followed an asymptotic monoexponential relationship. When the coarse lactose was added, the relationship fitted a bi-exponential equation showing an easily and a poorly dispersed fraction. Using model hydrophobic and hydrophilic APIs, this study has demonstrated the utility of an analytical approach that can parameterize deagglomeration behaviour of carrier-free and carrier-based inhalation formulations. The analytical approach provides the ability to systematically study the effect of material, formulation and processing factors on deagglomeration behaviour.

Quantitative Ultrasound Molecular Imaging

Ultrasound molecular imaging using targeting microbubbles is predominantly a semi-quantitative tool, thus limiting its potential diagnostic power and clinical applications. In the work described here, we developed a novel method for acoustic quantification of molecular expression. E-Selectin expression in the mouse heart was induced by lipopolysaccharide. Real-time ultrasound imaging of E-selectin expression in the heart was performed using E-selectin-targeting microbubbles and a clinical ultrasound scanner in contrast pulse sequencing mode at 14 MHz, with a mechanical index of 0.22–0.26. The level of E-selectin expression was quantified using a novel time–signal intensity curve analytical method based on bubble elimination, which consisted of curve-fitting the bi-exponential equation Itissue(t)=Afe−λft+Are−λrt to the elimination phase of the myocardial time–signal intensity curve. Ar and Af represent the maximum signal intensities of the retained and freely circulating bubbles in the myocardium, respectively; λr and λf represent the elimination rate constants of the retained and freely circulating bubbles in the myocardium, respectively. Ar correlated strongly with the level of E-selectin expression (|r|>0.8), determined using reverse transcriptase real-time quantitative polymerase chain reaction, and the duration of post-lipopolysaccharide treatment—both linearly related to cell surface E-selectin protein (actual bubble target) concentration in the expression range imaged. Compared with a conventional acoustic quantification method (which used retained bubble signal intensity at 20 min post-bubble injection), this new approach exhibited greater dynamic range and sensitivity and was able to simultaneously quantify other useful characteristics (e.g., the microbubble half-life). In conclusion, quantitative determination of the level of molecular expression is feasible acoustically using a time–signal intensity curve analytical method based on bubble elimination.