Quasi-steady State Conditions Research Articles

Optimization of cooling process under varied pulsed conditions in multi-stage thermoelectric systems

This paper addresses the issue of thermoelectric cooling in a pulsed quasi-steady state (repetitive) condition. This situation occurs, for example, for an electronic integrated circuit performing demanding tasks in a discontinuous manner. Using heat reservoirs of selected capacity that are part of the thermoelectric system and appropriate shaping of the time profile of the supplied electrical current, cooling temperatures not achievable in the steady state for the system can be reached in a pulsed manner for a specified period. This process is subject to optimisation. The analysis was carried out for a two-stage system with an internal (interstage) heat reservoir of a given thermal capacity. The aim of the study was to find the relationship between the level of the supercooling temperature, its repeatability and the ability to maintain this temperature for a given time. To this end, two supply current waveforms were adopted and optimised both without and with contact thermal resistance in the system. The lowest subcooling temperature of about 7 K lower than the steady-state temperature was obtained for a very long period and a very short holding time. Decreasing the period or increasing the holding time results in a non-linear increase in temperature. Similar effects are obtained for the contact thermal resistance present in each layer. A full map of the period-thermal resistance–temperature relationship was determined, as well as the supercooling potential curves.

Seasonal COP of a residential magnetocaloric heat pump based on MnFePSi

The performance of a magnetocaloric heat pump (MCHP) consisting of active magnetocaloric regenerators (AMR) of 12 layers of MnFePSi magnetocaloric materials (MCM) with a linear distribution of Curie temperatures was investigated using a 1D numerical model. The model predicted the heating power and coefficient of performance (COP) of the AMR for a fixed temperature span of 27K, between 281K and 308K, and variable flow rate and AMR cycle frequency. A maximum applied magnetic field strength of 1.4T was used. A well-insulated house with a maximum heating power demand of 3kW (under quasi steady state conditions) was considered. Ambient temperature in The Netherlands was taken as a reference for the estimation of the seasonal heating power demand. Without optimizing the design of the AMR, the model predicts a maximum single-AMR heating power equal to 43.5W when the AMR operates at 3Hz and 3Lmin-1, and a maximum COP equal to 5.8 when it operates at 1.5Hz and 1Lmin-1 Considering the maximum heating power of a single AMR, approximately 69 AMRs are needed to provide the design heating power demand of the house. It was found that it is possible to achieve an AMR seasonal COP of 5.6 by continuously adjusting the flow rate and frequency of operation of the MCHP along with the ON/OFF switching of some groups of AMRs in order to adjust the heating power of the MCHP to the heating power demand of the house.

Impact of heat infiltration on the cooling capacity evaluation of an evaporator for household refrigerator-freezers with a non-adiabatic capillary tube

This study experimentally evaluates the cooling capacity of an evaporator in household refrigerator-freezers, typically scaled in hundreds of Watts, and investigates the impact of heat infiltration from the environment. Despite the scarcity of both quantitative and qualitative research in this area, this study provides data from a lab-scaled vapor compression refrigeration system that mimics a real-world side-by-side refrigerator-freezer. Experiments were conducted under conditions reflecting the household refrigerator-freezer, yielding 74 data points under quasi-steady state conditions. Despite careful insulation, heat infiltration from the ambient to the refrigerant flow in the evaporator occurred due to the significant temperature differential, impacting the cooling capacity evaluation fatally with a heat balance error of 26%. However, when considering the effects of heat infiltration, the error in the evaporator heat balance dropped to 6% significantly. The findings highlight the sensitivity of evaporator’s cooling capacity, less than 300 W, to external thermal factors during empirical evaluation. This study underscores the challenges of heat infiltration and the importance of considering such factors when assessing evaporator cooling capacity. The provided comprehensive analyses significantly contribute to the experimental prototyping of evaporators, emphasizing the need to account for external thermal influences during the evaluation process.

Platform development for high-throughput optimization of perfusion processes:Part I: Implementation of cell bleeds in microwell plates.

The promise of continuous processing to increase yields and improve product quality of biopharmaceuticals while decreasing the manufacturing footprint is transformative. Developingand optimizing perfusion operations requires screening various parameters, which is expensive and time-consuming when using benchtop bioreactors. Scale-down models (SDMs) are the most feasible option for high-throughput data generation and condition screening. However, new SDMs mimicking perfusion are required, enabling experiments to be run in parallel. In this study, a method using microwell plates (MWP) operating in semi-perfusion mode with an implemented cell bleed step is presented. A CHO cell line was cultivated in a 24-well MWP (Vw = 1.2 mL) and grown at four high cell density (HCD) setpoints. Quasi steady-state condition was obtained by manually performing cell bleeds followed by a total medium exchange after centrifugation. Further, two HCD setpoints were scaled up (VW = 30 mL), comparing a squared six-well deepwell plate (DWP) to shake flasks (SF). This evaluation showed comparable results between systems (DWP vs.SF) and scales (MWP vs.DWP + SF). The results show that the well-plate-based methods are suitable to perform HCD and quasi steady-state cultivations providing a robust solution to industrially relevant challenges such as cell clone and media selection.

Analysis of internal flow characteristics of a multistage pump during start-up

In order to study the transient characteristics during the startup process of a multi-stage pump, the Flowmaster software was used to obtain the rotating speed and flow characteristic curves of the pump under different valve openings, and analyze its internal flow and structural characteristics based on numerical simulation. The study results indicate that the time required for the flow to reach a steady state lags significantly behind the time required for the rotational speed to reach a stable state during the initial stage of pump start-up. By comparing the pressure distributions of a multistage pump under quasi-steady state and transient conditions, it can be seen that the internal flow field evolution of the pump under transient condition during the startup process lagged behind that under quasi-steady state condition, which makes using quasi-steady state laws were not suitable for describing the changes in transient flow field. The deformation law of the first-stage impeller under stable and start-up conditions was similar. The impact of increased flow rate on deformation was relatively weak and the difference in deformation values under different flow rates was relatively small under transient condition.

Inertial Estimation in Power Grids Considering Load Contribution Based on FF-UKF

Abstract In modern power systems, the extensive integration of renewable energy sources leads to a reduction in system inertia, thereby affecting grid stability. This study proposes a novel method for estimating grid inertia, which, under quasi-steady state conditions, effectively incorporates load contribution by combining class noise signals collected by PMUs (Phasor Measurement Units) with the Forgetting Factor Unscented Kalman Filter algorithm (FF-UKF). The research initially analyzes the characteristics of various inertia sources in power systems dominated by renewable energy. Building on this, we propose a grid node equivalent inertia estimation model based on node equivalent frequency response, developing an FF-UKF-based algorithm that allows for the continuous dynamic estimation of inertia at various grid nodes. Simulation experiments conducted within the IEEE 39 bus system validate the method’s effectiveness and demonstrate the spatiotemporal distribution of grid inertia under varying levels of renewable energy penetration. This study is significant for understanding and enhancing frequency control and stability in power systems, providing key technical support for the modernization of the power system and the efficient integration of renewable energy.

Visualized investigation of a nitrogen pulsating heat pipe

This paper presents the results of a visualization study of a cryogenic pulsating heat pipe (PHP). The impact of radiation heat leakage was reduced by minimizing optical windows. Visual images of the adiabatic section of a 2-turn PHP with nitrogen as working fluid were obtained at a filling ratio of 50 % and an inclination angle of 90°. The lengths of the evaporator, adiabatic section, and condenser were 50 mm, 100 mm, and 50 mm, respectively. The adiabatic section was made of quartz, whereas the evaporator and condenser were made of stainless-steel capillaries soldered onto copper plates. The flow channel of PHP was 1 mm. The fluid characteristics of the PHP under quasi-steady state conditions at different heat inputs were captured using a high-speed camera. Based on the experimental results, the evolution of flow patterns and fluid motion characteristics, and the coupling relationship between flow and heat transfer were illustrated and discussed.

Static liquefaction in the context of steady state/critical state and its application in the stability of tailings dams

Mining operations produce large quantities of tailings that must be handled and stored safely in a technical framework that reconciles economic restrictions and environmental sustainability. Unfortunately, the history of tailings deposits is marked by episodes of catastrophic failures, which is confirmed by the recent tailings dam collapses that occurred in Canada (Mount Polley), Australia (Cadia) and Brazil (Samarco and Brumadinio). Due to this alarming empirical evidence left by the mining industry worldwide, there is international concern and a demand to build these deposits safely from every point of view. In this scenario, the main geotechnical parameter that requires significant attention is the undrained residual shear strength, which is crucial to ensure the physical stability of a tailings dam. The critical state soil mechanic (CSSM) and/or the steady state of deformation provide the conceptual framework for evaluating this strength mobilized by particulate materials. However, despite the fact that these concepts are long established, some important aspects of soil behavior have not been clearly incorporated, which can seriously affect the estimation of the residual undrained shear strength. In this paper the effects of strain rate and reorientation of platy particles in fine-grained soils, the existence of a quasi-steady state (condition of minimum undrained strength) in sandy soils and the limitations of the state parameter are analyzed and discussed. In this context, the main goals are to minimize misjudgments in the estimation of the undrained strength and to introduce an alternative tool, the flow index, If, to evaluate the susceptibility of the occurrence of flow failure in tailings dams.

Relating quanta conservation and compartmental epidemiological models of airborne disease outbreaks in buildings

We investigate the underlying assumptions and limits of applicability of several documented models for outbreaks of airborne disease inside buildings by showing how they may each be regarded as special cases of a system of equations which combines quanta conservation and compartmental epidemiological modelling. We investigate the behaviour of this system analytically, gaining insight to its behaviour at large time. We then investigate the characteristic timescales of an indoor outbreak, showing how the dilution rate of the space, and the quanta generation rate, incubation rate and removal rate associated with the illness may be used to predict the evolution of an outbreak over time, and may also be used to predict the relative performances of other indoor airborne outbreak models. The model is compared to a more commonly used model, in which it is assumed the environmental concentration of infectious aerosols adheres to a quasi-steady-state, so that the the dimensionless quanta concentration is equal to the the infectious fraction. The model presented here is shown to approach this limit exponentially to within an interval defined by the incubation and removal rates. This may be used to predict the maximum extent to which a case will deviate from the quasi steady state condition.

Effects of thermal mass on transient thermal performance of concrete-based walls and energy consumption of an office building

Reducing energy consumption and Greenhouse Gas (GHG) emissions is an essential part of the clean growth and climate change framework recently developed by the Canadian government, which emphasizes the importance of energy-efficient building constructions. In this paper, the effects of thermal mass and placement of the thermally massive layer within wall assemblies on the transient thermal performance of walls and energy performance of a case study office building were studied. Three climate conditions representative of the heating-dominated, temperate, and cooling-dominated climates were considered. As for the assessment of energy demands, two cases for the indoor air temperature were taken into account: (i) indoor temperature was maintained at 20°C throughout the year, and (ii) during summertime, there was a set-point of 24°C and a setback of 35°C during the rest of the day while during wintertime, the set-point and setback values were 22°C and 18°C, respectively. The cases were compared according to the resulting decrement factor, the time required to reach quasi-steady state conditions, amplitudes of changes of heat fluxes and indoor surface temperatures, and the energy demands. The results showed that, for the cases studied, the wall, for which the thermally massive layer is not directly exposed to the indoor and outdoor climate conditions, resulted in the lowest decrement factor, the minimum amplitude of changes of heat fluxes and indoor surface temperatures, and maximum time required to reach quasi steady-state conditions. As for the energy performance, on the other hand, the wall, for which the thermally massive layer is exposed to the interior and exterior climate conditions, performed best amongst the cases investigated.

Phenomenology of Neapolitan Pizza Baking in a Traditional Wood-Fired Oven.

Despite Neapolitan pizza is a globally renowned Italian food, its obligatory baking in wood-fired ovens has so far received little attention in the scientific community. Since heat transfer during pizza baking is not at all uniform, the main aim of this work was to analyze the phenomenology of Neapolitan pizza baking in a pilot-scale wood-fired pizza oven operating in quasi steady-state conditions. The different upper area sections of pizza covered or not by the main topping ingredients (i.e., tomato puree, sunflower oil, or mozzarella cheese), as well the bottom of the pizza and the growth of its raised rim, were characterized by visual colorimetric analysis, while the time course of their corresponding temperatures was monitored using an infrared thermal scanning camera. The maximum temperature of the pizza bottom was equal to 100 ± 9 °C, while that of the upper pizza side ranged from 182 °C to 84 or 67 °C in the case of white pizza, tomato pizza, or margherita pizza, respectively, mainly because of their diverse moisture content and emissivity. The pizza weight loss was nonlinearly related to the average temperature of the upper pizza side. The formation of brown or black colored areas on the upper and lower sides of baked pizza was detected with the help of an electronic eye. The upper side exhibited greater degrees of browning and blackening than the lower one, their maximum values being about 26 and 8%, respectively, for white pizza. These results might help develop a specific modelling and monitoring strategy to reduce variability and maximize the quality attributes of Neapolitan pizza.

Impact of beach face slope variation on saltwater intrusion dynamics in unconfined aquifer under tidal boundary condition

Density-dependent saltwater flow in coastal aquifers varies with the seaside tidal and beach slope conditions. This paper presents a set of laboratory-scale saltwater intrusion experiments under different beach slopes (15°, 20°, 25°, and 30°) for unconfined aquifer conditions. Experimental porewater pressure measurements were utilized for quantitative analysis. A new G channel-based image analysis technique is used for experimental image analysis and freshwater–saltwater interface identification. Experimental results were numerically validated using the two-dimensional Finite Element subsurface FLOW (FEFLOW) model. The time-varying analysis revealed that saltwater intrusion occurs rapidly on flatter beach slopes. In the case of a steeper beach slope, saltwater intruded less. Steeper slopes take more time to reach a quasi-steady condition. Tidal oscillations alter hydraulic gradient changes across the beach slope. This gradient change generated clockwise circulating saltwater flow within porous media in the inter-tidal zone. This circulating flow resulted in the formation of the upper saline plume (USP). The USP expanded with time and moved in a downward direction. Finally, a deformed elliptic-shaped USP was observed under quasi-steady-state conditions. Submarine groundwater discharge (SGD) pathways move the saltwater region through the intermediate zone of a saltwater wedge and USP on varying beach slopes. It is evident that SGD particles move along the saltwater–freshwater interface (SWI) zone and rise upward (up to the intersection point). The tracer experiments were started after attaining the quasi-steady state condition and continued till the tracer reached the intersection point of saltwater level and sloping beach face. The experimental data sets can be used as benchmark test cases.

A proposal to identify the maximal metabolic steady state by muscle oxygenation and VO2max levels in trained cyclists

PurposeNear-infrared spectroscopy (NIRS) sensors measure muscle oxygen saturation (SmO2) as a performance factor in endurance athletes. The objective of this study is to delimit metabolic thresholds relative to maximal metabolic steady state (MMSS) using SmO2 in cyclists.MethodsForty-eight cyclists performed a graded incremental test (GTX) (100 W-warm-up followed by 30 W min) until exhaustion. SmO2 was measured with a portable NIRS placed on the vastus lateralis. Subjects were classified by VO2max levels with a scale from 2 to 5: L2 = 45–54.9, L3 = 55–64.9, L4 = 65–71, L5 = > 71, which represent recreationally trained, trained, well-trained, and professional, respectively. Then, metabolic thresholds were determined: Fatmax zone, functional threshold power (FTP), respiratory compensation point (RCP), and maximal aerobic power (MAP). In addition, power output%, heart rate%, VO2%, carbohydrate and fat consumption to cutoff SmO2 point relative to MMSS were obtained.ResultsA greater SmO2 decrease was found in cyclists with > 55 VO2max (L3, L4 and L5) vs. cyclists (L2) in the MMSS. Likewise, after passing FTP and RCP, performance is dependent on better muscle oxygen extraction. Furthermore, the MMSS was defined at 27% SmO2, where a non-steady state begins during exercise in trained cyclists.ConclusionA new indicator has been provided for trained cyclists, < 27% SmO2 as a cut-off to define the MMSS Zone. This is the intensity for which the athlete can sustain 1 h of exercise under quasi-steady state conditions without fatiguing.

Rovibrational-Specific QCT and Master Equation Study on N2(X1Σg+) + O(3P) and NO(X2Π) + N(4S) Systems in High-Energy Collisions.

This work presents a detailed investigation of the energy-transfer and dissociation mechanisms in N2(X1Σg+) + O(3P) and NO(X2Π) + N(4S) systems using rovibrational-specific quasiclassical trajectory (QCT) and master equation analyses. The complete set of state-to-state kinetic data, obtained via QCT, allows for an in-depth investigation of the Zel'dovich mechanism leading to the formation of NO molecules at microscopic and macroscopic scales. The master equation analysis demonstrates that the low-lying vibrational states of N2 and NO have dominant contributions to the NO formation and the corresponding extinction of N2 through the exchange process. For the considered temperature range, it is found that nearly 50% of the dissociation processes for N2 and NO molecules occur in the quasi-steady-state (QSS) regime, while for the Zel'dovich reaction, the distribution of the reactants does not reach the QSS conditions. Furthermore, using the QSS approximation to model the Zel'dovich mechanism leads to overestimating NO production by more than a factor of 4 in the high-temperature range. The breakdown of this well-known approximation has profound consequences for the approaches that heavily rely on the validity of QSS assumption in hypersonic applications. Finally, the investigation of the rovibrational state population dynamics reveals substantial similarities among different chemical systems for the energy-transfer and the dissociation processes, providing promising physical foundations for the use of reduced-order strategies in other chemical systems without significant loss of accuracy.

Predicting Metabolic Adaptation Under Dynamic Substrate Conditions Using a Resource-Dependent Kinetic Model: A Case Study Using Saccharomyces cerevisiae.

Exposed to changes in their environment, microorganisms will adapt their phenotype, including metabolism, to ensure survival. To understand the adaptation principles, resource allocation-based approaches were successfully applied to predict an optimal proteome allocation under (quasi) steady-state conditions. Nevertheless, for a general, dynamic environment, enzyme kinetics will have to be taken into account which was not included in the linear resource allocation models. To this end, a resource-dependent kinetic model was developed and applied to the model organism Saccharomyces cerevisiae by combining published kinetic models and calibrating the model parameters to published proteomics and fluxomics datasets. Using this approach, we were able to predict specific proteomes at different dilution rates under chemostat conditions. Interestingly, the approach suggests that the occurrence of aerobic fermentation (Crabtree effect) in S. cerevisiae is not caused by space limitation in the total proteome but rather an effect of constraints on the mitochondria. When exposing the approach to repetitive, dynamic substrate conditions, the proteome space was allocated differently. Less space was predicted to be available for non-essential enzymes (reserve space). This could indicate that the perceived “overcapacity” present in experimentally measured proteomes may very likely serve a purpose in increasing the robustness of a cell to dynamic conditions, especially an increase of proteome space for the growth reaction as well as of the trehalose cycle that was shown to be essential in providing robustness upon stronger substrate perturbations. The model predictions of proteome adaptation to dynamic conditions were additionally evaluated against respective experimentally measured proteomes, which highlighted the model’s ability to accurately predict major proteome adaptation trends. This proof of principle for the approach can be extended to production organisms and applied for both understanding metabolic adaptation and improving industrial process design.

Performance analysis of aqueous LiCl and CaCl2 based falling film dehumidifier with surface modification

• Analysis is carried out on a falling film based liquid desiccant dehumidifier. • The surface is modified with sinusoidal profile to increase the dehumidification. • The sinusoidal wavy profile increases the desiccant surface area by 7%. • Aqueous LiCl solution enhances the dehumidification by 29.15% compared to CaCl 2 . • With aqueous LiCl, the modified surface increases the dehumidification by 33.18%. In summer air-conditioning, conventional vapor compression systems cool the process air to its dew point temperature for dehumidification and further heat it to required supply temperature. This involves extra cooling and subsequent heating. Liquid desiccant systems avert this issue by separately handling latent and sensible loads, while running primarily on low grade thermal energy. Falling film type liquid desiccant dehumidifiers are advantageous over other types, mainly, as they reduce desiccant carryover into supply air stream. The current work aims towards the analysis and the performance improvement of a falling film type dehumidifier with the help of wavy profile of the working surface. Detailed comparison of the two commonly used desiccants, i.e., LiCl and CaCl 2 are carried out to analyse the performance of the dehumidifier. The present work also includes the characterisation of the wave profile and the analysis in terms of various important parameters, such as, the dehumidification effectiveness, the moisture removal rate and the change in specific humidity, missing in earlier studies. In order to study the performance, a simplified 2–D transient finite volume model is taken into consideration to simulate a multiphase, multi-component conjugate heat and mass transfer system using ANSYS Fluent 19.2. The volume of fluid method is used to trace out the liquid–gas interface. With back-end modification of the solver, the thermophysical properties of the liquid film are evaluated using empirical relationships, as a function of temperature and concentration. The penetration model of mass transfer provides the local mass transfer coefficients. The moisture removing the potential of the aqueous solutions of LiCl and CaCl 2 are evaluated at quasi steady-state conditions. The numerical solver is validated with the already published experimental results with a maximum deviation of 10.31%. A sinusoidal wavy profile of the wall introduced in the system enhances the turbulence intensity by 3.8% and the dehumidification performance by 33.18% and 18% for LiCl and CaCl 2 , respectively. It is due to the enhanced liquid–gas interface area. The mean film thickness is found to improve by 15.25% and 13.38% for LiCl and CaCl 2 , respectively. The effect of process parameters on the performance of the dehumidifier is also studied. It has been observed that the dehumidification effectiveness decreases from 86.14% to 31.1% with increase in inlet air velocity from 0.2 m/s to 2.0 m/s. It has also been found that a lower concentration of the desiccant solution and lower velocity of air yield higher dehumidification effectiveness. However, the moisture removal rate of the system will be compromised. Compared to the previously studied cases, the current configuration of the sinusoidal profile with amplitude to wavelength ratio of 1:15, yields superior dehumidification performance.

Enhancement of daily and monthly electrical power of off-grid greenhouse integrated semi-transparent photo-voltaic thermal (GiSPVT) system by integrating earth air heat exchanger (EAHE)

In this communication, an attempt has been made to evaluate daily and monthly electrical power of off-grid greenhouse integrated semi-transparent photo-voltaic thermal (GiSPVT) system by integrating with earth air heat exchanger (EAHE) under quasi-steady state condition which has not been considered earlier. The analysis is based on basic energy balance equations which are function of climatic and design parameters. Analytical expressions for solar cell temperature and its electrical efficiency, room air and plant temperatures have been derived. Numerical computations have been carried out for a typical day by MATLAB program. The results have also been compared with respect to without earth air heat exchanger (EAHE). Based on outcome of numerical computation, the daily electrical power is increased by 7.5% due to cooling effect of semi-transparent PV module roof of GiSPVT by EAHE. An overall daily exergy of GiSPVT system has been found to be 4.60 × 107 Wh for a packing factor of 0.22. The monthly output of off-grid GiSPVT system is obtained as 861.28 kWh. Finally, the theoretical model has also been validated by experimental results of a typical winter climatic condition without earth air heat exchanger (EAHE) for climatic condition of Ballia (UP), India.

Up-Dated the Critical Issues of Corneal Cross-Linking (Type-I and II): Safety Dose for Ultra-Thin Cornea, Demarcation Line Depth and the Role of Oxygen

Purpose: To update analytic formulas for the overall efficacy of corneal collagen crosslinking (CXL) including both type-I and oxygen-mediated type-II mechanisms, the role of oxygen and the initiator regeneration. Also, to derive the formulas for the minimum corneal thickness and demarcation line depth. Study Design: Modeling the kinetics of CXL in UV light and using riboflavin as the photosensitizer. Place and Duration of Study: New Taipei City, Taiwan, between June, 2021 and July, 2021. Methodology: Coupled kinetic equations are derived under the quasi-steady state condition for the 2-pathway mechanisms of CXL. For type-I CXL, the riboflavin (RF) triplet state [T] may interact directly with the stroma collagen substrate [A] to form radical (R) and regenerate initiator. For type-II process, [T] interacts with oxygen to form a singlet oxygen [1 O2 ]. Both reactive radical (R) and [1 O2 ], can relax to their ground state, or interact with the substrate [A]) for crosslinking. Based on a safety dose, formulas for the minimum corneal thickness and demarcation line depth (DLD) are derived. Results: Our updated theory/modeling showed that oxygen plays a limited and transient role in the process, in consistent with that of Kamave. In contrary, Kling et al believed that type-II is the predominant mechanism, which however conflicting with the epi-on CXL results. For both type-I and type-II, a transient state conversion (crosslink) efficacy in an increasing function of light intensity (or dose), whereas, its steady state efficacy is a deceasing function of light intensity. RF depletion in type-I is compensated by the RF regeneration term (RGE) which is a decreasing function of oxygen. For the case of perfect regeneration case (or when oxygen=0), RF is a constant due to the catalytic cycle. Unlike the conventional Dresden rule of 400 um thickness, thin cornea CXL is still safe as far as the dose is under a threshold dose (E*), based on our minimum thickness formula (Z*). Our formula for thin cornea is also clinically shown by Hafez et al for ultra thin (214 nm) CXL. Conclusion: For both type-I and type-II, a transient state conversion (crosslink) efficacy in an increasing function of light intensity (or dose), whereas, its steady state efficacy is a deceasing function of light intensity. CXL for ultra thin corneas are still safe, as far as it is under a threshold dose (E*), based on our minimum thickness formula, which has a similar tend as that of demarcation line depth. the type-II efficacy also provides the survival rate for the treatment of corneal keratitis.

Analysis of Dynamic Efficacy Profile of Corneal Cross-Linking: Role of Oxygen and Rate Constants in Type-I and II Processes

Purpose: To explore (theoretically) the key parameters and their influence on the time profiles of photosensitizer (riboflavin), free radicals, singlet oxygen, oxygen and the efficacy of corneal collagen crosslinking (CXL) in both type-I and oxygen-mediated type-II mechanisms, specially the role of oxygen and the initiator regeneration.&#x0D; Study Design: Numerical solutions of the rate equation of CXL.&#x0D; Place and Duration of Study: New Taipei City, Taiwan, between October, 2021 and November, 2021.&#x0D; Methodology: Coupled kinetic equations are derived and numerically solved under the quasi-steady state condition for the 2-pathway mechanisms of CXL. The key parameters explored include (bI, V, Q', K, K',Q,P) and their influence on the time profiles of photosensitizer (riboflavin, C), radicals (R), singlet oxygen(S), oxygen (X) and efficacy (E), parameters of (K,K',Q) define the relative strength of type-I and type-II process. The oxygen depletion profile, X(t), and the associated singlet oxygen, S(t), depend on the parameters of V, Q' and the initial value of oxygen. The coupling strength given by (bI) governs almost all profiles, where b is an effective absorption parameter and I is the UV light intensity.&#x0D; Results: Our numerical method for CXL dynamic profiles demonstrated the following important features: (i) Type-I and type-II co exit in CXL, in the presence of oxygen. However, there is no type-II when oxygen is depleted or in a condition without oxygen. (ii) Type-I with bimolecular termination, the radical R(t) is a function of [K'(bIgC)]0.5, leading to the steady-state efficacy given by a scaling law of 1/(bI)0.5, in contract to that of type-II which is almost independent to the light intensity. (iii) The depletion rate (2 to 5 minutes) of X(t) is much faster than that of C(t) (10 to 20 minutes), (iv) The pure type-II profile, has a transition point from straight line to saturating curve and matches the depletion point of singlet oxygen S(t). (v) Improved CXL efficacy of type-I and type-II may be achieved by external supply of photoinitiator (riboflavin) and oxygen, respectively.

Critical Analysis of Corneal Cross-linking (Part-I): Formulas for Efficacy, Safety Dose, Minimum Thickness, Demarcation Line Depth and the Role of Oxygen

Purpose: To update and derive formulas for the efficacy and kinetics of corneal collagen crosslinking (CXL) including both type-I and oxygen-mediated type-II mechanisms, the role of oxygen, the initiator regeneration, safety dose, minimum corneal thickness and demarcation line depth.&#x0D; Study Design: Modeling the kinetics of CXL in UV light and using riboflavin as the photosensitizer.&#x0D; Place and Duration of Study: Taipei, Taiwan, between June, 2021 and July, 2021.&#x0D; Methodology: Coupled kinetic equations are derived under the quasi-steady state condition for the 2-pathway mechanisms of CXL. For type-I CXL, the riboflavin (RF) triplet state [T] may interact directly with the stroma collagen substrate [A] to form radical (R) and regenerate initiator. For type-II process, [T] interacts with oxygen to form a singlet oxygen [1O2]. Both reactive radical (R) and [1O2], can interact with the substrate [A]) for crosslinking. Based on a safety dose and a threshold dose, formulas for the minimum corneal thickness and demarcation line depth (DLD) are derived.&#x0D; Results: Our updated theory/modeling showed that oxygen plays a limited and transient role in the process, in consistent with that of Kamave. In contrary, Kling et al believed that type-II is the predominant mechanism, which however conflicting with the epi-on CXL results. For both type-I and type-II, a transient state conversion (crosslink) efficacy in an increasing function of light intensity (or dose), whereas, its steady state efficacy is a deceasing function of light intensity. RF depletion in type-I is compensated by the RF regeneration term (RGE) which is a decreasing function of oxygen. For the case of perfect regeneration case (or when oxygen=0), RF is a constant due to the catalytic cycle. Unlike the conventional Dresden rule of 400 um thickness, thin cornea CXL is still safe as far as the dose is under a threshold dose (E*), based on our minimum thickness formula (Z*). Our formula for thin cornea is also clinically shown by Hafez et al for ultra thin (214 nm) CXL.&#x0D; Conclusion: For both type-I and type-II, the transient state conversion (crosslink) efficacy in an increasing function of light intensity (or dose), whereas, its steady state efficacy is a deceasing function of light intensity. CXL for ultra thin corneas are still safe, as far as it is under a threshold dose (E*), based on our minimum thickness (Z*) formula, which has a similar tend as that of demarcation line depth (Z').