Development of a Mini-Freeze Dryer for Material-Sparing Laboratory Processing with Representative Product Temperature History

The goal of the work described in this publication was to evaluate a new, small, material-sparing freeze dryer, denoted as the “mini-freeze dryer or mini-FD”, capable of reproducing the product temperature history of larger freeze dryers, thereby facilitating scale-up. The mini-FD wall temperatures can be controlled to mimic loading procedures and dryer process characteristics of larger dryers. The mini-FD is equipped with a tunable diode laser absorption spectroscopy (TDLAS) water vapor mass flow monitor and with other advanced process analytical technology (PAT) sensors. Drying experiments were performed to demonstrate scalability to larger freeze dryers, including the determination of vial heat transfer coefficients, K _v . Product temperature histories during K _v runs were evaluated and compared with those obtained with a commercial laboratory-scale freeze dryer (LyoStar II) for sucrose and mannitol product formulations. When the mini-FD wall temperature was set at the LyoStar II band temperature (? 20°C) to mimic lab dryer edge vials, edge vial drying in the mini-FD possessed an average K _v within 5% of those obtained during drying in the LyoStar II. When the wall temperature of the mini-FD was set equal to the central vial product temperature, edge vials behaved as center vials, possessing a K _v value within 5% of those measured in the LyoStar II. During both K _v runs and complete product freeze drying runs, the temperature-time profiles for the average edge vials and central vial in the mini-FD agreed well with the average edge and average central vials of the LyoStar II.     

Heat and mass transfer scale-up issues during freeze-drying, III: Control and characterization of dryer differences via operational qualification tests

The objective of this research was to estimate differences in heat and mass transfer between freeze dryers due to inherent design characteristics using data obtained from sublimation tests. This study also aimed to provide guidelines for convenient scale-up of the freeze-drying process. Data obtained from sublimation tests performed on laboratory-scale, pilot, and production freeze dryers were used to evaluate various heat and mass transfer parameters: nonuniformity in shelf surface temperatures, resistance of pipe, refrigeration system, and condenser. Emissivity measurements of relevant surfaces such as the chamber wall and the freeze dryer door were taken to evaluate the impact of atypical radiation heat transfer during scale-up. “Hot” and “cold” spots were identified on the shelf surface of different freeze dryers, and the impact of variation in shelf surface temperatures on the primary drying time and the product temperature during primary drying was studied. Calculations performed using emissivity measurements on different freeze dryers suggest that a front vial in the laboratory lyophilizer received 1.8 times more heat than a front vial in a manufacturing freeze dryer operating at a shelf temperature of −25°C and a chamber pressure of 150 mTorr during primary drying. Therefore, front vials in the laboratory are much more atypical than front vials in manufacturing. Steady-state heat and mass transfer equations were used to study a combination of different scaleup issues pertinent during lyophilization cycles commonly used for the freeze-drying of pharmaceuticals.     

Heat and mass transfer scale-up issues during freeze-drying,I: Atypical radiation and the edge vial effect

The aim of this study is to determine whether radiation heat transfer is responsible for the position dependence of heat transfer known as the edge vial effect. Freeze drying was performed on a laboratory-scale freeze dryer using pure water with vials that were fully stoppered but had precision cut metal tubes inserted in them to ensure uniformity in resistance to vapor flow. Sublimation rates were determined gravimetrically. Vials were sputter-coated with gold and placed at selected positions on the shelf. Average sublimation rates were determined for vials located at the front, side, and center of an array of vials. Sublimation rates were also determined with and without the use of aluminum foil as a radiation shield. The effect of the guardrail material and its contribution to the edge vial effect by conduction heat transfer was studied by replacing the stainless steel band with a low-thermal conductivity material (styrofoam). The emissivities (ε) of relevant surfaces were measured using an infrared thermometer. Sublimation rate experiments were also conducted with vials suspended off the shelf to study the role of convection heat transfer. It was found that sublimation rates were significantly higher for vials located in the front compared to vials in the center. Additional radiation shields in the form of aluminum foil on the inside door resulted in a decrease in sublimation rates for the front vials and to a lesser extent, the center vials. There was a significant decrease in sublimation rate for goldcoated vials (ε≈0.4) placed at the front of an array when compared to that of clear vials (ε≈0.9). In the case of experiments with vials suspended off the shelf, the heat transfer coefficient was found to be independent of chamber pressure, indicating that pure convection plays no significant role in heat transfer. Higher sublimation rates were observed when the steel band was used instead of Styrofoam while the highest sublimation rates were obtained in the absence of the guardrail, indicating that the metal band can act as a thermal shield but also transmits some heat from the shelf via conduction and radiation. Atypical radiation heat transfer is responsible for higher sublimation rates for vials located at the front and side of an array. However, the guardrail contributes a little to heat transfer by conduction.     

Evaluation of manometric temperature measurement (MTM), a process analytical technology tool in freeze drying, part III: Heat and mass transfer measurement

This article evaluates the procedures for determining the vial heat transfer coefficient and the extent of primary drying through manometric temperature measurement (MTM). The vial heat transfer coefficients (K_v) were calculated from the MTM-determined temperature and resistance and compared with K_v values determined by a gravimetric method. The differences between the MTM vial heat transfer coefficients and the gravimetric values are large at low shelf temperature but smaller when higher shelf temperatures were used. The differences also became smaller at higher chamber pressure and smaller when higher resistance materials were being freeze-dried. In all cases, using thermal shields greatly improved the accuracy of the MTM K_v measurement. With use of thermal shields, the thickness of the frozen layer calculated from MTM is in good agreement with values obtained gravimetrically. The heat transfer coefficient “error” is largely a direct result of the error in the dry layer resistance (ie, MTM-determined resistance is too low). This problem can be minimized if thermal shields are used for freeze-drying. With suitable use of thermal shields, accurate K_v values are obtained by MTM; thus allowing accurate calculations of heat and mass flow rates. The extent of primary drying can be monitored by real-time calculation of the amount of remaining ice using MTM data, thus providing a process analytical tool that greatly improves the freeze-drying process design and control.     

Evaluation of manometric temperature measurement, a process analytical technology tool for freeze-drying: Part I, product temperature measurement

This study examines the factors that may cause systematic errors in the manometric temperature measurement (MTM) procedure used to evaluate product temperature during primary drying. MTM was conducted during primary drying using different vial loads, and the MTM product temperatures were compared with temperatures directly measured by thermocouples. To clarify the impact of freeze-drying load on MTM product temperatures, simulation of the MTM vapor pressure rise was performed, and the results were compared with the experimental results. The effect of product temperature heterogeneity in MTM product temperature determination was investigated by comparing the MTM product temperatures with directly measured thermocouple product temperatures in systems differing in temperature heterogeneity. Both the simulated and experimental results showed that at least 50 vials (5 mL) were needed to give sufficiently rapid pressure rise during the MTM data collection period (25 seconds) in the freeze dryer, to allow accurate determination of the product temperature. The product temperature is location dependent, with higher temperature for vials on the edge of the array and lower temperature for the vials in the center of the array. The product temperature heterogeneity is also dependent upon the freeze-drying conditions. In product temperature heterogeneous systems, MTM measures a temperature close to the coldest product temperature, even, if only a small fraction of the samples have the coldest product temperature. The MTM method is valid even at very low product temperature (−45°C). Published: February 10, 2006     

Spatial Variation of Pressure in the Lyophilization Product Chamber Part 2: Experimental Measurements and Implications for Scale-up and Batch Uniformity

Product temperature during the primary drying step of freeze-drying is controlled by a set point chamber pressure and shelf temperature. However, recent computational modeling suggests a possible variation in local chamber pressure. The current work presents an experimental verification of the local chamber pressure gradients in a lab-scale freeze-dryer. Pressure differences between the center and the edges of a lab-scale freeze-dryer shelf were measured as a function of sublimation flux and clearance between the sublimation front and the shelf above. A modest 3-mTorr difference in pressure was observed as the sublimation flux was doubled from 0.5 to 1.0 kg·h^?1·m^?2 at a clearance of 2.6 cm. Further, at a constant sublimation flux of 1.0 kg·h^?1·m^?2, an 8-fold increase in the pressure drop was observed across the shelf as the clearance was decreased from 4 to 1.6 cm. Scale-up of the pressure variation from lab- to a manufacturing-scale freeze-dryer predicted an increased uniformity in drying rates across the batch for two frequently used pharmaceutical excipients (mannitol and sucrose at 5% w/w). However, at an atypical condition of shelf temperature of +10°C and chamber pressure of 50 mTorr, the product temperature in the center vials was calculated to be a degree higher than the edge vial for a low resistance product, thus reversing the typical edge and center vial behavior. Thus, the effect of local pressure variation is more significant at the manufacturing-scale than at a lab-scale and accounting for the contribution of variations in the local chamber pressures can improve success in scale-up.     

Glass Delamination: a Comparison of the Inner Surface Performance of Vials and Pre-filled Syringes

The occurrence of glass delamination is a serious concern for parenteral drug products. Over the past several years, there has been a series of product recalls involving glass delamination in parenteral drugs stored in vials which has led to heightened industry and regulatory scrutiny. In this study, a two-pronged approach was employed to assess the inner surface durability of vials and pre-filled syringes. Non-siliconized syringes were used in order to directly compare glass to glass performance between vials and syringes. The vial and syringe performance was screened with pharmaceutically relevant formulation conditions. The influence of pH, buffer type, ionic strength, and glass type and source was evaluated. In addition, an aggressive but discriminating formulation condition (glutaric acid, pH 11) was used to ascertain the impact of syringe processing. Advanced analytical tools including inductively coupled plasma/mass spectrometry, scanning electron microscopy, atomic force microscopy, and dynamic secondary ion mass spectroscopy showed significant differences in glass performance between vials and syringes. Pre-filled syringes outperform vials for most tests and conditions. The manufacturing conditions for vials lead to glass defects, not found in pre-filled syringes, which result in a less chemically resistant surface. The screening methodology presented in this work can be applied to assess suitability of primary containers for specific drug applications.Key words: borosilicate vials, glass delamination, glass corrosion, hydrolytic resistance, pre-filled syringes     

Evaluation of a New Wireless Temperature Remote Interrogation System (TEMPRIS) to Measure Product Temperature During Freeze Drying

The purpose of this research was to evaluate a new wireless and battery-free sensor technology for invasive product temperature measurement during freeze-drying. Product temperature is the most critical process parameter in a freeze-drying process, in particular during primary drying. The product temperature over time profile and a precise detection of the endpoint of ice sublimation is crucial for comparison of freeze-drying cycles. Traditionally, thermocouples are used in laboratory scale units whereas resistance thermal detectors are applied in production scale freeze-dryers to evaluate temperature profiles. However, both techniques show demerits with regard to temperature comparability and biased measurements relative to vials without sensors. A new generation of wireless temperature sensors (Temperature Remote Interrogation System, TEMPRIS) were used in this study to investigate for the first time their value when applied to freeze-drying processes. Measurement accuracy, capability of accurate endpoint detection and effect of positioning were delineated by using product runs with sucrose, mannitol and trehalose. Data were compared to measurements with 36-gauge thermocouples as well as to non-invasive temperature measurement from Manometric Temperature Measurements. The results show that the TEMPRIS temperature profiles were in excellent agreement to thermocouple data when sensors were placed center bottom in a vial. In addition, TEMPRIS sensors revealed more reliable temperature profiles and endpoint indications relative to thermocouple data when vials in edge position were monitored. The results of this study suggest that TEMPRIS may become a valuable tool for cycle development, scale-up and routine manufacturing in the future.     

Factors influencing changes in moisture content during storage of freeze-dried vaccines in vials

Previous studies have demonstrated that the water content of freeze-dried vaccines increases during storage. The reasons for these variations in water content are discussed in this paper. Different possible mechanisms have been considered: microleakages at the closure sealing point, water vapour transfer through the closure (permeation, loss and uptake of water by the stopper). Several types of vials and closures were studied, under different conditions of storage. Regardless of the vial form selected, the probability of microleakages was low. The stopper would seem to play an important role in the water transfer mechanisms. The moisture content of the stopper determines its equilibrium relative humidity (ERH) and whether there will be moisture transfer between the stopper and the vial contents and between the stopper and the storage atmosphere.     

Genetic variability among archival cultures of Salmonella typhimurium

The existence in our laboratory of over 10000 Salmonella typhimurium LT2 cultures sealed in agar stab vials for 33-46 years offers an opportunity for evolutionary and mutational studies. In each of 77 vials examined, 10(3)-10(5) colony forming units per vial were recovered (less than 0.01% of the original population) even after decades of undisturbed storage. Considerable genetic variability was observed in these populations. Three genetic variables, chromosome fragment size as determined by pulsed-field gel electrophoresis, extensive mutational reversions from nutritional auxotrophy to prototrophy, and differences in protein content as assayed by sodium dodecyl sulfate polyacrylamide gel electrophoresis, were measured.     

Amino acid composition of leaf,grain and bracts of japonica rice (<Emphasis Type="Italic">Oryza Sativa</Emphasis> ssp. <Emphasis Type="Italic">japonica</Emphasis>) and its response to nitrogen fertilization

Heat stress is one of the main abiotic stresses that limit plant growth. The effects of high temperature on oxidative damage, PSII activity and D1 protein turnover were studied in three wheat varieties with different heat susceptibility (CS, YN949 and AK58). The results showed that heat stress induced lower lipid peroxidation in AK58 and YN949 than CS, which was related to different changes of SOD, CAT, POD and H₂O₂. Similarly, AK58 and YN949 performed better PSII photochemical efficiency (F_v/F_m, ΦPSII and ETR) under high temperature, which was attributed to rapid synthesis and degradation of D1 protein. Moreover, higher expression of D1 protein turnover-related genes (PsbA, STN8, PBCP, Deg1, Deg2, Deg5, Deg8, FtsH1/5 and FtsH2/8) and SOD activity in AK58 and YN949 under normal conditions also established a basis for acclimatizing high temperatures, thereby alleviating PSII photoinhibition and reducing oxidative damage when exposed to heat stress.     

Ethylene loss from the gas phase of container-seal systems

Ethylene losses from the gas phase of various container-seal systems were studied to develop acceptable methods for containing ethylene during experiments. Ethylene at an initial amount of 104 μI I^-1 was stored in glass vials at near atmospheric pressure for 20 h at 25–27°C and at 35% relative humidity external to the vials. Crimped serum vials sealed with saturated (NH₄)₂SO₄ solution, neoprene rubber septa, nitrile rubber (Hycar) septa, butyl rubber septa, and brown translucent silicone rubber septa lost ethylene at the rate of 1.8, 10.2, 16.2, 16.5, and 40.2 nl m^-2s^-1, respectively, over the 20-h period. Screw-capped reaction vials sealed with white silicone rubber septa lost ethylene at the rate of 30.2 nl m^-2s^-1. The (NH4)₂SO₄ solution was utilized as a seal by inverting a vial so that the salt solution covered the internal surface of the vial septum. Saturated (NH₄)²SO₄ solution is an effective seal. Silicone rubber should be avoided as a seal in systems for containing ethylene. Ethylene production values in the literature may be underestimates where silicone rubber seals have been used.     

Evaluation of manometric temperature measurement, a process analytical technology tool for freeze-drying: Part II measurement of dry-layer resistance

The purpose of this work was to study the factors that may cause systematic errors in the manometric temperature measurement (MTM) procedure used to determine product dry-layer resistance to vapor flow. Product temperature and dry-layer resistance were obtained using MTM software installed on a laboratory freeze-dryer. The MTM resistance values were compared with the resistance values obtained using the “vial method.” The product dry-layer resistances obtained by MTM, assuming fixed temperature difference (ΔT; 2°C), were lower than the actual values, especially when the product temperatures and sublimation rates were low, but with ΔT determined from the pressure rise data, more accurate results were obtained. MTM resistance values were generally lower than the values obtained with the vial method, particularly whenever freeze-drying was conducted under conditions that produced large variations in product temperature (ie, low shelf temperature, low chamber pressure, and without thermal shields). In an experiment designed to magnify temperature heterogeneity, MTM resistance values were much lower than the simple average of the product resistances. However, in experiments where product temperatures were homogenous, good agreement between MTM and “vial-method” resistances was obtained. The reason for the low MTM resistance problem is the fast vapor pressure rise from a few “warm” edge vials or vials with low resistance. With proper use of thermal shields, and the evaluation of ΔT from the data, MTM resistance data are accurate. Thus, the MTM method for determining dry-layer resistance is a useful tool for freeze-drying process analytical technology.     

Electronic structure,rovibrational, and dipole moment calculations for the AsCl molecule

The potential energy curves of the 19 lowest-lying singlet and triplet electronic states in the ^2S+1Λ^(+/?) representation of the AsCl molecule have been investigated using the complete active space self-consistent field (CASSCF) with multireference configuration interaction (MRCI+Q) method including single and double excitations and with the Davidson correction. The harmonic frequency ω _e, the internuclear distance R _e, the dipole moment, and the electronic energy with respect to the ground state T _e were calculated for the electronic states considered. By using the canonical functions approach, the eigenvalue E _v, the rotational constant B _v, and the abscissae of the turning points R _min and R _max were calculated for the electronic states up to the vibrational level v?=?60. The values obtained in the present work agree well with corresponding values available in the literature for several electronic states. Fifteen new electronic states were investigated here for the first time.     

On fast solid-body rotation of the solar core and differential (liquid-like) rotation of the solar surface

On the basis of a two-component (two-fluid) hydrodynamic model, it is shown that the probable phenomenon of solar core rotation with a velocity higher than the average velocity of global rotation of the Sun, discovered by the SOHO mission, can be related to fast solid-body rotation of the light hydrogen component of the solar plasma, which is caused by thermonuclear fusion of hydrogen into helium inside the hot dense solar core. Thermonuclear fusion of four protons into a helium nucleus (α-particle) creates a large free specific volume per unit particle due to the large difference between the densities of the solar plasma and nuclear matter. As a result, an efficient volumetric sink of one of the components of the solar substance—hydrogen—forms inside the solar core. Therefore, a steady-state radial proton flux converging to the center should exist inside the Sun, which maintains a constant concentration of hydrogen as it burns out in the solar core. It is demonstrated that such a converging flux of hydrogen plasma with the radial velocity v _r (r) = ?βr creates a convective, v _r ?v _φ/?r, and a local Coriolis, v _r v _φ/r,φ nonlinear hydrodynamic forces in the solar plasma, rotating with the azimuthal velocity v _φ. In the absence of dissipation, these forces should cause an exponential growth of the solid-body rotation velocity of the hydrogen component inside the solar core. However, friction between the hydrogen and helium components of the solar plasma due to Coulomb collisions of protons with α-particles results in a steady-state regime of rotation of the hydrogen component in the solar core with an angular velocity substantially exceeding the global rotational velocity of the Sun. It is suggested that the observed differential (liquid-like) rotation of the visible surface of the Sun (photosphere) with the maximum angular velocity at the equator is caused by sold-body rotation of the solar plasma in the radiation zone and strong turbulence in the tachocline layer, where the turbulent viscosity reaches its maximum value at the equator. There, the tachocline layer exerts the most efficient drag on the less dense outer layers of the solar plasma, which are slowed down due to the interaction with the ambient space plasma (solar wind).     

Wheat cultivars selected for high Fv/Fm under heat stress maintain high photosynthesis,total chlorophyll,stomatal conductance,transpiration and dry matter

The chlorophyll fluorescence parameter F_v/F_m reflects the maximum quantum efficiency of photosystem II (PSII) photochemistry and has been widely used for early stress detection in plants. Previously, we have used a three‐tiered approach of phenotyping by F_v/F_m to identify naturally existing genetic variation for tolerance to severe heat stress (3 days at 40°C in controlled conditions) in wheat (Triticum aestivum L.). Here we investigated the performance of the previously selected cultivars (high and low group based on F_v/F_m value) in terms of growth and photosynthetic traits under moderate heat stress (1 week at 36/30°C day/night temperature in greenhouse) closer to natural heat waves in North‐Western Europe. Dry matter accumulation after 7 days of heat stress was positively correlated to F_v/F_m. The high F_v/F_m group maintained significantly higher total chlorophyll and net photosynthetic rate (P_N) than the low group, accompanied by higher stomatal conductance (g_s), transpiration rate (E) and evaporative cooling of the leaf (ΔT). The difference in P_N between the groups was not caused by differences in PSII capacity or g_s as the variation in F_v/F_m and intracellular CO₂ (C_i) was non‐significant under the given heat stress. This study validated that our three‐tiered approach of phenotyping by F_v/F_m performed under increasing severity of heat was successful in identifying wheat cultivars differing in photosynthesis under moderate and agronomically more relevant heat stress. The identified cultivars may serve as a valuable resource for further studies to understand the physiological mechanisms underlying the genetic variability in heat sensitivity of photosynthesis.     

Evaluation of wild <Emphasis Type="Italic">Arachis</Emphasis> species for cultivation under semiarid tropics as a fodder crop

Wild Arachis genotypes were analysed for chlorophyll a fluorescence, carbon isotope discrimination (ΔC), specific leaf area (SLA), and SPAD readings. Associations between different traits, i.e., SLA and SPAD readings (r =–0.76), SLA and ΔC (r = 0.42), and ΔC and SPAD readings (r = 0.30) were established. The ratio of maximal quantum yield of PSII photochemistry (F_v/F_m) showed a wider variability under water deficit (WD) than that after irrigation (IR). Genotypes were grouped according to the F_v/F_m ratio as: efficient, values between 0.80 and 0.85; moderately efficient, the values from 0.79 to 0.75; inefficient, the values < 0.74. Selected Selected genotypes were evaluated also for their green fodder yield: the efficient genotypes ranged between 3.0 and 3.8, the moderately efficient were 2.6 and 2.7, the inefficient genotypes were of 2.3 and 2.5 t ha^?1 per year in 2008 and 2009, respectively. Leaf water-relation traits studied in WD and IR showed that the efficient genotypes were superior in maintenance of leaf water-relation traits, especially, under WD. Potential genotypes identified in this study may enhance biomass productivity in the semiarid tropic regions.     

The effect of sample composition and vial type on Ĉerenkov counting in a liquid scintillation counter

The effect of sample vial type and sample composition on the ?erenkov count rate detected from ³²P and ³⁶Cl was studied using a liquid scintillation counter. When counting was done in the noncoincident mode, glass vials allowed higher counting efficiency than plastic vials. In the coincident mode light scattering caused by polyethylene and polyproplyene vials allowed higher counting efficiency than glass vials. Highest coincident counting efficiency was from plastic minivials in a glass carrier vial. Increased solute concentration in samples caused increased counting efficiency due to changes in the refractive index of the solution. This can cause significant counting efficiency changes with no sample channel ratio change in density gradient fractions. The use of wavelength shifters is shown to be inappropriate when the sample pH varies, as this can change the fluorescent properties of the shifters and thereby the observed count rate.     

Solvent Removal and Spore Inactivation Directly in Dispensing Vials with Supercritical Carbon Dioxide and Sterilant

A process is described using supercritical carbon dioxide to extract organic solvents from drug solutions contained in 30-mL serum vials. We report drying times of less than 1 h with quantitative recovery of sterile drug. A six-log reduction of three spore types used as biological indicators is achieved with direct addition of peracetic acid to a final concentration of approximately 5 mM (~0.04 %) to the drug solution in the vial. Analysis of two drugs, acetaminophen and paclitaxel, indicated no drug degradation as a result of the treatment. Furthermore, analysis of the processed drug substance showed that no residual peracetic acid could be detected in the final product. We have demonstrated an effective means to simultaneously dry and sterilize active pharmaceutical ingredients from organic solvents directly in a dispensing container.KEY WORDS: drying, paclitaxel, peracetic acid, sterilization, supercritical carbon dioxide     

Underestimated chlorophyll <Emphasis Type="Italic">a</Emphasis> fluorescence measurements on <Emphasis Type="Italic">Buxus microphylla</Emphasis> red winter leaves

Leaves under stressful conditions usually show downregulated maximum quantum efficiency of photosystem II [inferred from variable to maximum chlorophyll (Chl) a fluorescence (F_v/F_m), usually lower than 0.8], indicating photoinhibition. The usual method to evaluate the degree of photoinhibition in winter red leaves is generally by measuring the F_v/F_m on the red adaxial surface. Two phenotypes of overwintering Buxus microphylla ‘Wintergreen’ red leaves, with different measuring site and leaf thickness, were investigated in order to elucidate how red pigments in the outer leaf layer affected the Chl a fluorescence (F_v/F_m) and photochemical reflectance index. Our results showed that the F_v/F_m measured on leaves with the same red surface, but different leaf thickness, exhibited a slightly lower value in half leaf (separated upper and lower layers of leaves by removing the leaf edge similarly as affected by winter freezing and thawing) than that in the intact leaf (without removing the leaf edge), and the F_v/F_m measured on the red surface was significantly lower than that on the inner or backlighted green surface of the same thickness. Our results suggest that the usual measurement of F_v/F_m on red adaxial surface overestimates the actual degree of photoinhibition compared with that of the whole leaf in the winter.