We derive approximate equations of motion for excited state dynamics of a multilevel open quantum system weakly interacting with light to describe fluorescence-detected single molecule spectra. Based on the Frenkel exciton theory, we construct a model for the chlorophyll part of the LHCII complex of higher plants and its interaction with previously proposed excitation quencher in the form of the lutein molecule Lut 1. The resulting description is valid over a broad range of timescales relevant for single molecule spectroscopy, i.e. from ps to minutes. Validity of these equations is demonstrated by comparing simulations of ensemble and single-molecule spectra of monomeric LHCII with experiments. Using a conformational change of the LHCII protein as a switching mechanism, the intensity and spectral time traces of individual LHCII complexes are simulated, and the experimental statistical distributions are reproduced. Based on our model, it is shown that with reasonable assumptions about its interaction with chlorophylls, Lut 1 can act as an efficient fluorescence quencher in LHCII. It is often argued that this conversion is remarkably efficient. However, it has to be distinguished between the Most of our current knowledge about the early processes of photosynthesis was obtained by ultrafast spectroscopy. While conventional bulk spectroscopies are extremely useful in following ultrafast photo-induced events in photosynthesis, whenever structural inhomogeneity of the sample is involved, the information obtained from these spectroscopies becomes obscured by an inevitable ensemble averaging. Some well established spectroscopic methods, such as hole-burning1415The system studied in this work, the light harvesting complex II (LHCII) of higher plants, is the plants’ major light-harvesting antenna containing almost half of all the chlorophyll in the chloroplast. Correspondingly, most of the light absorption and subsequent energy transfer processes in plants and algae occur in this complex. The LHCII antenna occurs naturally in a trimeric form and its main function is to deliver excitation energy to the nearby photosystem II (PSII). Given the major role of LHCII in light-harvesting and energy transfer, it is not surprising that it is also implicated in participating in regulated energy dissipation, the so-called non-photochemical quenching (NPQ)792122In recent years, single-molecule spectroscopy (SMS) experiments on several photosynthetic antenna complexes including the LHCII were performed. Fluorescence spectral peak distributions26As far as the theory of the SMS of LHCII is concerned, the ensemble-averaged spectra and also the peak distributions of LHCII trimers can be successfully explained by the disordered excitonic modelThe paper is organized as follows: we first discuss the Frenkel exciton model as a basis for the formulation of equations of motion for the populations of the excited states of chromophore aggregates with strong interchromophore couplings. We introduce equations of motion for excitonic populations valid over a broad (from ps to min) timescale range. We discuss their generality and the range of validity. It is argued that these equations provide an ideal means for the description of the SMS experiments. We apply our equatios to LHCII photosynthetic antenna complexes. All results are compared to the experiment. It is shown that our equations give correct fluorescence spectrum and peak statistics, i.e. appropriate steady-state population, under typical SMS experiment condition. Then we model the intensity traces, while the switching behaviour is included by incorporating one particular previously proposed NPQ mechanism, namely energy transfer to lutein Lut 1. The switching between on and off states is controlled by a 2-level model, where the switching causes a change of the Chl a612 - Lut 1 coupling. It is shown that using realistic parameters we are able to reproduce the experimental results. The details of our energy relaxation theory and of the stochastic model of switching are given in In the usual SMS experiments, time-resolved  fluorescence of the studied molecules is observed. If the excited state life time of the studied chromophores is sufficiently long (nanoseconds in the case of chlorophylls studied here), the expected fluorescence spectra can be calculated from the steady state, quasi-equilibriated populations of the excited electronic eigenstates of the molecular system, assuming canonical equilibrium. Depending on the strengths of the chromophore-chromophore resonance interaction and the system-bath couplings, the eigenstates can be approximated either by the excited eigenstates of the electronic subsystem or the excited state of the individual chromophores forming the aggregate. In the present paper, we treat both cases within one formalism provided by the framework of the Frenkel exciton model.gi〉 and |ei〉 are the electronic ground and excited states of the chromophore denoted by index i, respectively. The states |i〉 form a complete Hilbert subspace for the case that exactly one molecule of the aggregate is excited. The molecular system Hamiltonian, HS, is however rarely diagonal in the basis of the states |i〉 and resonance couplings Jij between excited electronic states |i〉 and |j〉 occur in all situations interesting for light-harvesting. In the absence of a protein environment, the light would resonantly excite eigenstates of the system Hamiltonian. In all realistic cases, the interaction of the system with its environment co-determines the excitation frequencies, and prescribes thus a “preferred basis” of electronic states in which it is the most advantageous to formulate the energy transfer theory.The Frenkel exciton model provides an excellent tool for the treatment of pigment-protein complexes on femto- and pico-second time scalesJij exceeding the typical reorganization energy λ of the protein bath of the chromophores i and j, (Jij > λ), we include Jij explicitly into the system Hamiltonian. The Hamiltonian is diagonalized to obtain electronic eigenstates, and the effect of the protein bath is included via perturbation theory yielding a Redfield type relaxation tensor. In the opposite case (Jij < λ) we neglect the resonance coupling in the system Hamiltonian, and its effects are included perturbatively yielding Förster type energy transfer rates between localized excited states430In the case of the resonance interaction Let us first focus on deriving a closed set of equations for the excited state populations. Extensive work was done in the last years on developing methods to accurately describe the system dynamics following an ultrafast excitation by external light. The traditional Redfield and Förster approaches were superseded by more accurate (exact in some cases) methods, such as HEOM323336373839Commonly, equations of motion for some relevant degrees of freedom (DOF), electronic states in our case, are derived by reducing the Liouville - von Neumann equation for the total density matrix to an equation for the so-called reduced density matrix (RDM). These equations describe time evolution of a molecular system for a fixed average configuration of the protein environment (assuming fast fluctuations around this fixed average configuration), and they are therefore suitable for the description of ultrafast laser experiments. However, on the timescale relevant in SMS (up to tens of seconds), usage of these equations is actually not appropriate. First of all, some transient effect at the short times affect even the long time properties of the system and the steady state population dynamics, and second, slow changes in the protein environment can entirely change the energy landscape including the case that one has to change the theoretical limit  in which one works. The latter case is especially difficult to treat and requires to go beyond the traditional master equation approaches which we apply here. In this work we therefore concentrate on the extension of the validity of the master equation approach towards long times under the assumption that the dependence of the Hamiltonian of the system on time is negligible within one absorption emission time scale (nanoseconds). As for the transient effects at short time, when dealing with fast dephasing of optical coherences, short time transient effects are responsible for the absorption lineshape. This aspect of the transient effects will be taken into account in full.Spontaneous emission of photons by chlorophylls occurs with a nanosecond life-time. Another class of transient effects, namely dynamic electronic coherence due to excitation by light, is therefore also unimportant and its treatment can be avoided. We therefore derive approximative equations for the population dynamics only, with the validity in the range from picoseconds to tens of seconds. The full derivation including all the approximative steps can be found in section IV of the SI. Here we present a brief, intuitive version outlining the basic concepts.W(t) which follows the Liouville–von Neumann equation. There are several methods how to arrive to a master equation (in a convolution-less form) for the RDM ρ(t) = TrBW(t)31Our Hamiltonian consists of the system, bath and system-bath interaction terms, and we formally assume some total density matrix whereH consists of the bath-renormalized system Hamiltonian HS (t0) and the system-light interaction, which is (in the dipole approximation) given by the dipole moment operator μ and the electric field strength E (t). . The bath is completely eliminated in the reduced description, and its effects are represented by the relaxation tensor t0, in which the initial condition for the propagation is set, or more precisely, the relaxation tensor depends on the quantity t − t0. An exact relaxation tensor would also depend on E(t). In a standard derivation of t = t0. In general, the choice of t0 is arbitrary, and we should make it such that the temporal profile of the excitation field is non-zero for t > t0 only. However, in most of the practical theoretical approaches, the evolution of the bath due to excitation of the system is reflected in the relaxation tensor τc. By choosing t0 such that t − t0 > τc for times t for which |E(t)| > 0, we could always make the relaxation tensor constant during the action of the pulse. This is obviously an artifact of the approximations used. For a smooth envelope of the external field changing on the same or slower timescale than τc, there is no good choice of t0. The relaxation tensor always becomes constant before the action of the excitation pulse is over. Luckily, for weak external field excitation we do not need to account for the E(t) beyond low orders of perturbation theory. In this regime, there is a natural choice of time t0 which enables us to correctly account for the transient time dependence of the relaxation tensor even for a steady state externally driven by steady state light. It is important to note, that the relaxation tensor The total Hamiltonian ρii and coherences ρij, i ≠ j are assumed independent), although this we do only to simplify the resulting equations. Secular approximation could be avoided if one so wishes, at the cost of treating the full RDM. We will base our treatment here on W(t) is presented in Section IV of the SI, where we also discuss approximations involved in disposal of aditional terms which arise in the rigorous procedure. Keeping thus only terms of the first order of explicit appearance of the field E(t) in Let us now formulate the equations of motion for the excited state evolution in the linear regime of the system’s interaction with the electric field. The validity of the linear regime has been discussed e.g. in refs j to i), i, including the rate of radiative and nonradiative depopulation γi is responsible for the absorption lineshape . The evolution operator element reads asAs expected, the optical coherence is proportional to the electric field t − t′ by a Dirac delta pulse, E(t) ≈ δ(t). The time t − t′, not t0, is therefore a correct physical start of the bath reorganization. We fix the wrong start of the bath reorganization by correcting t0 = t − t′. It is important to note that such a correction of the behaviour is not possible directly in t0 = t − t′ is actually not a solution of γi would quickly become constant for t − t0 > τc and the transient effects for t − t0 ≈ 0 would be lost completely. However, in t0 = t − t′ is due to a different treatment of the bath. In a response function approach, of which the linearization of the full equations of motion with respect to the field is a variant, it is in general possible to account for the bath in a more consistent way than in master equations. We discuss this issue in more detail in Section IV.C of the SI. In ordinary master equations for RDM, the bath is correctly described at t0, and the description of its subsequent evolution after t0 is extremely limited. An example of such limitation is discussed e.g. in ref. The element t0 → −∞. We can expect that the simultaneous action of pure dephasing and external driving by a field with a slowly varying envelope creates a steady state optical coherence. The dependence on t0 in the upper limit of the integral describes a transient evolution of the optical coherence after switching on the interaction with the field. Now that the short time time-dependent nature of the dephasing rates is taken into account correctly by properly placing the start of the bath reorganization to the time t − t′, we can set t0 → −∞ and write:In most biological energy transferring systems, the pure dephasing is much faster (hundreds of fs) than the population relaxation (units and tens of ps). It is therefore reasonable to set the upper limit of the integration in t is a global time which can run through the whole minutes long SMS experiment. The evolution operator changes on an ultrafast time scale, but this timescale is scanned in the integration over the variable t′. The properties of the Hamiltonian HS (t) change on a very slow time scale , and so does the evolution operator element t − t0 small, Here we defined t − t0, although they may depend weakly on the time t, i.e. kij = kij(t) and Γi = Γi(t). Now, we are ready to insert The purpose of deriving Pi(t) = ρii(t), and we used the fact that μi0 and even Here, we defined E(t)E(t − t′) would thus be replaced by 〈E(t)E(t − t′)〉 which can be interpreted as a quantum mechanical expectation value. The latter expression has the form of two-time correlation function of the electric fields of the light and its Fourier transform is the power spectrum of the light42In Now, inserting we arrive atW42Our effort has yielded a closed set of equations for excitonic populations only. The population changes are given by the transfer rates between electronic levels, population quenching and a source terms expressed as an overlap of the excitonic spectra with the light spectrum. All quantities are in principle dependent on time, most importantly the excitonic absorption spectrum and all rates can weakly depend on time to simulate slow changes of the protein and chromophore configurations. Also the light spectrum can be considered time-dependent by generalizing the Wiener-Khintchine theorem for the instaneous power spectrum W(t) (in SI) to It should be noted that equations of the type of 50According to crystalographic studies, LHCII complex consists of three monomeric units, each containing 14 chlorophylls and four carotenoids: two luteins, neoxanthin and a carotenoid of the xanthophyll cycle−1. Although the blue Chl b shoulder is not perfectly reproduced, the agreement between measured and theoretical absorption is good in the region of our excitation, and the fluorescence (FL) spectrum shows a good agreement in general. We therefore conclude that our excitonic model captures correctly the features of the studied system that are the most relevant in the present study.In The FL spectrum in The calculated bulk spectra seem to be in a good agreement with the experiment. Our model also reproduces successfully the statistics from the SMS experiments. In The next feature of the LHCII single molecular spectra that we need to address is the significant amount of blinking, i.e. reversible switching to the off state. Since the measured dwell times in the off state are in the range of seconds, which is significantly longer than the lifetime of any long-living species such as triplet statesQY state. Due to its short excited state life-time, Lut could in principle act as an excitation (and fluorescence) quencher. Let us test this mechanism within our model to see if it can account for the observed blinking. The important parameters of the lutein in context of our model are its S1 state site energy relative to its groundstate and the coupling to chlorophylls, in particular to Chl a612.One of the possible mechanism of FL quenching in LHCII, proposed by Ruban and coworkers77−1. The energy dependence agrees well with the one obtained by Ruban−1) and the plateau enables Lut to act as an efficient quencher even in disordered systems.In −1. Due to large reorganization energy, 14500 cm−1 corresponds to the zero-phonon line at 13900 cm−1 and thus agrees with experimental observations−1 in our simulations of blinking. We define the quenched state by the value of 12 cm−1 for coupling of the Lut 1 to Chl 612 and the unquenched state by the zero coupling. Our model allows any type of time dependency of the Chl-Lut coupling to be used, and it could in principle accommodate input from structure based MD studies and quantum chemical treatment of the (Dexter type) coupling of the Chl QY and the Lut S1 states. However, a much rougher phenomenological model of the Chl-Lut coupling changes enables a better discussion of the feasibility of the proposed quenching mechanism than the parameter free ab initio calculations suffering from uncertainties in the structural information. Next we proceed to model the blinking statistics.In et al. in ref. et al., see SI and refs As mentioned in the Introduction, the blinking statistics alone can be well described by a two-level model proposed by Valkunas et al.To connect the two PES model to our particular Lut quenching model, we assume that the change of protein conformation somehow changes the Lut-Chl coupling. The Lut S1 state does not have a dipole moment, and the resonance coupling similar to those between allowed states does not occur here. The two different protein conformations responsible for the quenched/unquenched states would then result in two slightly different orientations/positions of the pigments, leading to different strengths of the coupling. This mechanism is in accord with recent quantum-chemical study by Duffy −1 for couplings and 1 cm−1 for energies. For every realization of the disorder a 60 s trace is modelled. This is repeated for 200 realizations of the disorder, reflecting the experimental conditions. The resulting statistics are presented in Finally, we can connect the two models described above and simulate the blinking behaviour. To this end we continuously model the fluorescence of the LHCII complexes, and output the intensity (and spectrum) every 10 ms corresponding to the experimental integration bins. Simultaneously, we let the protein do the RW on its PES, and we adjust the Chl/Lut coupling, when the protein switches between PES. To obtain more realistic traces, either the site energies or couplings can be slightly varied after every jump, resulting in different energy levels. Such a procedure, however, does not lead to qualitatively different conclusions and it can be in principle omitted. In the calculations presented here, we used Gaussian disorder with the FWHM of 0.3 cmTotal dwell times in h(2) (τ) = 〈I(τ)I(0)〉/〈I(0)〉2. This quantity is well-known from single-molecule measurements, where it is often used to characterize the blinking behaviourh(2) (τ) obtained from 50 measured long enough traces, compared with the model. We can see that the agreement between experiment and theory is good, indicating that our model gives reasonable switching between the intensity levels. The shape of the correlation function is given by the dwell time statistics, see also For the reasons stated above, the level access frequency distribution is not well suited for comparison of the model with the experiment. A more appropriate measure of the blinking would be the intensity-intensity correlation function defined as et al.et al.We have derived approximate equations of motion for populations evolution on the timescale of the SMS experiment. We have shown that the weak illumination regime, in which the SMS experiment is performed, allows for an effective source term description of the light-matter interaction in which short time transient effects arising in the photoinduced evolution of molecular systems can be consistently accommodated side by side with the slow evolution of the protein bath observed in SMS experiments. We demonstrated the validity and scope of application of our equations by simulating our single molecule experiment on LHCII monomers. Based on the recent research in elucidating the NPQ mechanism in LHCII and the connection between fluorescence quenching and energy dissipation we implemented energy transfer to Lut 1 as a blinking mechanism. Based on our calculations we were able to confirm the findings of Duffy et al.The agreement between the theory and experiment also serves as a good demonstration of the scope of our equations. They provide a description for controlling the energy transfer in the system by modulating the parameters of the excitonic model. We are aware of the remaining phenomenological nature of our connection of the 2-level switching model with the excitonic model. Further improvements in the direction of introducing more parameters with a particular physical meaning, for example the relation to the actual PES shape, are needed and will be subject to further study. Also recent experimental observations indicate the presence of more relevant timescales in the intensity traces suggesting the inadequacy of a 2-level model with one reaction coordinate. Finally, although some connection between the fluorescence blinking and NPQ was already shown by Krüger μg/mL phospholipase A2 (Sigma)β-D-maltoside) and then immobilized on a PLL  coated cover glass. Addition of an oxygen scavenging mix of 750 μg/ml Glucose Oxidase, 100 μg/ml Catalase and 7.5 mg/ml Glucose  to the closed sample chamber inhibited the formation of highly reactive singlet oxygen and improved the photostability of complexes.Trimeric LHCII complexes of spinach were isolated from freshly prepared thylakoid membranes as described earlierC as described previouslyvia a CCD camera  with an integration time of one second and the wavelength integrated fluorescence intensity via an avalanche diode  with a binning time of 10 milliseconds. The fluorescence of one complex was analyzed for either one minute or until it photo-bleached and a set of 200 complexes served as the basis for statistical analysis. The fluorescence peak distribution was obtained by fitting of a skewed Gaussian to the fluorescence spectrum as shown in Kruger et al.A confocal microscope was used to measure the fluorescence of single complexes at 5 °The equations of motion, S are the source terms. where t0 can be send to −∞ and the populations then depend only parametrically on time t. The weak dependence of S and t makes it possible to explain changes in the populations of the emitting states of a molecular system due to slow changes of the protein environment and the structure of the molecular system.This expression enables us to find the populations at any time without the need to solve for all the previous times. If we aim at steady state, How to cite this article: Malý, P. et al. Single Molecule Spectroscopy of Monomeric LHCII: Experiment and Theory. Sci. Rep.6, 26230; doi: 10.1038/srep26230 (2016).


Probiotic treatments are thought to increase the levels of commensal bacterial species that populate the human gut, causing no harm to their host and playing an important role in maintaining gut health. This study is an investigation of the effect of a probiotic treatment on the level of a known commensal bacterium in the guts of healthy human subjects, which was significantly increased with probiotic treatment compared with a control. The authors concluded that the probiotic may thus help to promote gut health. These results were subsequently disputed on publication of conflicting evidence from another research group. In response, the authors of this study conducted their assay with a larger sample size, shown in Fig. t-test p < 0.05), although the difference between probiotic and control treatments appears slightly smaller.Bar charts are often used to display results, but can misrepresent or obscure patterns in the data. The original data from this study are summarized in Fig. t-test used here; the data should therefore have been analysed using a non-parametric test, such as the Mann–Whitney U test. The split between high and low responses to probiotic treatment observed in the original study was a potentially biologically interesting result, and the factors that determine a high-level response may be worth investigating, but this was not the conclusion that was reached by the authors.However, when the data are displayed in a scatter plot, showing the response of each individual to the probiotic treatment in the original study Fig. , a more A further issue arises from the way the results were presented in the study. Note that the y-axis spans 10 % in the original Fig.


Saúde Não Tem Preço (SNTP)] for access to diabetes treatment medicines in Brazil.In 2011, private pharmacies associated to the Brazilian Ministry of Health provided patients with two types of insulin (regular human insulin and isophane insulin or NPH) and three oral antidiabetic medications (5 mg glibenclamide and 500 and 850 mg metformin) free of charge. The aim was to evaluate the impact of the “Health Has No Price” Program [This longitudinal and observational study is based on the number of units of oral hypoglycemic agents, insulin and insulin analogues supplied in 55,000 private pharmacies from February 1, 2010 to January 31, 2012. The number of tablets  and international units  supplied in the first 12 months of the SNTP Program were compared with the number of tablets and international units supplied in the 12 months prior to its implementation.The insulins in the SNTP program had the highest percentage change in the number of international units supplied; regular human insulin increased by 97.8 % and isophane insulin (NPH) by 78.0 %. Among the oral hypoglycemic agents, 5 mg glibenclamide increased by 65.9 %, and 500 and 850 mg metformin increased by 46.8 and 39.9 %, respectively, in the number of tablets dispensed in the first year of the SNTP Program. Among the hypoglycemic agents not available in SNTP, 4 mg glimepiride had the highest percentage increase in units supplied (19.2 %) in the same period. Among the insulin analogues, which were not available in the SNTP Program, insulin glulisine showed the greatest increase in units dispensed (34.2 %).The SNTP Program contributed to increased access to medicines for the treatment of diabetes in Brazil. According to the World Health Organization (WHO), access to essential medications is one of the five indicators of progress in securing the right to health . AlthougAccording to Cameron et al. , even whAlthough the Brazilian Public Health System [Sistema Único de Saúde (SUS)] has the duty to provide medications for the treatment of diabetes that are included in the national list of essential medicines , 8, BahiTo increase access to medications in Brazil, in 2006 the state began to subsidize approximately 90 % of the cost of drugs used for the treatment of diabetes and hypertension through a co-payment system associated with the Ministry of Health that covered medications purchased from private pharmacies . In FebrWe performed a longitudinal observational study of the access to antidiabetic medications in Brazil after the implementation of the SNTP Program. Data were collected from 55,000 pharmacies, representing approximately 76 % of private pharmacy establishments in the country, from February 1, 2010 to January 31, 2012 [The number of supplied units of all medicines for the treatment of diabetes in the SNTP Program increased in the first 12 months of the SNTP Program compared with the 12 months prior to the implementation of the program. The percentage of variation ranged from 39.9 to 97.8 %. Four sulfonylureas , one biguanide (metformin) and three fixed-dose combinations marketed in Brazil were included in the analysis of oral antidiabetic medications. The number of tablets supplied in the SNTP program increased from 39.9 to 65.9 % in the first year of the program. No other oral antidiabetic medication showed a comparable increase in the number of units supplied. The number of tablets dispensed (none in the SNTP Program) of the three fixed-dose combinations analyzed decreased after implementation of the SNTP Program  showed an increase in the number of international units dispensed Table .Table 2NThis is the first study describing the impact of the SNTP Program on the access to antidiabetics in Brazil. The results confirmed a significant expansion of access to the diabetes treatment medications included in the SNTP Program, especially compared with other medications of the same therapeutic classes that are available in the Brazilian market. The analysis of the percentage change in the number of oral antidiabetic tablets and the number of international units of insulin supplied, whether as single agents or fixed-dose combinations, indicates that access expansion was greater for medicines included in the SNTP Program.It was further observed that a lack of some fixed-dose combinations in the SNTP Program may result in the prescription of two individual medicines. The four fixed-dose combinations analyzed and formulated with active ingredients of single agents can be obtained at no cost in associated pharmacies. These combinations exhibited a decrease in the number of units dispensed after the start of the SNTP Program. This result may indicate a preference for the prescription of medicines available through the program.The implementation of the SNTP Program, through an agreement between private pharmacies and the Ministry of Health, increased the access to medicines for the treatment of diabetes in Brazil. Also, the number of associated pharmacies increased from 14,003 in December 2010 to 22,470 establishments in July 2013, covering 3664 cities [The initiative by the Ministry of Health to subsidize the purchase of medications in private pharmacies began in 2006 through a co-payment system in which the government was responsible for approximately 90 % of the cost of some antidiabetic and antihypertensive medicines. From 2011, the government began to pay the full cost of medications included in the SNTP program . The conMortality due to diabetes declined in Brazil over the 15 years between 1996 and 2011, minimally in men but considerably in women . HoweverThe number of dispensed units of oral antidiabetic medications included in the SNTP Program was eight times higher than the growth in the pharmaceutical market in Brazil during the same period (12.7 %). The highest percentage increase in oral antidiabetics was observed for 5 mg glibenclamide (65.9 %). The highest variation in the number of tablets was for 500 mg metformin, with an increase of over 135 million tablets compared with the 12 months preceding the implementation of the SNTP Program.The insulin medications included in the SNTP Program showed the greatest significant changes in the number of international units dispensed. The increase was 97.8 % for regular human insulin and 78.0 % for isophane insulin (NPH). Among the antidiabetic medications not included in the SNTP program, only insulin glulisine significantly increased (34.2 %), but this increase was still less than the growth observed for the insulin types included in the program.Despite the observed increase in the number of international units of insulin analogues dispensed, health technology assessments conducted by the National Technology Implementation Commission  for SUS in 2013, recommended against the inclusion of the fast-acting insulin analogues  for the treatment of type 1 diabetes  and the It is important to note that a limitation of the results of this study did not include medicines used in hospital or dispensed for free at pharmacies of the Brazilian Public Health System, which according to Gialdi , represeThe results of this study reveal that the SNTP Program has significantly contributed to an increase in access to medications for the treatment of diabetes, indicating that this public health policy has achieved its goal.


Large-scale public health interventions with rapid scale-up are increasingly being implemented worldwide. Such implementation allows for a large target population to be reached in a short period of time. But when the time comes to investigate the effectiveness of these interventions, the rapid scale-up creates several methodological challenges, such as the lack of baseline data and the absence of control groups. One example of such an intervention is Avahan, the India HIV/AIDS initiative of the Bill & Melinda Gates Foundation. One question of interest is the effect of Avahan on condom use by female sex workers with their clients. By retrospectively reconstructing condom use and sex work history from survey data, it is possible to estimate how condom use rates evolve over time. However formal inference about how this rate changes at a given point in calendar time remains challenging.We propose a new statistical procedure based on a mixture of binomial regression and Cox regression. We compare this new method to an existing approach based on generalized estimating equations through simulations and application to Indian data.Both methods are unbiased, but the proposed method is more powerful than the existing method, especially when initial condom use is high. When applied to the Indian data, the new method mostly agrees with the existing method, but seems to have corrected some implausible results of the latter in a few districts. We also show how the new method can be used to analyze the data of all districts combined.The use of both methods can be recommended for exploratory data analysis. However for formal statistical inference, the new method has better power. Assessing the impact of large-scale interventions is essential in the context of scarce resources . For insNevertheless, the impact of these programs must be assessed and the assessment of intermediate outcomes is essential as a prerequisite for understanding the mechanism through which the interventions may have an impact. One strategy proposed by Lowndes and collaborators  consistsOur objective in this paper is to propose an alternative to the GEE-based method to make inferences about pre- and post-intervention differences on the basis of such reconstructed data. Though we apply the method to the analysis of condom use in FSWs, the proposed method is a combination of standard analysis tools and is applicable to any context where one seeks to make inferences about the effect of an intervention on the rate of occurrence of a given outcome when baseline data are not available but can be assessed retrospectively using a questionnaire.In terms of broad statistical strategy, the idea is to use the fact that the data observed are times-to-events and that the goal of the analysis is to make inferences about a change-point in the rate of occurrence of one of these events. Recently, Minard and collaborators  comparedThe paper is organized as follows. In the methods section we describe the type of datasets under consideration, quickly review the GEE method, describe our proposed Cox-binomial approach and give the details of the simulation study and real data application through which the methods will be compared. The results of these comparisons are summarized in the results section. A discussion of the strengths and weaknesses of the proposal along with ideas for further research are outlined in the discussion section. An appendix with technical details as well as a file with the R code required to implement the new method are also provided.t0, on the basis of such data. In the condom use study, we are interested in the detection of changes in how FSWs start CCU before and after 1-1-2004, date at which the Avahan program started its prevention intervention [The method that we propose can be applied to cross-sectional studies where participants are randomly recruited in a specified target population at a specific point τ in calendar time (or over a relatively short period of time about τ). For instance in the condom use study, women involved in sex work at well-defined locations were sampled in 2006 (with the exception of a few districts where the sampling was done in 2007 or 2008). Even though we do not consider it in this paper, survey weights can presumably be added to the methods to handle data obtained with sampling schemes other than simple random sampling. Each participant recruited is asked to provide two dates: (i) the date at which she became part of the target population and (ii) the date at which some permanent status change took place. In the condom use study, each woman was asked (i) at what date she started her career as a sex worker and (ii) if she consistently uses the condom with her occasional clients and if so, since when. The objective is to make inferences about differences in how permanent status change takes place before and after a given calendar time, say rvention . Becauservention  the naturvention . Consequt, say Rt = Ut/Nt, is fairly straightforward with the data that are available. As illustrated in Table one of Lowndes et al., the denominator Nt of the rate is the number of women in the survey who begun sex work before time t while the numerator Ut is the number, among the Nt women who begun sex work before t, who started CCU before t. As long as the intervention does not have an impact on the length of the career as FSW (more on this in the Discussion), then these crude estimates of the rate of condom use should be unbiased.Getting crude estimates of the rate of CCU at any given calendar time Rt is steadily increasing with t, the question of interest is whether this rate of increase changes after calendar time t0. A first visual assessment can be done by plotting Rt as a function of t for several values of t and seeing whether the slope of the relationship changes after t0. Lowndes et al. formally tested whether the difference in the average slope was different before and after 1-1-2004 by fitting a binomial regression model with linear link, with a subject being a FSW, the repeated response being whether the FSW consistently uses the condom in a given calendar year and the covariates being indicators corresponding to the calendar years and testing the appropriate contrast for significance.Under the assumption that t at which the rate Rt is calculated. Hence treating the condom use statuses at each t as a cluster of longitudinal observations may not be appropriate. But most importantly, the method is very likely to conclude that the slope after time t0 is not different from, or maybe even significantly lower than, the slope before time t0 when the rates before t0 are already high. This is easily seen with an example: if the condom use rate goes from 70% to 90% from 2001 to 2003, then it would have to go from 90% to more than 110% from 2004 to 2006 in order for the average slope to be steeper after 1-1-2004 than before 1-1-2004, which is of course impossible. Hence this test of change in average slope cannot possibly assess whether CCU increases after a given calendar time if the rate of CCU is already high before that calendar time. Moreover, as discussed previously, the literature suggests that an approach based on time-to-event modeling is likely to be more powerful.There are two main drawbacks with this GEE-based method. First, each FSW is not observed at every given time t0 and that (ii) only uses the two dates provided by the FSWs (time at start of career as FSW and time at start of CCU) as data inputs.Our objective is to propose a method based on time-to-event modeling that, unlike the GEE approach, (i) does not lose its efficiency when condom use is already high before Di denote the calendar time at which woman i begins her career as FSW. Let Yi = 1 if she consistently uses the condom when she starts working as a FSW and let Yi = 0 otherwise. Let Ci denote the amount of time during which woman i works as a FSW before starting CCU. Note that when Yi = 1 woman i consistently uses the condom at the start of her career and thus Ci = 0. On the other hand, when Yi = 0 woman i does not use the condom as soon as she starts her career and therefore Ci > 0. If we denote by Fi the length of the career of woman i as a FSW, then if Ci < Fi, woman i will start to consistently use the condom before the end of her career. Conversely, if Ci > Fi, then woman i will not use the condom consistently during her career. This notation is illustrated in Figure Our strategy is based on the following assumption in terms of the chronology of CCU. We suppose that when they begin their career, FSWs either immediately start CCU, either they do not. If they do not, then they might eventually start CCU at some time before the end of their career, or they might not. Mathematically, let i may only be included in the study if she started her career before τ (Di < τ) and if her career does not end before τ (Di + Fi > τ); this is the case for women B, C and D in Figure Di and Yi from the information provided by the FSWs taking part in the study. However we only get a lower bound on Fi  and therefore its value is right-censored for every FSW in the study, i.e., 100% of the observations of Fi are right-censored. As for Ci, we know its exact value if FSW i has started CCU before τ  if she does not use the condom consistently at the time of data collection τ , we use a mixture model [Ci = 0  with probability πi and that Ci > 0  with probability 1-πi. Then for the conditional distribution of Ci given Ci > 0, we can use any standard survival model.Our main interest is in the distribution of re model . We suppt0, we must model πi and the distribution of Ci when Ci > 0 as functions of t0; of course, other covariates can be included in the model and we give the details of the general model in Appendix A. There are several modeling options for πi. In our case, because we are mainly interested in comparing how FSWs start CCU before and after the intervention, we use a simple binomial regression model. Let xi = 0 if FSW i started her career before t0  that takes on value 0 when t < t0 and value 1 when t ≥ t0; once again, other covariates (or stratification variables) can be used and a more general formulation of the model is given in the Appendix. Then a change in the risk of starting to consistently use the condom at time t0 can be estimated by fitting a Cox model to the dataset comprised of FSWs for whom Ci > 0, with Ci as response and zi(t) as time-dependent covariate:As for the distribution of Ci and Fi are independent, we show in Appendix A that the two models can be fitted independently of each other with standard binomial and Cox regression software. Effect of t0 on each model can be assessed separately, or the likelihood ratio  statistics to test whether xi and zi(t) are significant in their respective models  can be added together. Under the null hypothesis of no change in CCU at t0, this sum of two likelihood ratio  statistics approximately follows a chi-squared distribution with two degrees-of-freedom.Under the assumption (which we discuss below) that The Cox-binomial method described above can also be used on clustered data. As we show in the Appendix, all one has to do is fit the two models  with methods that will yield robust “sandwich” variance estimates of the parameter estimators and then use a Wald test on two degrees of freedom instead of a likelihood ratio test.As a referee suggested, this Cox-binomial model can be approximated by a single Cox model by imputing a very small positive time to the observations that have the event at time zero. This modeling approach is easier to implement and can be more easily generalized, as is the case when one wishes to include random effects, for instance. However we do not advocate the use of this approximation when the individuals who have an event time equal to zero represent a non-negligible proportion of the sample, as will be the case in our data application.Fi) followed a Weibull distribution with shape 3 and scale 40. Condom use was simulated according to the Cox-binomial model, whereby each woman started to consistently use the condom at the beginning of her career with probability π1 if she started sex work before 1-1-2004 (time t0) and with probability π2 if she started sex work after 1-1-2004. For women who did not consistently use the condom at the beginning of their career, we simulated the duration of sex work until CCU (Ci) from a piecewise exponential distribution with rate h1 before 1-1-2004 and rate h2 after 1-1-2004. The specific sets of values of π1, π2, h1 and h2 used in the simulations are given in Tables We ran some simulations to compare the properties of the two methods. The simulation algorithm and the parameter values were chosen so that the simulated samples were roughly similar to the samples in the real dataset to be discussed below. In all runs, we simulated a population of 800 women. Their dates of birth were randomly generated according to a normal distribution with mean 1973 and standard deviation 7. The age at which they began sex work was simulated from a normal distribution with mean 22 and standard deviation 4. The duration of their career as FSWs  the datResults of the analysis of the same data with the Cox-binomial approach are summarized in Table We also tried the single Cox model approximation by fitting the Cox model above to the data from all FSWs where the event time for FSWs starting CCU at career start set equal to 1 day. Since we have many districts where initial CCU is high, the method leads to questionable results in some districts. The full results are reported in Additional file To have a population-averaged effect of the intervention, we combined the data from all the districts and re-did the Cox-binomial analysis. For the binomial part of the model, we used GEE with an independence working assumption and a logit link; attempts with a log link failed to converge. For the Cox part, we used the same model as for the district-wise analyses, but fitted the model using the marginal approach  as data inputs, unlike the GEE method which creates a cluster of observations of arbitrary size for each individual. Third, its implementation in practice is quite simple and can be done using standard software for Cox and binomial regression. In this paper, all analyses were performed with R [The method proposed in this paper has several strengths. First and foremost, it remains powerful at detecting change even when the prevalence of permanent status change is high before d with R   and the amount of time spent in the target population before status change takes place (random variable Ci). If there is no such independence, then inferences on the distribution of Ci cannot be made independently of Fi and both the proposed Cox-binomial method and the GEE approach break down. This may be further compounded by the fact that the distribution of Fi observed in the sample is not the same as the distribution of Fi in the target population due to the length bias phenomenon inherent to any prevalent cohort sampling scheme [There are some limitations to the method of which the users should be aware. An important technical issue is that all inferences in the GEE method or in the method proposed in this paper rely on an assumption that cannot be tested with the type of dataset described in this study. Indeed, the validity of the inference relies on the independence between the amount of time spent in the target population  is that it assumes that changes in the probability of status change is instantaneous at time It can also be argued that the scope of the simulation study presented here is somewhat limited, as we did not fit models where the model assumptions were false. But because our objective was to determine whether the Cox-binomial approach overcomes the loss of power of the GEE method when the model assumptions are true, we feel that additional simulations under more general conditions are not necessary at this stage and should be considered in future research.A key limitation that arises when we apply our method to the study of CCU in FSW in India is that the method that we propose here does not address the potential bias due to the “before-after” design of this kind of study. In this particular case, it is very difficult to control for many sources of bias that could cause CCU to evolve in time because no district that was not part of the intervention could be added to the analysis.Ci and Fi, or at the very least to derive a test of independence between these two variables. The fact that the distribution of Ci has a point mass at zero and a hazard rate that may both have a change point at calendar time t0 represents an additional modeling challenge.The problem of inference from length biased data has been studied in the statistical literature, for example using nonparametric methods  or invert0 in a more flexible way. For instance in the case where we suppose the change to take place at an unknown time t0, fitting the proposed Cox-binomial model with several values of t0 and keeping the value of t0 yielding the largest likelihood ratio test statistic is a sensible avenue. However in this case the p-value of the tests cannot be approximated by simple chi-squared distributions anymore. Determination of such p-values has been studied for an ordinary Cox model [As a matter of fact it should be possible to model the manner in which the point mass or the hazard change following the intervention at time ox model , but furOur aim in this paper was to improve the efficiency of the methods used to assess intervention outcomes on the basis of reconstructed data. We proposed a method based on a mixture of a Cox proportional hazards model and a binomial regression model. When applied to an analysis of condom use by female sex workers in India, the method yielded results quite similar to those obtained with a GEE-based approach in districts where initial condom use was low, but yielded results more plausible than those of the GEE-approach in districts where initial condom use was high.n independent FSWs. Let the observed data be i = 1, …, n, where Di is the calendar time at which FSW i started her career, Fi is the total duration of the career of woman i as a FSW, Ci is the amount of time during which woman i worked as a FSW before starting to consistently use the condom, δi = 1 if i must be a FSW at time τ, i.e., Di < τ and Di + Fi > τ. Let Yi = 1 if Yi = 0 otherwise. Then for inference about the distribution of Ci and Fi, the likelihood function will be proportional to (with the slight abuse of notation whereby “Pr” may denote a probability or a density).Suppose that the data are collected at calendar time τ. At that time, we observe Di, Ci and Fi are independent, we can factor the above probabilities as:If we assume that fC,SC, and SF respectively denote the density of Ci, the survival function of Ci and the survival function of Fi . We see that (*) is the likelihood for inference on the distribution of Ci based on a right-censored sample and that (**) is the likelihood for inference on the distribution of Fi on the basis of a sample of length biased data. Most importantly, we notice that (**) does not depend on the distribution of Ci and therefore inference about this latter distribution using only (*) will be valid and efficient.where g and Cox regression models given by Eq. 1 and Eq. 2, where this time xi and zi(t) can be covariate vectors:Let us now rewrite (*) under the binomial regression with link function L asTerm (a) is the contribution to the likelihood of FSWs who consistently use the condom at the start of their career, term (b) is the contribution of FSWs who are observed to start CCU after the beginning of their career and term (c) is the contribution of FSWs who have not yet begun CCU at the time of data collection. By regrouping the terms, we can rewrite Ci with right-censored data and a time-varying covariate based on the sample comprised of FSWs who do not use the condom at the start of their career. Efficient semi-parametric inference about γ can be obtained by replacing (##) with the Cox partial likelihood, which is what most standard survival analysis software do. We therefore get that the overall likelihood is the product of the likelihood for ordinary binomial regression and the likelihood for Cox regression.We recognize (#) as the likelihood for ordinary logistic regression based on the entire sample. As for (##), it is the full likelihood for inference on the parameters of the survival model for K clusters . Standard software that implement binomial and Cox regression for clustered data will output consistent estimators of β and γ, along with their respective robust “sandwich” variance estimators. Typically, β is obtained by solving for β an estimating equation of the form γ is obtained by solving for γ an estimating equation of the form θ =  ', then estimating β and γ separately amounts to solving Let us assume that the data come from The authors declare that they have no competing interests.TD and BA surveyed the statistical literature and investigated the theoretical properties of the Cox-binomial method. TD ran the simulation study and re-analyzed the Indian data. TD wrote the manuscript. CML designed the estimation of retrospective data in absence of baseline and participated in the interpretation of the results. MA participated in the literature review, the development of the Cox-binomial method and the interpretation of the results. All authors read, critically reviewed and approved the final manuscript.The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-2288/14/2/prepubTable with additional analysis results. This is a PDF file that contains a table that summarizes the results of the analysis of the Indian data with a single Cox model and where FSWs who start CCU at the beginning of their career are given an event time equal to 1 day.Click here for fileR code for the Cox-binomial method. This is a PDF file from which the R code to implement the Cox-binomial analysis method described in this paper can be copied and pasted into R or into an R program editor.Click here for file


F be a free Lie algebra of finite rank over a field K. We prove that if an ideal Let  F be a free Lie algebra of finite rank K. By F respectively. An ideal V in the free Lie algebra F is called a verbal ideal if for any V. Let V be a non-trivial verbal ideal of F. An element of F is said to be primitive if it can be included in a free generating set of F. Similarly an element of the relatively free Lie algebra F / V is called primitive if it is extendible to a free generating set of F / V.Let L (Bahturin g and let h be a primitive element of L. It is known that if g is a primitive element in L (Chirkov and Shevelin L such that L and L. In Chirkov and Shevelin (h of h and g are conjugate by means of an inner automorphism of L. This result was obtained by Evans (L, holds for the Lie algebras Let Bahturin . For \doShevelin  proved tby Evans  for freemoshenko . In the moshenko  in the cF be the free Lie algebra generated by a set K of characterisitic zeroF and R of F we denote by R. In the case where R is an ideal of F, u of F we denote by F generated by the element u.Let X and the mappings Fox  gave a df of For any elements T indicates transpose.Let G,  the lower central seriesFor any Lie algebra R be an ideal of F. If u is an element of F, then we denote the images of u under the natural homomorphisms as follows: by F / R,  by Let In Umirbaev , UmirbaeUmirbaev .LetConsider the composition mappingThis mapping induces the mappingsSince the kernel of the mapping F the components For any element f of For each Hence the linear mappingWe need the following technical lemmas. The first lemma is an immediate consequence of the definitions.LetJ be an arbitrary ideal of and Then if and only if for eachThe next lemma can be found in Yunus .LetR be an ideal ofF and Then if and only ifF be the free Lie algebra generated by a set K of characteristic zero and let R be a non-trivial verbal ideal of F.Let f of F the vector For an element Umirbaev  has provLet An element of is primitive if and only if the vector is unimodular inWe are going to consider the case An element of the free metabelian Lie algebra is primitive if and only if the image is primitive in the free nilpotent-by-abelian Lie algebra whereSuppose that the element Let It is clear that Y is linearly independent modulo Y in the algebra H is linearly independent modulo H. Hence the image of Now suppose that Bahturin  we see tAs a consequence of the result of Chirkov and Shevelin , we obtaLet be a primitive element of the algebra and let where If then is also primitive.Let SinceShevelin , we obtaThe mapping The following lemma will play a crucial role in proving our main result.LetR be a verbal ideal of and let Then if and only if there exist an element and an element such thatwhere  and is the ideal generated by the element in the algebrar be an element of the ideal R, F generated by v. Any element of the ideal F depending on the element v. Applying the Jacobi identitiy and the anticommutativity, these commutators can be rewritten as linear combinations of commutators of the formLet If r is written as a linear combination of elements of the form (Now assume that the element the form . WithoutThereforeLet now The kernel of the natural homomorphism g of F can be written as Then there exists an element In contrast to the case of free metabelian Lie algebras we can show that there exists an element There is an element in the algebra such that the ideal of contains the element but the elementsv and are not conjugate modulo by means of an inner automorphism.We consider the element n in Fox  for grouWe haveNow consider the images Clearly By Lemma 6 w can not be written in the form Now we are going to verify that the element F equal to Assume that the rank of Let us calculate the derivative sides of . We haveTaking the image under the homomorphism It is well known that the set Thus every element of  side of  in the fThenWe note that in the algebra So from  we get7\Using  we obtaiIn this work we found a relation between the generator of a one-generated ideal of a relatively free Lie algebra and a primitive element which is contained in this ideal. One can expects to adopt our results for ideals of some relatively free Lie algebras which have more than one generator.


To assess the conclusiveness of Cochrane Eye and Vision Group Reviews (EVGRs). We tested the hypotheses that: (1) the majority of EVGRs are inconclusive; (2) most reviews state the need for further and better studies; (3) the conclusiveness of a given review is affected by the number of randomized controlled trials (RCTs) included and the cumulative number of patients and eyes studied.A retrospective study of all EVGRs available in the Cochrane Library in June 2013. For each EVGR we recorded the number of RCTs found by the reviewers, the number of RCTs included for final analysis as fulfilling inclusion criteria, the total cumulative number of patients and eyes studied, the stated need for further and better studies, the reason stated for further studies and the type of conclusion reached by the reviewer(s). We used the Kruskal–Wallis test to determine differences between ‘‘conclusive’’ and ‘‘inconclusive’’ studies in terms of the outcome variables studied. The correlation between the number of included studies and cumulative sample size was studied using regression analysis.Out of 106 EVGRs, 52.8% were conclusive. In 83.9% of the conclusive EVGRs one treatment/strategy/drug was found to be better than the alternative. The average number of available and included RCTs was significantly higher in conclusive EVGRs (P = 0.007 and P = 0.003 respectively). The total cumulative number of patients and number of eyes studied was approximately ten times higher in the conclusive EVGRs (P < 0.001 and P < 0.015 respectively). A similar percentage of RCTs was included in both conclusive and inconclusive reviews (76 vs. 73%). The vast majority of EVGRs, whether conclusive (84%) or inconclusive (96%), stated the need for further and better studies (P = 0.042). Fifty eight percent of the EVGRs justified the need for further studies for at least two reasons. The reason that was stated the most was a need for a larger amount of RCTs (67%).In approximately half of the cases, EVGRs allow the reader to reach a clinically applicable conclusion. Larger total cumulative participants, total cumulative number of eyes studied and number of RCTs performed all increase the likelihood of an EVGR to be conclusive. In 1993, the Cochrane collaboration was founded in response to Archie Cochrane’s call for systematic reviews of randomized controlled trials (RCTs) in healthcare [The Cochrane collaboration has been noted by Grimshaw to be “the best single resource for methodologic research and for developing the science of meta epidemiology” . The ultIt has been suggested that the goals of the Cochrane reviews are not always reached: indeed, not all Cochrane reviews are conclusive and even when they are it is often stated that there is a need for more and better studies –5. BasedWe therefore designed the current study of all 106 Cochrane Eye and Vision Group Reviews (EVGRs) available until June 1 2013. We aimed to assess the conclusiveness of the EVGRs.Similar to previous definitions we characterized conclusiveness by the ability or not to reach a practical definitive conclusion stating that one treatment was significantly better or not than another treatment or placebo –5. BasedWe selected all of the 106 EVGRs available in the Cochrane Library on 1 June 2013 [The type of conclusion reached by the reviewers was classified into five subcategories: (1) the treatment/strategy/drug was found to be better than the alternative (other treatment/strategy/drug or placebo); (2) no significant differences were found between the two treatments/strategies/drugs; (3) no decision could be reached because the existing RCTs were of poor quality; (4) no decision could be reached because of not enough data; (5) no decision could be reached because of outdated existing RCTs. The first two categories of reviews were defined by us as ‘‘conclusive’’, and the last three as ‘‘inconclusive’’. For the purpose of determining conclusiveness, only the main outcome was considered.P value of <0.05 was considered to be statistically significant.Minitab version 16.1  was used for statistical analyses. We used the Kruskal–Wallis test to determine differences between ‘‘conclusive’’ and ‘‘inconclusive’’ studies in terms of the outcome variables studied. The correlation between the number of included studies and cumulative sample size was studied using regression analysis. Results are expressed as mean ± SD, median (range) or number (%). A We identified 106 EVGRs. The range, median, and mean number of RCTs examined, number of RCTs included for analysis, total cumulative number of patients enrolled, total cumulative number of eyes studied, the stated need or not for further and better studies and type of conclusion reached by the reviewers are described in Table In a few of the reviews it was impossible to retrieve either the number of total cumulative participants (5%) and in many reviews it was impossible to retrieve the total cumulative number of eyes studied (42%) as they were not stated by the reviewers.Contrary to our hypothesis, a very small majority of EVGRs was conclusive. In fact, 52.8% of EVGRs fulfilled our criteria for being conclusive. Thus, a researcher or clinician who wants a definite answer on a specific issue raised and summarized by the Cochrane Eye and Vision Group will get this answer approximately half of the time.In the vast majority 83.9%) of the conclusive reviews one treatment\strategy or drug was found to be better than the alternative or placebo and only in 16.1% of conclusive reviews no significant differences were found. This point, is probably related to the fact that when a significant difference is found there is an intuitive conclusion that the answer is definitive, while when no differences are found (when the null hypothesis cannot be rejected) there is still a remaining issue of potentially insufficient power (that might still be improved by increasing the sample size). An alternative explanation could be publication bias. Indeed, articles with positive results are more likely to be published than those reporting negative results , 8. They3.9% of tThere was a stated need for further and better studies in 84% of conclusive EVGRs and in 96% of inconclusive ones. Although, the difference between 96 and 84% was statistically significant (P = 0.042), it is still apparent that in both groups the vast majority of EVGRs stated such a need. Fifty eight percent of the EVGRs justified the need for further studies for at least two reasons but the reason that was stated the most was a need for a larger amount of studies (67%). The second most frequently stated reason was the need for further studies in subgroups (34%), while the third most frequently stated reason was the need for further studies because of multiple or new strategies\drugs\therapies (33%). Thus, it appears that in most cases whether or not current science supports one type of evidence, the Cochrane Eye and Vision Group often concludes that there is room for more evidence, although there are limited resources for research.It is worth noting that three of our previous reports of the conclusiveness of Cochrane reviews in neonatology , pediatrA limitation of the EVGRs was that it was not always possible to retrieve either the number of total cumulative participants or the total cumulative number of eyes studied as they were not stated by the reviewers. We suggest that there is room for improvement in the reporting of RCTs which should all clearly state both numbers. Another limitation of the study is that other characteristics of EVGRs such as the types of comparisons included and how broad or narrow the questions are were not collected and analyzed. In addition, the field of Ophthalmology is so highly specialized and therefore, retina specialists, for instance, may have better success with using EVGRs to answer clinical questions as opposed to neuro-ophthalmologists or glaucoma specialists. An additional limitation of this study is that though it does not provide insight regarding the quality of the EVGRs or their usefulness. An inconclusive review may be of very good quality and be thorough, of great help to the end-user (summarizing evidence from many sources into one article), and pertinently identifying gaps in our understanding and priorities for future research. In fact, an inconclusive review may be more useful than a conclusive one. Finally, the primary purpose of Cochrane reviews is really to establish a level of evidence by performing a systematic review of the literature. Its primary purpose might not be to “render decisions” regarding whether a treatment is better or not, and in fact it may appear that Cochrane review groups discourage authors from being prescriptive in their discussion and conclusions. In addition, Cochrane reviews provide information on other aspects of treatment such as side-effects encountered but the scope of our study was to review the primary outcomes of the reviews.In summary, we found that the EVGRs allow, in approximately half of the cases, the reader to reach a clinically applicable conclusion. The Cochrane Eye and Vision Group, in a large majority of the reviews, emphasize the weaknesses of both conclusive and inconclusive reviews and suggest avenues for future and better research. The percentage of conclusive Cochrane reviews is lower in ophthalmology than in other fields of medicine studied in a similar fashion.


Label-free microscopy techniques have numerous advantages such as low phototoxicity, simple setup and no need for fluorophores or other contrast materials. Despite their advantages, most label-free techniques cannot visualize specific cellular compartments or the location of proteins and the image formation limits quantitative evaluation. Differential interference contrast (DIC) is a qualitative microscopy technique that shows the optical path length differences within a specimen. We propose a variational framework for DIC image reconstruction. The proposed method largely outperforms state-of-the-art methods on synthetic, artificial and real tests and turns DIC microscopy into an automated high-content imaging tool. Image sets and the source code of the examined algorithms are made publicly available. Quantitative Phase-contrast Microscopy67911DIC microscopy images can be converted to show the optical path length distribution using the image formation model. Image formation in a DIC microscope starts as a light ray enters into a polarizer that creates plane polarized light. A Wollaston prism splits the light into two perpendicularly polarized light rays which are focused on the specimen by the condenser lens. These two light rays pass the sample by a minute shear. The distance between the rays, i.e. the shear distance, is smaller than the spatial resolution of the microscope’s objective. Materials with different refractive indices and the specimen’s thickness generate a phase shift between the light rays. Next a second lens, i.e. the objective transmits the lights to another Wollaston prism that recombines them. Finally, the second polarizer, called the analyzer creates plane polarized light perpendicular to the light of the first polarizer. The two light rays interfere at this point and generate a contrast imageThe prisms are often called DIC or Nomarski prisms. The Nomarski prism can be considered as the combination of the condenser or the objective lens with a Wollaston prism. The interference plane of a Nomarski prism is placed a few millimeters outside of its center, thus placing the specimen in the interference plane makes the use of lenses unnecessary.I by the Point Spread Function (PSF) of the DIC microscope. In linear models the PSF is often chosen to be the first derivative of a Gaussian function or the difference of two Dirac delta functions16x,y) on the domain Ω. The convolution is written as a local integral which has a window W =  × , where 2d + 1 is the window size and ∈W. Furthermore, let dΩ = dxdy and dW = dξdη represent the infinitesimal area elements of the integrals in the image and in the local domains, respectively. The shear direction is denoted by a unit vector u = [u v]T,(u2 + v2 = 1). The model is generalized with an appropriately chosen kernel function K and becomes:The mathematical description of the DIC image formation model was described in several recent studies1314x and y.Note that the integral in microlithThe presented linear image formation limits the accuracy by ignoring diffraction and partial coherence effects. However, in Supplementary Discussion 1 we compare simulated DIC images generated by both the linear model and Here we propose a novel DIC reconstruction algorithm and give the most comprehensive overview of existing methods along with a broad range of comparisons. Furthermore, the tools used for DIC image reconstruction are made publicly available. Our new framework is based on energy minimization. The energy function uses a term that forces similarity to the original DIC image and a total variation-based regularization term. The first utilizes the PSF of the DIC microscope. The PSF is incorporated into our model by local integrals. We show that the derivation operation can be moved from the kernel to the image, which significantly accelerates the computations. Several other reconstruction methods are also described. The algorithms’ source codes are provided with the paper. We compare the reconstruction quality using three different test sets that are made publicly available. The algorithms open up the possibility of using DIC as a quantitative imaging modality.www.highcontentanalysis.org.In this section we describe our variational framework191717After reconstructing the DIC images by each algorithm, we compute the similarity of the results to the corresponding ground truth images. After removing the meaningless negative values, we normalize both the result and the ground truth images between 0 and 1 to compare reconstruction quality. A general approach is to calculate the Mean Squared Error (MSE) between the result and the ground truth images. A lower MSE value means better reconstruction. Higher pixel intensity differences increase the MSE value more than smaller differences. We remark that other conventional metrics such as correlation, norm and Mean Average Error gave the same ranking of the algorithms.In real cases when no ground truth is available, comparing the convolved result image to the input DIC image might be the only way to measure quality. However, it can be a misleading metric because of the imperfect PSF, the noise and the optional smoothness term. In the real tests we show two problem-specific ways of obtaining ground truth images for real DIC images.I given G and K. In a variational framework an energy function has to be defined. The energy function usually has the form of:The goal of DIC reconstruction algorithms is to reconstruct Edata term has low value when I convolved with K is similar to G. Ereg ensures spatial regularization to have locally smooth regions where G is smooth . To find the minimizer, the variable I is usually updated in the direction of the gradient of the function.We propose a model, where We propose the following variational framework. The energy function is formulated asλ is a weight function, providing trade-off between data-driven reconstruction and denoising. TV denoising modelThe data term ensures that the energy is low when the reconstructed image convolved by the PSF is similar to the input DIC image. Our choice of the smoothness term is the Total Variation (TV) term, where x and ∂y denote the partial derivatives. Assuming that lower order terms contribute significantly more than higher order terms, for sufficiently small local integrals the ‘bilinear’ approximation of the EL equation can be formed as:The EL equation of the data term contains the local derivatives of the perturbation function under local integrals. The analytical solution of the EL equations is complex. To overcome the difficulty, we use Taylor series. Let ∂The EL equation of the TV smoothness term is defined pointwise as follows:K can be arbitrarily chosen and used in the equations at this point. Simplifications can be made by using special kernels. The first choice is a rotationally symmetric kernel KR. In case of KR, the one dimensional slices of the function along the parameter lines x or y become even functions, hence all terms having odd m or n in the weight function are eliminated and the bilinear approximation in The finite kernel function G is the gradient of the DIC image, ∇∇I is the Hessian of the primary image. Note that rotational symmetry is not a necessary condition, axis symmetry with axis aligned to the shear direction and going through the origin of the local integration window is sufficient.ξ → ξ − x, η → η − y to the local integral in However, the DIC PSF and its approximations do not satisfy the requirements. By moving the calculations of the derivations from the image to the kernel function with the parameter transformations K0 that has all derivatives zero on the boundary. Note that infinite and bounded kernels automatically satisfy this property. The rationale behind using This form allows the use of the correct PSF. The partial derivatives become more complex, but higher order terms can be cancelled by using a kernel function σ = 0.5. The generated DIC images and the PSF are the inputs of the algorithms. The mentioned σ value assumes ideal conditions which are not present in a microscope. However, since some of the algorithms do not support any other PSF, σ = 0.5 allows us to perform a fair comparison. Furthermore, we have a noisy test set by adding 20 dB noise to the images.For the quality test of the algorithms on the synthetic dataset we have created 20 ground truth images of simple shapes, e.g. ellipse, rectangle or pentagon, and their rotated versions. The images are grayscale, but 15 of them contain only the minimum and maximum intensities, i.e. they can be considered as binary. The other 5 contain a range of different intensities. The simulated DIC images are created by convolving the ground truth images with an estimated PSF which is included in the dataset. The PSF we used is the difference of two Dirac delta functions which is a close approximation of the first derivative of the Gaussian function with τ = 100 fs, λ = 785 nm, 100 MHz repetition rate) was focused into an ~18 μm thick layer of SU-8 2007 photoresist  mixed with rhodamine 6G by a 100x oil immersion objective . The sample was mounted on and translated by a piezo translation system  in 3 dimensions during the laser illumination. The photoresist layer was produced by spin coating 30 μL of SU-8 on a 170 μm thick cover slip and soft-baking it at 95 °C for 10 minutes to remove its solvent. For the step-like structures only one laser beam was used, but for the other structures the original single laser beam was split into four beams with a spatial light modulator  in order to produce four identical structures in a rectangular arrangementFor the quality test of the algorithms on micro-structures we created polymerized fluorescent surface-attached objects. Our dataset of polymerized objects consists of 6 different shapes: squares, square-shaped blocks of increasing height (referred to as step-like structures), triangles, rings, circles and hangar-like forms. The surface-attached test structures were polymerized by two-photon polymerization (TPP)x and y axes, respectively. The AUC is the area under the FPR/TPR plot. Higher AUC value indicates better reconstruction. An AUC value of 1 indicates that the result is equivalent to the ground truth and the thresholded image is always the expected regardless of the threshold value used.The third quality test of the algorithms consists of 60 DIC images of CHO cells. The images were taken at the time when the cells had just started their attachment to the bottom of the dish. We made hand-segmentation of all the images which we use as ground truth for quality measurement of the reconstructions. Since the reconstructions are not binary images, comparing them to the binary hand-segmentations is not a reliable quality measurement method. Segmentation is a different and broad area of image processing and is out of the focus of the current work. Basic segmentation algorithms find a global threshold value derived from the examined image’s histogram. To overcome the problem of thresholding Receiver Operating Characteristics (ROC) Area Under Curve (AUC) is used. To calculate the AUC, the result image was thresholded by every possible value and both the True Positive Rate (TPR) and the False Positive Rate (FPR) were determined for every threshold value. The ROC space is then defined by FPR and TPR as It is important to note that the proposed algorithm is tested to reconstruct DIC images of tissue samples. A DIC image of a brain tissue and the corresponding reconstruction is shown in Z dimension should be imaged where the refractive indices of both the object and the surrounding medium is known. Finally, assuming the discussed linear image formation model, a unit change in pixel intensity in the reconstructed image can be expressed in terms of optical path length change, which then can be used to measure further samples. However, the noise and diffraction effects cannot be accounted from a single image and can introduce errors. In λ = 0.1), that high jumps are preserved and small differences  are flattened. The blurring effect in the bottom of The reconstructed images of the algorithms show the lateral morphology of the examined samples. Furthermore, the reconstructed images show proportions of the optical path lengths relative to the surrounding medium. The lowest value in the image means that the corresponding light rays went through no other material but the surrounding medium. The highest value represents the longest optical path length through the sample. To obtain the exact optical path length distribution, the microscope system has to be calibrated and a quantitative measurement can be performed as follows: The illumination has to be set to a constant value. The microscope software should be set that it does not allow histogram operations (e.g. stretching) on the image. Then an object with known www.highcontentanalysis.org. The algorithms are tested on 3 image sets, namely on a synthetic dataset with a generated PSF, on real DIC images of fluorescent polymerized micro-structures and on images of cells in biological samples with hand-segmentation. The image sets are made publicly available in BBBC. The reconstructions are compared to the ground truth images of the corresponding sets. Every algorithm is able to reconstruct DIC images so that the result image is visually acceptable. Some techniques generate artifacts like bright stripes in the shear direction. When it comes to processing thousands of images, small errors can accumulate resulting in false segmentation. This paper along with the publicly available source code provides a basis for automated high-throughput label-free microscopy. The provided implementations can be used to convert the qualitative DIC images into quantitative ones after calibrating the system. The converted, quantitative DIC images are similar to what other quantitative phase imaging techniques provide with the advantage that DIC is widely available and a cost-effective solution. The reconstructed images are appropriate for morphological analysis or tracking of living cells. Furthermore, a fluorescent channel is saved which can be used to stain specific compartments or speed up the acquisition.In this paper we describe 7 different DIC reconstruction algorithms of 3 types: inverse filtering algorithms, linear equation solvers and energy minimization frameworks. The source code of the algorithms is made publicly available on H of a function f is the convolution of the function by 1/πx:The Hilbert transform17k and l that define the signum function have to be perpendicular to the DIC shear direction. Let H now denote the 2D Hilbert transform and F denote the Fourier transform. The real part of the inverse Fourier transform gives the resulting Hilbert transformed image:The required convolution in Fourier space is a multiplication. In 2D the spatial frequencies I would be a simple division in Fourier space of the DIC image with the PSF. However, dividing by zero would produce large errors. Wiener filtering17If we consider the image formation model written in where the overline is the conjugate transpose.Wiener filtering is one technique to avoid division by zero in Fourier space. If we add regularization terms to the objective function, they can also prevent that values close to zero occur in the divisor. In such an approachA is the Fourier transform of the 2D discrete Laplace operator and./ is the point-wise division. This algorithm is referred to as ‘Yin’.where H note the transfer matrix of the image formation model, g note G and f note I by converting them to column vectors. The transfer matrix H has to be matched with the column- or row-order conversion of the variables G and I. The general objective function can be written as:The reconstruction task can be formulated as a linear equation systemThe smoothness term in the objective function forces the reconstruction to have smooth areas, while the sparsity term makes the pixel intensities in the reconstruction to have small values, close to zero.The described algorithm differs from the original such that the flat-field correctionR stands for the smoothness term which represents the Laplace operator. The matrix W which stands for the sparsity term is a diagonal matrix with positive weights on the diagonals and zeros elsewhere. The objective function is written as:One special form of the objective function uses L2 norm and weighted L1 sparsity besides the data term. The matrix W can optionally be updated during the iterations by a log-sum penalty function, which can speed up the convergence. This algorithm is referred to as Sparseness-Enhanced Multiplicative Update (SEMU).The general objective function written in Previously an energy function for DIC image reconstruction was formulated asn is the normal vector of the shear direction, b is a binary function that indicates whether a pixel belongs to the background or not, λ1 and λ2 are weight constants and Idb is the desired background pixel value. The directional derivative perpendicular to the shear removes the bright stripes that appear in the shear direction as artifacts due to noise and the imperfection of the image formation model. Determining variable b is generally impossible since objects can appear anywhere in the image. One way is to use the smoothed version of the variance filtered DIC image or its thresholded version for b, but it does not guarantee a correct solution. The Euler equation of the energy function is shown in where Let ‘Feineigle’ refer to this algorithm, which solves the problem by iteratively updating the reconstruction based on this function.How to cite this article: Koos, K. et al. DIC image reconstruction using an energy minimization framework to visualize optical path length distribution. Sci. Rep. 6, 30420; doi: 10.1038/srep30420 (2016).