Capturing high-quality images via mobile devices in low-light or backlighting conditions is very challenging. In this paper, a new, single image brightening algorithm is proposed to enhance an image captured in low-light conditions. Two virtual images with larger exposure times are generated to increase brightness and enhance fine details of the underexposed regions. In order to reduce the brightness change, the virtual images are generated via intensity mapping functions (IMFs) which are computed using available camera response functions (CRFs). To avoid possible color distortion in the virtual image due to one-to-many mapping, a least square minimization problem is formulated to determine brightening factors for all pixels in the underexposed regions. In addition, an edge-preserving smoothing technique is adopted to avoid noise in the underexposed regions from being amplified in the virtual images. The final brightened image is obtained by fusing the original image and two virtual images via a gradient domain guided image filtering (GGIF) based multiscale exposure fusion (MEF) with properly defined weights for all the images. Experimental results show that the relative brightness and color are preserved better by the proposed algorithm. The details in bright regions are also preserved well in the final image. The proposed algorithm is expected to be useful for computational photography on smart phones. Exposure time and ISO values are usually carefully tuned by professional photographers to capture well-posed images under various lighting conditions ,2. A paiDirectly brightening the low-light image is probably the most intuitive and simplest way to improve the visibility of dark regions. Unfortunately, such an intuitive way causes another problem, i.e., relatively bright regions might be saturated and thus lose corresponding details . To addrBoth the LIME-  and the In this paper, a new single image brightening algorithm is introduced to achieve the above objective, and the proposed algorithm is supposed to be embedded in mobile devices such as digital cameras and smartphones. Unlike the algorithm in , it is aPropose a simple method to brighten a low-light or backlighting image by fusing additional virtual images;Reduce the possible color distortion of the generated virtual image due to inaccurate IMF;Present a simple method to alleviate the noise in virtual image.All the input image and two virtual images are fused via a state-of-the-art multiscale exposure fusion algorithm, as in , to prodThe rest of this paper is organized as follows. Two virtual images are generated in In this section, two virtual images are generated and both of them are brighter than the input image. To avoid the brightness change from appearing in the brightened images, the virtual images are generated by using the IMFs that are computed from the available CRFs as follows:The IMFs between input image and virtual images are computed via CRFs. The CRFs are generated using the algorithm in  by usingLet the CRFs shown in , there ic-th color channel of image c-th color channel of image Let the input image be denoted as z is smaller than a threshold z is above the threshold [The function hreshold . Here, tIn other words, the IMF from a dark image to a bright one is not reliable if the pixel value is less than the threshold Case 1: None of Case 2: Some of A brightening algorithm under the assumption of the linear IMFs generates a brightened pixel by multiplying a pixel to be brightened by a constant. Such a constant brightening algorithm can avoid the color distortion while it causes the brightness change. On the other hand, a brightening algorithm based on the general IMFs can avoid the brightness change while it causes the color distortion for pixels in underexposed regions of the input image. In this subsection, the advantages of both the algorithms are combined to design an algorithm to brighten the pixels in the underexposed region.Let pixel The values of Consider the pixel Equation  is a claClearly, the values of  that in ,14. As aA dark pixel includes noise. If the pixel  WGIF in . Here, ZThe values of Similar to Equation , the valSince the noise is almost included in the detail layer, the noise is avoided from being amplified by the brightened method .The input image and two virtual images look like three differently exposed images, but they are different from a set of differently exposed images which is captured by a digital camera. Therefore, a different method is adopted to define weights for the three images.As pointed out in the introduction, a possible issue for the single image brightening is that relatively bright regions might be overexposed in the final image because of the brightening. Clearly, this can be avoided if the details in the relatively bright regions in the final image are from the corresponding regions in the input image. To achieve this objective, two different functions are adopted to define the weights for the three images.One function is used to determine amplification factors of all the pixels in the first image. To brighten the dark regions while preserving the details in the bright regions, the bright regions are assigned high weights in the low-light image. The weight is defined asThe other is to measure contrast, exposure level, and color saturation of all the pixels in the three images and it is defined the same as in :(13)w2(zIt can be shown in Equations  and 15)15) that To get the good fused image, in this subsection, the three images are fused via a gradient domain guided image filtering (GGIF) based on multiexposure images fusion (MEF) . The weil-level Gaussian pyramid and GGIF be l-level is computed asl-level Gaussian pyramid of the luminance component of the image l-level fused image is presented asLet Algorithm 1: Single image brightening and the corresponding CRFs Input: a low-light image Output: a brightened image Step 1 Compute IMFs from the available CRFs Step 2 Generate two virtual images with larger exposure times Case1 the value of pixel above 5 do      Brighten the pixel via Equation (17)end  Case2 the value of pixel below 5 do     1. Constructing weight matrix by Equation (2)   2. Decompose input image as base layer and detail layer using WGIF   3. Compute brighten constant    4. Brighten the pixel using Equation (9)end  Step3 Fuse the input image and two virtual images to produce the          final image using Equations (10)–(16).The final fused image can be reconstructed from In this section, extensive experimental results are provided to verify the performance of the proposed algorithm. All images are captured by us using a Nikon D7200. It should be noted that the differently exposed images are also captured at the same time.In this subsection, the effect of exposure ratios of two virtual images on the quality of enhanced image is analyzed. For the same scene, four groups of enhanced images are generated by fusing virtual images with different exposure ratios. In addition, the quality of different exposure images is also discussed. The ground truths of enhanced image are nine real exposure images and the ground truth of virtual image is the real image with the same exposure time as virtual image. The SSIM  index maps are shown in In this subsection, the suitable parameters are selected by a well-used image quality, i.e., the MEF-SSIM in . The tesWhen analyzing the influence of Then, the influence of different pairs of In this subsection, we compare our algorithm with seven state-of-the-art image enhancement algorithms, including two data-driven algorithms ,19 and fFirstly, the possible color distortion of eight algorithms is analyzed. Since a different light source may introduce luminance change that can affect the overall fluctuation of RGB values in the enhanced image, instead of calculating the absolute difference of RGB value, the angular color between two color vectors respectively produced by enhanced image and ground truth is computed as in ,27. As tThe 24 color errors of eight algorithms are shown in Next, the contrast distortion is analyzed in terms of PCQI  , which cThe MEF-SSIM is adopted to further evaluate the performance of eight algorithms. Due to the lack of ground truth, the reference images for the MEF-SSIM are nine real, different exposure images. The nine images contain more information than one dark image, so it is fairer to use this evaluation strategy. The assessment is shown in Besides the objective evaluation, partial enlargements of brighten images are presented in In this subsection, efficiency of the noise reduction is evaluated. When the pixel value is less than 5, the constant amplification will lead to noise amplification, as shown in To reduce the amplified noise and preserve the detail, the base layer of the input image is amplified by Formula  while thIt should be pointed out that the WGIF-based smoothing could be omitted if a stack of images is captured. Frame averaging could be used to reduce noise in the dark regions by properly detecting moving regions. If all the corresponding raw images are available, it is not difficult to detect the moving regions.The running time of these six algorithms is also compared by testing three image sizes on an AMD 2600X CPU. The results are presented as a bar graph, shown in The proposed algorithm outperforms the other five algorithms. However, the proposed algorithm assumes that the accurate CRFs are available. This is not an issue if the proposed algorithm is embedded in a model device. However, this assumption is not true for those images that are downloaded from the Internet. It is very difficult to estimate the accurate CRFs if there is only one image. If the CRFs are not accurate, the IMF between the input image and virtual images are not accurate too. In other words, the brightened image could be a little poor, such as the color distortion in In this paper, we proposed an effective single image brightening algorithm. The proposed algorithm is supposed to be embedded in mobile devices such as digital cameras and smart phones. Two virtually brightened images are generated via intensity mapping functions (IMFs) which are computed by the camera response functions (CRFs). The input image and two virtual images are fused to preserve the natural structure. Since the three images are different from the three differently exposed images that are captured by a camera directly, the weights of these images are specially designed so as to preserve details in bright regions of the input image in the final image. Experimental results show that the proposed algorithm outperforms existing algorithms. The proposed algorithm can be embedded in mobile devices such as digital cameras and smart phones as an app.It should be pointed out that the CRFs are assumed to be available for the proposed algorithm. Unfortunately, this is not always true. As shown in ,30, a le


The connections between index coding and matroid theory have been well studied in the recent past. Index coding solutions were first connected to multi linear representation of matroids. For vector linear index codes, discrete polymatroids, which can be viewed as a generalization of the matroids, were used. The index coding problem has been generalized recently to accommodate receivers that demand functions of messages and possess functions of messages. In this work we explore the connections between generalized index coding and discrete polymatroids. The conditions that need to be satisfied by a representable discrete polymatroid for a generalized index coding problem to have a vector linear solution is established. From a discrete polymatroid, an index coding problem with coded side information is constructed and it is shown that if the index coding problem has a certain optimal length solution then the discrete polymatroid is representable. If the generalized index coding problem is constructed from a matroid, it is shown that the index coding problem has a binary scalar linear solution of optimal length if and only if the matroid is binary representable. The broadcast nature of the wireless medium is utilized by many applications such as multimedia content delivery, audio and video on-demand and ad-hoc wireless networking. The index coding problem introduced by Birk and Kol  aims to Bar-Yossef et al.  studied Has-set and demands another subset of messages called the Want-set. The wireless broadcast channel is assumed to be noiseless. The source is aware of the messages possessed by each receiver and it aims to reduce the number of transmissions required to satisfy the demands of all the receivers.An instance of the conventional index coding problem involves a source that possesses all the messages and a set of receivers. Each receiver possesses a subset of messages called the side information or the The problem of index coding has been extended in many directions. The problem of index coding with the restricted information problem is introduced in . In the Has-set and the Want-set may contain functions of messages rather than subsets of messages. Note that the conventional index coding problem is a special case of the functional index coding problem. The problem with the Has-sets being linear combinations of messages was studied in [Has-sets and Want-sets to be linear combinations of the messages and the corresponding index coding problem is referred to as the generalized index coding problem. For the generalized index coding problem, a generalized minrank parameter, which gives the optimal length for linear encodings, was found in [In a functional index coding problem, the udied in ,12 whereudied in  considerfound in . The papfound in .Has-set of the receivers is as follows: Consider the scenario with one source and four receivers Index coding also finds application in the field of coded caching . Once thThe equivalence between index coding problems and network coding problem is established in . From a We establish a connection between vector linear index codes for a generalized index coding problem and representable discrete polymatroids. It is shown that the existence of a linear solution for a generalized index coding problem is connected to the existence of a representable discrete polymatroid satisfying certain conditions determined by the generalized index coding problem.From a discrete polymatroid, we construct a generalized index coding problem and show that if the generalized index coding problem has a vector linear solution of optimal length over the binary field then the discrete polymatroid is representable over the binary field. An example to illustrate that the converse of the above result is not true, is also provided.A generalized index coding problem is constructed from matroids and it is shown that the constructed problem has an optimal binary scalar linear solution if and only if the matroid is binary representable. This enables us to construct a generalized index coding problem from a binary representable matroid and the constructed index coding problem has an optimal binary scalar linear solution. Also, it is shown that certain generalized index coding problems do not have a binary scalar linear solution of optimal length using the above result.n-linear representation. In this paper, we show that the generalized index coding problem constructed from binary representable matroids has optimal perfect linear solutions. It is also shown the if the generalized index coding problem has an optimal perfect linear solution, the matroid is binary representable. The above result can be used in the construction of generalized index coding problems having optimal scalar linear solutions. A part of the content of this paper was presented in . In thisThe organization of the paper is as follows. In Notations: The set r in which the v of length r and v indexed by the elements of A. For S, S and for a vector v. For u and v. For a vector v. For a matrix M, M and for a set S, M indexed by the set S. For vector subspaces V, the sum of vector spaces is the vector space a set of messages a set of receiver nodes An index coding problem x denotes the message demanded by the receiver R and H denotes the side information possessed by R. Each one of the messages q elements. In an index coding problem, the source can take n instances of each message and encode them together such that each receiver is able to decode all n instances of the demanded messages.For a receiver node l and dimension n for the index coding problem R. An index coding solution for which f is linear.An index code over Has-set, which consists of functions of messages. The demands of the receiver are described by a Want-set. Each receiver The index coding problem was generalized to the functional index coding problem in . In the In this paper, we consider those generalized index coding problems for which the functions demanded and possessed by the receivers are linear combinations of the messages.Definition 1.An instance 1. A source equipped with the message vector 2. A set of clients or receivers n instances of the messages and perform encoding operations such that the demands of the receivers are satisfied. Since the functions in the Has-set of a receiver Has-set, each represented by a matrix Has-set of receiver knowledge matrix. Note that Want-setdemand matrices. Each function Want-set of receiver demand matrix.The source can combine l and dimension n for the generalized index coding problem An index code over f for a generalized index coding problem is linear it can be described as L is a matrix of order L is called as the matrix corresponding to the linear index code f and the code f is referred to as the linear index code based on L.When the index code Has-set. The length l and dimension n of an index coding solution for the index coding problem For an index coding problem ) . Computi) . The lowDefinition 2.An index coding solution for which .An indExample 1.Consider the generalized index coding problem with the message vector The source can satisfy the demands of all the receivers by transmitting three messages Matroids are mathematical structures that capture the fundamental properties of dependence, which are common to graphs and matrices. In , the conIn this subsection, we list a few basic definitions and results from the matroid theory. For a comprehensive treatment, the readers are referred to ,33.Definition 3.Let E be a finite set. A matroid (I1) (I2) If (I3) If E is called the ground set of the matroid and is also referred to as independent sets of The set E is called a basis of E that is not in dependent set. A minimal dependent set circuit. The set of all circuits of matroid A maximal independent subset of (C1)No proper subset of a circuit is a circuit.(C2)If The axioms Each circuit of a matroid is a set that captures the dependencies existing in a matroid. An index coding problem induces certain dependencies. However, these dependencies are not minimal. Rather than trying to find the minimal dependent sets, a common approach is to use the notion of a rank function of matroid defined below to characterize the dependencies.rank function is associated, the domain of which is the power set of E and codomain is the set of non-negative integers. The rank of any X that is a member of A function called the (R1)(R2)(R3)E with rank function Note that the rank of an independent set is equal to the cardinality of the independent set. A matroid is fully described by its rank function and a matroid Example 2.Consider the matroid V such that A over A as its representation is called the vector matroid of A and is denoted by A. For a subset S of the ground set A with columns corresponding to the elements of the ground set in S.A matroid Example 3.For the matroid considered in Example 2, consider the matrix E is said to be multi-linearly representable of dimension n over V over n over k is the rank of the matroid. Let M be the matrix obtained by concatenating the matrices It was established in , that thDiscrete polymatroids are multi-set analog to matroids. Linear representations of discrete polymatroids generalize the notion of linear and multi-linear representation of matroids. In this paper, we establish connections between vector linear index codes for the generalized index coding problem and representations of discrete polymatroids. In this subsection, we review the definitions and results from discrete polymatroids. For a comprehensive treatment, interested readers are referred to ,37.Definition 4.A discrete polymatroid If For all .A discLet (D1)For (D2)(D3)A function nditions :(D1)For The difference between discrete polymatroids and matroids is better understood by comparing the properties of the rank functions of each of these structures. It can be observed that the main difference is that the rank of a matroid The notion of basis and circuits is also extended to the case of discrete polymatroids. A vector be equal . A discrExample 4.Consider a discrete polymatroid on the ground set Consider a discrete polymatroid Definition 5.A discrete polymatroid shown in , that pe.A discA discrete polymatroid can be constructed from any finite set of vector subspaces of a vector space. Let Example 5.Consider the set of matrices Definition 6.For a discrete polymatroid .For a I of the matroid I there exists a unique vector B of a matroid b of D of C of matroid Discrete polymatroids can be viewed as a generalization of matroids ,36,37. TExample 6.Consider the uniform matroid The set of vectors belonging to the discrete polymatroid The set of minimal excluded vectors of l and dimension n for a generalized index coding problem to the problem of representation of a discrete polymatroid satisfying certain conditions.In this section, we explore the connections between the generalized index coding problem and representable discrete polymatroids. Theorem 1 below connects the existence of a linear index code of length Theorem 1.A linear index code over (C1) (C2) For every receiver Proof. A is the concatenation of matrices f forms an index code of length l and dimension n over First we prove the if part. Consider a discrete polymatroid f over l and dimension n exists for the generalized index coding problem f can be written as I be the identity matrix of size I. Let A is the identity matrix, condition (C2) is satisfied. □To prove the only if part, we assume that a vector linear index code Theorem 1 is a generalization of the result obtained in  where thCorollary 1.Corresponding to a receiver A. The columns of the matrix A corresponds to the entries of the discrete polymatroid. By imposing the restrictions, condition (C2) can be expressed in terms of the elements of the ground set.For conventional index coding, the matrix L to correspond to a linear index code for a generalized index coding problem The necessary and sufficient conditions for a matrix found in . TheoremExample 7.Consider the generalized index coding problem of Example 1. There are five messages and since the solution is scalar, dimension is one. Consider the set of matricesAlso let Clearly Example 8.Consider the generalized index coding problem with the message vector The vector linear index code of dimension two is described by the matrixFor Discrete polymatroids can be viewed as a generalization of matroids, as explained in Consider a discrete polymatroid (i)The set of source messages (ii)The set of receivers Receivers in  For a basis vector Receivers in  For a minimal excluded vector Define Receivers in  Define Has-set and The presence of receivers in the set vided in . The difproof in  is modifExample 9.Consider the discrete polymatroid The set of messages possessed by the source is There is only one excluded vector Third set of receivers A connection between an optimal perfect linear solution for the generalized index coding problem Theorem 2.If an optimal perfect linear index coding solution of dimension n over Proof. n over Let C is of order D is of order X and the columns of the matrix The matrix D has rank D to be the identity because if not we can define C. Let From this it follows that the matrix X and possess messages Consider a set S can be divided into two categories depending upon the value of S can be written as The elements of the subset This is true for every In Theorem 2, a generalized index coding problem is constructed from a discrete polymatroid and then it is shown that the discrete polymatroid is representable over the field eorem in . This isExample 10.Consider the discrete polymatroid described in Example 9. The set of receivers constructed from the discrete polymatroid is provided in Example 9. Consider the perfect index code in which the source transmits It was shown in the proof of Theorem 2 that the matrix It can be verified that the matrix C is a representing matrix for the discrete polymatroid Example 11.Consider the discrete polymatroid The set of basis vectors for the problem is The set of minimal excluded vectors of Third set of receivers The discrete polymatroid Though the discrete polymatroid has a binary representation, the generalized index coding problem In this section, we construct a generalized index coding problem from a matroid. The construction explained in Definition 7.Given a matroid 1. 2. (a) (b) (c) Y remains the same in both There is a one to one correspondence between a matroid Remark 1.Every receiver in an index coding problem introduces a dependency between demanded messages, messages available as side information and transmitted messages. Matroids and discrete polymatroids captures these dependencies existing between its elements. Each message and the transmitted index code are viewed as elements in the ground set and the dependency between them is captured. However, for the set of dependent elements to characterize a matroid, it needs to satisfy certain axioms referred to as circuit axioms provided in the paper. The generalized index coding problem constructed in Definition 7 captures all the dependencies.Theorem 3.Consider a matroid Proof. From Theorem 2 and from the fact that there is a one to one correspondence between discrete polymatroid M be a matrix representing the matroid k, the matrix M is a Let Consider the following linear map f is a map from f is an optimal perfect scalar linear index code for Has-sets and the transmitted messages.Receivers in Since Receivers in Since the matroid is representable over a binary field, we have In a similar way, all receivers belonging to Receivers in Note that f is an optimal perfect linear index code. This completes the proof. □The index code is clearly linear and also Theorem 3 shows the existence of a relationship between binary representability of matroids and solutions to certain generalized index coding problems. Theorem 3 is illustrated in Example 12. We use the theorem to show that not every generalized index coding problem has a perfect binary solution in Example 13.Example 12.The uniform matroid Receivers in Receivers in Receivers in The optimal perfect linear index coding solution for the index coding problem is given by the map The index code is as follows: A receiver licit in .Example 13.Consider the index coding problem with coded side information The set of messages Receivers in Receivers in Receivers in The above index coding problem is constructed from the uniform matroid It can be verified that the above generalized index coding problem does not have an optimal perfect scalar binary linear solution as implied by Theorem 3. Since the matroid does not have a linear representation over the binary field, the generalized index coding problem constructed from it does not have an optimal scalar perfect linear solution.In this work, we established a few connections between generalized index coding and discrete polymatroids. It is shown that the existence of a linear solution for a generalized index coding problem is connected to the existence of a representable discrete polymatroid satisfying certain conditions determined by the generalized index coding problem. From a discrete polymatroid, a corresponding generalized index coding problem is constructed and it is shown that a representation to the discrete polymatroid exists if an optimal perfect vector linear solution exists for the generalized index coding problem. An example is provided in the paper to illustrate that the converse of the above result is not true. When a similar generalized index coding problem is constructed from matroids, we show that a binary representation to the matroid exists if and only if the constructed index coding problem has an optimal binary scalar linear solution. The connection is helpful in determining whether the index coding problem has an optimal perfect binary scalar linear solution.Has-set. The elements of the Has-set can be made into any other linear combinations and further study could be done. A possible direction is to construct a discrete polymatroid for any generalized index coding problems. There may exist generalized index coding problems having non-linear solutions for which a connection to a non-representable discrete polymatroid could be established. This has not yet been explored and requires further investigation. Similar extensions can be considered to Theorem 3. Connections between the matroids representable over a non binary field and the generalized index coding problems constructed from those matroids is also another open problem. The connections between error correcting index codes for generalized index coding problems and discrete polymatroids could also be explored.The results of this paper could be extended in the following directions. The construction explained in


The authors wish to make the following corrections to this paper :The body weight given as the weight of the 35th week of age is in fact the weight of the 49th week of age. However, the data presented are correct and the changes do not alter their interpretation.2.3. Experimental Procedure, 1st paragraph, the sentence:There was an error in the original article. On page 4, Section “Body weight (g) was measured at hatch and during the experimental period  using a digital table scale  with a weighing accuracy of 0.1 g.”should be“Body weight (g) was measured at hatch and during the experimental period  using a digital table scale  with a weighing accuracy of 0.1 g.”Due to the mistake mentioned above, we need to make the following changes to figures and tables:Replace With new Replace With new And replace With new The authors would like to apologize for any inconvenience caused to the readers by these changes.


The quality by design approach was introduced to the biopharmaceutical industry over 15 years ago. This principle is widely implemented in the characterization of monoclonal antibody production processes. Anyway, the early process phase, namely the inoculum expansion, was not yet investigated and characterized for most processes. In order to increase the understanding of early process parameter interactions and their influence on the later production process, a risk assessment followed by a design of experiments approach was conducted. The DoE included the critical parameters methotrexate (MTX) concentration, initial passage viable cell density and passage duration. Multivariate data analysis led to mathematical regression models and the establishment of a designated design space for the studied parameters. It was found that the passage duration as well as the initial viable cell density for each passage during the inoculum expansion have severe effects on the growth rate and viability of the early process phase. Furthermore, the variations during the inoculum expansion directly influenced the production process responses. This carry‐over of factor effects highlights the crucial impact of early process failures and the importance of process analysis and control during the first part of mAb production processes. CHOChinese hamster ovary cellsFMAfeed medium AFMBfeed medium BFMEAfailure mode and effect analysismAbmonoclonal AntibodyMLRmultiple linear regressionMTXmethotrexateMVDAmultivariate data analysisPMproduction mediumQbDquality by designRPNrisk priority numberSMstock mediumVCDviable cell density1st centuryCurrent Good Manufacturing Practice for the 21 initiative [PAT – A framework for Innovative Pharmaceutical Manufacturing and Quality Assurance [Q8 Pharmaceutical Development, Q9 Quality Risk Management and Q10 Pharmaceutical Quality Systems [The Quality by Design (QbD) principle is a risk‐based approach to pharmaceutical development and manufacturing . It emerssurance  and the  Systems , 5, 6.The inoculum expansion was assessed as a critical part of the mAb production process by examination of critical process parameters in a design of experiments approach. Our research resulted in the definition of a designated design space and new feedback strategies for a robust process control. This highlights the importance of early process understanding and investigation, while marking the first step towards a full process characterization regarding quality by design principles. Implementing the conducted concept in the process development was thereby shown to be crucial for the studied process as well as similar cell culture processes.Before introducing this guidance the pharmaceutical industry used a traditional approach for process development and regulation: A rigid manufacturing process with batch to batch quality controls and no methodical connection between process, product and clinical application. The QbD paradigm, imposed by the ICH guidelines, was defined as “a systematic approach to development that begins in predefined objectives and emphasises product and process understanding and process control based on sound science and quality risk management” . The objThe streamlined operation starts with the product and process definition, identification of process parameters and a general risk assessment, often using the Failure Mode and Effect Analysis (FMEA) , 10. SubThereby, design space can be described as the acceptable range of process parameters, which is located in a broad characterisation range and inherits the operating range with optimal set points. Working within the defined design space is therefore not considered to be a process change and hence needs no further validation, resulting in cost savings and the maintenance of a steady workflow.This work will focus on the QbD implementation of a monoclonal Antibody (mAb) production process using a Chinese Hamster Ovary (CHO) cell cultivation process , 15. Con22.12 Incubator  using a MaxQ CO2 Plus shaker platform . The cultivation was performed in proprietary and chemically defined cell culture media, all part of the Sartorius Stedim Cellca medium platform. The inoculum expansion was performed using stock medium (SM), whereas the production process used production medium (PM). Additionally, two feeds were used during the production process. Macro nutrients (e.g. glucose) were added using feed medium A (FMA), while micro nutrients (e.g. amino acids) were supplemented using feed medium B (FMB) .For this study a DG44 CHO suspension cell line producing an IgG1 monoclonal Antibody (mAb) was used (Sartorius Stedim Cellca GmbH). Cells were cultivated in shake flasks  in a Heracell 240 CO6 cells/mL), was thawed and transferred to a 15 mL Falcon tube  with 10 mL stock medium. The suspension was centrifuged at 190 x g for 3 min using a Microstar17 centrifuge . After removal of the supernatant, the pellet was resuspended in 10 mL pre‐warmed (36.8°C) stock medium and transferred to a 500 mL shake flask with 140 mL pre‐warmed stock medium. The inoculum expansion was conducted over 16 days at 36.8°C and 7.5% CO2 with a shaking rate of 120 rpm. Cells were passaged by centrifugation of the needed amount of cell suspension, removal of the supernatant and resuspension in fresh stock medium to the initial passage viable cell density (VCD). During the first three passages, the required amount of methotrexate (MTX) was added to the stock medium. From the second passage, 125 mL shake flasks with a working volume of 25 mL were used for the experiments.For the first passage of inoculum expansion a cryo vial, containing 1 mL CHO suspension  from day 3. Due to the cultivation in shake flasks the pH and the dissolved oxygen were not controlled, yet the process was previously analyzed and shown to be reproducible and comparable to bioreactor cultivations of different scales. To improve the comparability all experiments were simultaneously conducted in the same incubator with identical process conditions.The production process was performed in 125 mL shake flasks with 25 mL pre‐warmed production medium. All production cultivations were inoculated to an initial viable cell density of 0.3 × 102.2Samples were taken daily during the inoculum expansion as well as during the production process. Viable cell densities and viabilities were measured using a Cedex HiRes  with a 1:2 dilution in 10 % phosphate‐buffered saline (PBS). Growth rates of the production process were calculated by linear regression of the natural logarithm of viable cell densities against culture duration. The inoculum growth rate relates to the respective last passage of every inoculum expansion (N‐1‐step), in order to ensure optimal comparability of the examined factor effects. Viabilities were calculated as average over the culture duration for the inoculum expansion as well as the production process. The mAb titer was analyzed during the production process by using the Cedex Bio . Therefore, cell separation was performed by centrifugation for 5 min at 190 x g. Specific antibody titers were calculated by dividing the final antibody titer by the integral viable cell concentration over the entire production process duration.2.3The risk assessment was performed using the FMEA approach . The FME2.41 = MTX concentration, F2 = passage duration, F3 = initial passage viable cell density) for a central composite design with three centre‐point runs. The resulting design is illustrated in the supplements. Hereinafter, the factor settings are described as 0 for centre‐point level and –1/1 for the low and high levels of the full factorial cube, respectively. The additional levels for the star of the central composite design are described as –2 and 2.The design and analysis was performed using the DoE software MODDE 12 . The three parameters with the highest RPN during the risk assessment were used as factors  term is the fraction of the variation of the response explained by the model. The adjusted R‐squared (R2adj) term is adjusted for the degrees of freedom of the model.Multiple linear regression (MLR) was used to fit the mathematical model. Various model statistics were investigated in order to evaluate the conducted model. The R‐squared  term. If the y data are not used for calibration, then the Q² is calculated as follows.Here, Ri). The tested null hypothesis is that a fit of the intercept‐only model and the model Riare equal. The reproducibility r compares the replicate variability to the overall variability of the experimental data.The model p‐value represents the significance of the fitted model. It tests the null hypothesis, that the coefficient is equal to zero, for each term. Here, the p‐value belongs to an f‐test, which compares an intercept‐only model (just a constant y = const) with the model under consideration  due to standard operation procedure and good laboratory manufacturing practise.The methotrexate concentration has a significant influence on the antibody production and severe toxic effects on the CHO cells (Severity = 5) . A failu2), the balance between too short passages, leading to an insufficient viable cell density for the expansion of the seed steps, and too long passages, leading to consumed nutrients, can be a critical aspect (Severity = 3). Also this parameter can be of special interest because other failures in the system, e.g. the preparation of the production bioreactor, can lead to a delay in the process and longer passage duration. Likewise, the tight schedule in production and a failure in seed culture could lead to shortened time available for the new inoculum expansion (Probability = 3). In reality, the layout of the inoculum expansion can also be dependent on other factors like working hours and days in the industry. Therefore, the understanding of the impact of the passage duration in combination with the other critical process parameters is needed to define a robust design space for the inoculum expansion.For the passage duration  would be detected quickly; however, a readjustment is virtually impossible without time consuming preparation of new shake flasks and medium (Detection = 4). The readjustment of the passage viable cell density is also logistically impossible in a scaled‐up approach with seed bioreactors due to the preparation of the needed reactor. The probability of a failure was considered to be low yet possible, due to rare inaccuracies during the passages (Probability = 2). It was also considered to show a direct non‐severe impact on the nutrient consumption and thereby the growth rate and viability (Severity = 2). Therefore, the initial passage VCD is used as factor F3.21), the passage duration (F2) and the initial passage viable cell density (F3) were combined in a central composite DoE.The ICH Guidelines determined the implementation of a Design of Experiments approach to investigate the single and combined influence of critical process parameters. Accordingly, the MTX concentration , while the passage duration could only be varied on three levels . As explained in the Material and Methods, a passage duration lower than 2 days (–1 level) did not result in the minimum viable cell number needed for sufficient inoculum expansion. Longer passages than 5 days (1 level) did not fit in the experimental design and total inoculum expansion duration of 16 days. Furthermore, previous experiments show that inoculum expansion passages of more than 5 days result in severe negative effects due to consumed nutrients. The centre‐point experiment on level 0 was conducted with four passages of 3 days and one passage of 4 days to fulfil the total duration of 16 days. The respective last passage of every experiment was cultivated 3 days before inoculation of the production processes. Figure During the inoculum expansion the growth rates and cell viabilities of each experiment were monitored as responses for the early process steps. The growth rate was calculated for the respective last passage of the inoculum expansion. These responses provide specific information on the inoculum expansion culture. The growth rate determines when the minimum viable cell number for inoculation of the next passage or the production bioreactor will be reached. An inoculum expansion with a high proliferation rate also shortened the lag phase of the production process. Therefore, improvements in the inoculum growth rate could lead to reduced process time and production costs. A maximized viability during the inoculum expansion is crucial for the maintenance of the culture and the successful inoculation of the production bioreactor.In order to investigate the influence of the determined inoculum expansion process parameters on the later process steps, all inoculum cultures were used to inoculate scaled‐down production processes. These were simultaneously cultivated at standard conditions and sampled daily. The growth rates, average viabilities and the antibody titer were monitored as responses for the later state of the process. To obtain an optimal production process all of these responses should be maximized. A high growth rate leads to an early reach of an acceptable VCD for sufficient antibody production rates. An optimal viability ensures the maintenance of the culture during the entire production process. Moreover, the high viability is important to minimize the amount of cell debris, DNA and HCPs that are released to the medium and have to be removed expensively during the downstream part. To provide a profitable process the final product titer obviously has to be maximized. Additionally to the antibody titer, the specific titer was investigated as a response. It elucidates the cell specific productivity for the studied culture conditions. Thereby, it is possible to establish a specific production control between optimized growth and productivity. Typically, quality attributes in the biopharmaceutical industry include the quality of the product, such as the bioactivity or the glycosylation of the antibody. Yet, we concluded that the quality attributes for the inoculum expansion in our experimental set up have to be the condition of the final inoculum. That includes the growth rate, viability and also the productivity of the following production process. These were rated as sufficient responses for a meaningful conclusion regarding the inoculum expansion performance and its direct influence on the production.3.3Multiple linear regression (MLR) was used to analyse the factors and evaluate the responses  by fitting mathematical models. The regression models were used to determine effects of the studied factors (process parameters) and their interactions. Factors, which include zero in its confidential interval, are insignificant and hence eliminated from the corresponding model. The resulting main effects are plotted in Figure Negative coefficients regarding the total mAb titer can be explained by the connection between viable cell density and total product concentration. Evidently, a higher cell count during the cultivation leads to an increased titer. Therefore, the explained negative effects on the growth rate influence the total mAb titer, which is why the specific mAb titer was calculated and used as an additional response. In contrast to the discussed responses, the studied parameters show consistently positive effects on the cell specific mAb titer. This could signify that cells, growing under suboptimal cultivation conditions in regard to growth and viability, show an increased specific antibody production. Again, the passage duration (Pas) and its interaction with the initial passage viable cell density (VCD*Pas) show the most significant effects, supporting the concept of counteraction between optimal growth and specific productivity. Also, the MTX concentration (MTX) shows a comparatively high effect on the specific mAb titer, indicating the importance of balance between selection pressure and ideal cultivation conditions.2R and 2adjR values mostly over 0.9. The 2Q term, representing the predictive power of the model and its ability to generalize to unseen data, is also sufficient for all responses with the lowest value for the production viability at 0.62. Model significance, represented by the p‐value, shows a great meaningfulness for all responses with values close to zero. Also the reproducibility of the model is ensured for all responses with reproducibility values all over 0.7. In summary, the model statistics elucidate well fitted regression models for all selected responses. Also, the predictive power as well as the reproducibility is sufficient for the analysis of parameter effects. Since the model shall be used for future predictions and the establishment of a design space, the predictive power is particularly important. Thus, the observed response values were plotted against the predicted response values, to enable further insights on the model and possible outliers. The resulting observed vs predicted plots for all responses are shown in Figure To investigate the meaningfulness of the regression models, various model statistics were analysed. The full model statistics table is shown in the supplements. All models show a good fit to the experimental data with For the evaluated responses the plots show an overall strong predictive power. Furthermore, this plot allows an explanation for the comparatively low model statistic values of the production viability. It can show possible individual outliers as well as the biggest overall spread of data points. These were further investigated by analysis of the response residuals and the normal probability of distribution, which implied no significant outliers. In summary, the models were verified by analysis of the model statistics and the observed vs. predicted plot. Overall well fitted models with strong predictive power and a great reproducibility were determined.The observed interaction effects of the passage duration and the initial passage VCD were further investigated by analysis of the response contour plots shown in Figure Furthermore, the non‐linearity as well as the interaction of the parameter effects, which were observed in the effect plot, is detailed in the contour plots. This can be seen particularly in the inoculum viability contour plot with an anticipated optimum at –1 level for the passage duration and 1 level for the passage VCD. The presence of a predictable optimum underlines the effect interaction of factors. Shown similarities between the inoculum expansion and the production process responses also underline the hypothesis that the early process steps have a considerable influence on the production process. These investigations highlight the importance of a sound monitoring and control strategy for the shown parameters.The total mAb titer was shown to be the most robust response in relation to the passage duration and the initial passage VCD. Again, the optimum was anticipated below –1 level for the passage duration. Besides that, the contour plot shows a substantial robust working area with no considerable loss in antibody titer. That is likely due to the cell line and process development, which was focused on the optimization of the produced antibody titer.In contrast, the specific antibody titer shows an estimated optimum at the upper end of the examined space. Increasing passage duration as well as increasing initial passage viable cell density equally improved the specific productivity of the cells. Anyway, the increased productivity could still not compensate the negative effects on the growth rate and therefore the total cell number and final product titer. Taking only the studied factor effects into account, it was shown to be yet more worthwhile to improve the growth and viability of the cells in order to increase the total mAb titer.Therefore, the respective growth rate and viability responses as well as the total mAb titer response were used for further investigation. On that basis a design space for the studied process was calculated. Monte Carlo simulations were used to compile the needed probability statistics. The resulting design space is shown in Figure 6 cells/mL.A robust design space, marked in green, was determined around the –1 level for the passage duration and 0 level for the initial passage viable cell density. Increasing MTX concentration shows a negative effect on said design space. The set standard operation for the passage duration is located at the boundary of the acceptable probability values. Consequently, it would be beneficial for the process safety to either decrease the MTX concentration to broaden the design space or to shorten the passage duration to shift the process further towards the design space midpoint. Mathematical optimization of the three parameters resulted in the following optimal set points. The passage duration and the MTX concentration should therefore be decreased to 2 days and 7.5 nM, while the initial passage viable cell density should be slightly increased to 0.225 × 104The quality by design principle determined by the FDA was applied to the early process steps of a CHO cell cultivation. Inoculum expansion process parameters were compiled and potential risks were assessed by failure mode and effect analysis. The impact of selected parameters and their interactions were investigated using a design of experiments approach in scaled down shake flasks. Multivariate data analysis was used to analyse the experimental data and calculate regression models fitting to the measured responses. Analysis of the effect‐ and response contour plots identified the passage duration as a key process parameter and its interaction effects with the initial passage viable cell density as a crucial part of the studied process. It also showed that the parameters in the inoculum expansion have a critical impact on later production process performance.A reduced MTX concentration and passage duration improved the overall viability and growth rate of the inoculum expansion and the production process. Additionally, an opposite effect of the studied process parameters on the specific productivity was observed, which still could not compensate the discussed negative coefficients in terms of total mAb production. Further analysis of the responses resulted in the definition of a design space for the studied parameters. It showed the acceptable working range for the process, which could be expanded with decreased MTX concentration. Furthermore, it was shown to be robust for a mean initial passage viable cell density, while the optimum for the passage duration was found at the experimentally possible minimum. Based on these results, the early process steps were assessed as a critical part of the process and should consequently be investigated and analysed for newly developed processes and subsequently monitored and controlled using appropriate PAT possibilities.Leading forward, the findings of this study will be connected to parameter effects of the production process to further increase the understanding of the process. In the course of those future studies, experiments will be carried out using the Ambr® microbioreactor platforms by Sartorius Stedim. In order to achieve further insights, product quality attributes, namely the bioactivity, glycosylation and charge variants of the produced mAb will be taken into account. Thereby, this study is considered to be the first step towards a full process characterization regarding QbD principles, highlighting the importance of early process understanding and investigation.We confirm that all corresponding authors agree with the submission and publication of this paper and that there is no conflict of interest concerning financial and personal relationships. The manuscript does not contain neither experiments using animals nor human studies. Furthermore, we confirm that the article has not been published previously by any of the authors and is not under consideration for publication elsewhere at the time of submission.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.


An attempt was made to understand the large spatial variation of these levels. The seasonal and diurnal variation studies were used in unraveling the behavior of the radioactive isotopes in indoor environment and the same was explained with the help of a simplified mathematical model. Quantification of inhalation dose due to radon and thoron was done with suitable occupancy factors.Elevated levels of radon and thoron in the indoor atmosphere may cause the deleterious effects on the mankind. Mining sites and their environs attract a special interest in radon studies as higher levels are frequently reported in the habitats. In the present study, radon and thoron levels were measured in the dwellings of Buddonithanda, a village in the environs of proposed uranium mining site, with pin-hole (SSNTDs) dosimeters for the period of a year. The measured radon and thoron levels were found to vary widely from 14 to 675 Bq m The first one is more abundant, has half-life of 3.8 days and comes from the decay of 226Ra. The latter has a very short half-life of 55.6 s and comes from the decay of 224Ra1. Radon and thoron can enter human body by inhalation and most of the inhaled will be exhaled. However, a small fraction of the concentration of the gases might stuck in the lungs/ respiratory tract and these trapped radioactive elements on successive disintegration emit alpha particles that possibly ionize the lung tissues and results in the lung damage3. Epidemiological studies have confirmed that the exposure to radon in work places and dwellings increase the risk of developing lung cancer. Exposure to indoor radon and its isotopes have been determined to be the second leading cause of lung cancer after tobacco smoking3. The studies on uranium miners proved to be a positive risk coefficient on health and the measurements of radon and thoron levels are made inevitable in the indoor environment. This attention has been picked up the pace during last few decades and has become a global observable fact.Radon, being inert gas and radioactive in all of its isotopes, attracts much importance from radiological pollution point of view. The investigations across the globe indicate that half of the average annual natural background radiation dose comes from radon and its isotopes. Out of the various isotopes, the isotopes which are practically significant to the inhalation radiation dose are 4. Generally, the exposure to 222Rn and its daughter products contribute more to radiation dose than that of 220Rn5. However this perception has been changed, due to many systematic investigations across the world during the last few decades suggesting that, the 220Rn is also significantly contributes to the inhalation dose if the thorium content is rich in materials used for construction and local geology8.The concentration of radon and thoron gases in the indoors is largely influenced by the materials used for construction, life style of dwellers, geology and meteorological conditions of the study area10. The mining activity possibly enhances the environmental nuclear radiation levels in the adjoining areas. Buddonithanda, the village chosen for the present investigation, is situated in the close proximity of proposed mining site. This investigation aims to estimate radon, thoron levels and associated average annual effective inhalation dose to the population of Buddonithanda village. The pin-hole dosimeters were installed in the dwellings chosen randomly across the entire village covering different types of dwellings for the period of one year during November 2016 to October 2017 and covered nearly 45% of the dwellings of village.Atomic Minerals Directorate for Exploration and Research (AMDER), Hyderabad, has conducted several geological studies in Chitrial area of Nalgonda district and established that it is one of the prospecting potential areas for uranium explorationThe village Buddonithanda is located in the southern (south-east) part and almost 140 km away from the capital city (Hyderabad) of Telangana State. Most of the dwellings in the village were constructed with locally available materials such as bricks, stones, mud, dried gross, leaves and few are with cement and asbestos. This is the first systematic study in the neighboring village of proposed mining site and the outcomes of this investigation will be certainly a reference data for future studies to understand the effect of mining on the environmental nuclear radiation levels after mining comes into operation. The estimated radon and thoron levels in the different types of dwellings, seasonal/diurnal variation and inhalation dose due to radon and thoron to habitants of Buddonithanda village are discussed in this paper.Radon and thoron levels in the dwellings of Buddonithanda were measured with passive and active techniques namely, pin-hole dosimeters for time integrated measurements to account for seasonal variation and long term inhalation dose, RAD7 for short term measurements to account for diurnal variation.12. The mixture of radon and thoron gas from the ambient air enters dosimeter through a filter paper from face side and normally the filter paper obstructs the entry of unwanted particles from the environment. The ambient air containing radon and thoron gases enters the first compartment and radon gas diffuses through central pinhole disc (HDPE) to second compartment13. Hence the detector in the first compartment detects both radon and thoron while the second detects only radon because the diffusion of thoron to this compartment is impractical due its short half-life.It is one of most versatile methods for mixed field environment of radon and thoron. It consists of two compartments separated by a central pinhole disc made up of High Density Poly Ethylene (HDPE) material. Each compartment has equal in dimensions of length 4.1 cm and radius 3.1 cm−3. Since RAD7 is a humidity-sensitive device, KMnO4 is used as a desiccant15. In the present investigation, the diurnal variation of indoor radon and thoron concentration was studied using RAD7 . The measurements were carried out in a dwelling of the study area for the complete cycle of a day with one hour interval.The RAD7 is a versatile comprehensive device used to assess the radon and thoron concentration instantaneously in the indoors and outdoors from the ambient air. It is solid-state semiconductor detector-based device in which the detection limit of radon and thoron is in between 4 and 400,000 Bq m−2 per Bq d m−3 for radon and thoron16 respectively.Measurements were carried out in the dwellings of Buddonithanda village using pinhole dosimeters with Solid State Nuclear Track Detector (SSNTD) and these are LR-115 type-II, strippable films. These SSNTDs were placed at specific position in the dosimeter; dosimeters were installed in dwellings approximately 1ft below from the ceiling and a minimum of 10 to 15 cm distance from the adjoining walls. The dosimeters were left in the dwelling for about three months, after the stipulated period the detectors were retrieved and reinstallation was done with a fresh batch of detectors. This process is repeated for a period of a year on quarterly basis and retrieval rate in the present study is nearly 73%. The retrieved SSNTDs were chemically etched using 2.5 N of NaOH solution at 60 °C for 90 min in constant temperature bath without stirring. The etched films were dried at room temperature and the recorded tracks were counted using a spark counter. The track densities were estimated into activity concentration using the calibration factors 0.017and 0.010 tr cm−1) was calculated for indoors with the below formula by assuming the dose conversion factor for radon as 9 nSv y−1 and for thoron 40 nSv y−11 and with appropriate occupancy factor.Rn and CTn are the concentration of radon and thoron; OF is occupancy factor; the factors 0.40 and 0.12 are taken as equilibrium factors for radon and thoron12 respectively.Annual effective inhalation dose due to radon and thoron in  and for thoron from 21 to 704 Bq m−3 with geometric mean of 121 Bq m−3 . The measured average concentration of radon and thoron levels is comparatively higher than the global average of 40 Bqm−3 for radon and 10 Bqm−3 for thoron1. It can be observed that, the radon and thoron levels in the study area are largely varied and distributed arbitrarily in a small region. The wide fluctuation in airborne radioactivity levels in the small area is unexpected and this may be attributed to the different category dwellings and varied life style of the residents though there is no observable difference in geology within the study area.The annual average concentrations of radon and thoron in the dwellings of Buddonithanda village measured during November 2016 to October 2017 are shown in Table −3, about 30% and 37% of dwelling were recorded the average radon and thoron levels above 150 Bq m−3, respectively. It is observed that the radon and thoron activity followed lognormal distribution. It is very familiar that the radon/thoron activity concentrations follow log-normally in large areas19 but it is unexpected that the radon levels varying widely in a small area12. The asymmetric distribution of radon and thoron concentrations around the average or mean indicates the disproportionate weight of higher concentrations over the lower ones in the computation of the arithmetic mean. This problem can be avoided by taking the geometric mean and, thus, this statistics is the one recommended generally by radon and thoron experts for estimating the average values of concentration17. The maximum (max) concentration is based on the few farthest values in the distribution and the minimum (min) concentration is usually reported by large numbers of measurements19. The spatial variation of radon and thoron levels in the present study area is consistent with the earlier findings18, although they are not confined to a small region. This indicates that the influential parameters of residential radon like (1) the life style of the people (2) structure of dwellings may not be the same for each case despite the fact that the geology is same.To understand the wide range of the activity concentrations of radioactive isotopes, the best and yet simple statistical tools, histogram and probability distribution plots are employed. The distribution of measured radon and thoron levels in the study area for a period of one year for all the measurements is shown in Figs. 20 and Suman et al.12.The diurnal behaviour of indoor radon and thoron levels helps in understanding the variation of these levels with life style of dwellers. The simultaneous measurements were made with RAD7 in a selected dwelling in winter season. The acquisition of the data started at 9:00 am on February 01, 2018 and continued till next day morning in the intervals of one hour. The measured radon and thoron levels are shown in Fig. 22. Most of the mathematical models are based on following mass balance equationSeveral researchers studied indoor radon levels with mathematical models23.CRn is indoor radon concentration; CRo is the outdoor radon concentration; ERn is exhalation rate; v is ventilation rate and in steady state conditions the equation takes the formThe rate change of indoor radon concentration, treating all sources contributing the indoor activity concentration constant, is given by the following equation−1. The radon decay constant In general, in the moderate conditions the typical ventilation rates rages from 0.1 to 1.5 hIt is clear from Eq. , that in24.However, the thoron concentration was found to be varying scattered because a small change in the environmental conditions results in large variation of thoron levels see Fig. . This caCTn is indoor thoron concentration; CTo is the outdoor thoron concentration; ETn is exhalation rate; v is ventilation rate and −1. Average ventilation rate existing in the dwelling is much smaller than Mathematically, the expression for indoor thoron concentration, similar to Eq. , under s25.x” distance from source; D is diffusion coefficient in air. With the given constant values for D and 23. However, studies showed that the decrement is not that rapid and thoron concentration observed to drop to 10–40% at 1 m distance from the source26. The air circulation in the room promotes the thoron gas to diffuse more distance. Thus, during the night air circulation is lower and hence the concentration of the gas suppressed and it increases with increase in air currents during dawn/dusk. In summary, concentration of radon increases with decrease in ventilation rates whereas the thoron gas concentration is aided with air exchange rates in the dwellings. This property discriminates both the isotopes and can be used in separating them.According to Eq. , the ind29. Rationales for elevated radon levels in winter can be attributed mainly to (1) The life style of the people in the forest environment that limits the air circulation inside the dwellings in winter season by closing the ventilation systems longer time compared to other seasons (2) the enhanced emanation rate of radon from floor and walls because of the positive temperature gradient exists between inside and outside the dwellings. The variation of thoron levels with seasons in certain cases is unlike the radon because of its unusual behavior results an inversion current flow of the thoron gas than other conventional gases, may be attributed to its short half-life31. This might be the reason the ratio of measured thoron levels between the winter and summer is found to be little lower than the unity (0.92).The seasonal variation of residential radon/thoron was monitored by time integrated technique. The dosimeters were installed in the dwellings covering the four seasons of the year and estimated seasonal variation of average radon and thoron concentration levels for the dwellings is shown in Figs. 33. The difference of the thoron levels between the mud and cement floor, mud and cement wall are relatively higher than radon levels of identical floor and wall, this may be due to the concealing effect of thoron emanation by the cement because of its shot half-life.It is recognized that the airborne radioactivity levels, are mainly because of not only the soil underneath of the dwelling, but also noticeably depends upon the materials used for the construction and ventilation parameters. To understand this, an attempt is made to estimate the radon and thoron levels in different types of dwellings with respect to the roof, floor and walls. The variation of radon and thoron levels in different type of roofs is shown in Fig. 1 and for thoron is 0.1212. Occupancy factor is another principal factor in the estimation of inhalation dose. United Nations Scientific Committee on Effects of Atomic Radiation1 suggested the occupancy factor of 0.8 . However, in rural areas the dwellers usually leave the house in early hours to the fields and will be back only in the evening hours. Therefore, the present study conducted in a forest village, it is appropriate to consider an occupancy factor of 0.6 . Table −1 with a geometric mean of 1.78 mSv y−1 and due to thoron it varies from 0.53 to 17.76 with the geometric mean of 3.05 mSv y−1. The estimated dose is higher when compare with the global average inhalation dose due to radon and thoron1.In the calculation of annual effective inhalation dose due to radon and thoron gases, the important parameters are equilibrium and occupancy factors. The significant parameter used in the estimation of dose is the equilibrium factor (EF) related with ventilation rate, which is measure of disequilibrium between radon and its daughters; thoron and its daughters. In the present investigation the average EF for inhalation dose is used as 0.40 for radon−3 (arithmetic mean122 ± 98 Bq m−3) and 121 Bq m−3 (arithematic mean166 ± 159 Bq m−3) in the present study area and are observed to be higher than global average concentration of 40 Bq/m−3 and 10 Bq/m−3, respectively. The distribution plots of radon and thoron levels show an asymmetrical  around the average activity. The diurnal studies indicate the radon levels are high during the day and night time while the same downturn during dawn and dusk. Contrary to the radon the variation of thoron activity is explained on the basis of air circulation rates. Among the different types of dwellings, the airborne radiation levels were found to be relatively high in dwellings constructed with mud compared to other types. The annual average inhalation dose exposure due to radon and thoron to community in the investigated area is found to be relatively higher.The calculated geometric mean values of activity concentration of radon and thoron are found to be 94 Bq m


Using first principles calculations of extended air–water and oil–water interfaces, we unravel a mechanism that does not require the presence of OH–. Small amounts of charge transfer along hydrogen bonds and asymmetries in the hydrogen bond network due to topological defects can lead to the accumulation of negative surface charge at both interfaces. For water near oil, some spillage of electron density into the oil phase is also observed. The computed surface charge densities at both interfaces is approximately The origin of the apparent negative charge at hydrophobic–water interfaces has fueled debates in the physical chemistry community for decades. The most common interpretation given to explain this observation is that negatively charged hydroxide ions (OH The accumulation of negative charge at hydrophobic–water interfaces has been a source of debate for a long time. Here the authors use ab initio calculations to show that the charge accumulation at air–water and oil–water interfaces is caused by subtle charge transfer processes. This experimental observation has served as the seed for one of the most hotly debated topics in physical chemistry for the last several decades with numerous conflicting interpretations underlying the origins of the negative charge8. Here, we make an important leap in our understanding of this problem providing a framework that helps rationalize the observed phenomena that is rooted in what we propose is a generic charge transfer mechanism associated with the interfacial structure at the surface of water and oil. The electrokinetic experiments of both air and oil droplets paint a very similar picture despite having rather disparate chemistries namely, that the zeta potential  tell a less consistent picture ranging from the presence of H24. At the surface of water, the charge transfer leads to a triple layer of charge with negative surface charge a couple of Angstroms from the surface  that is constructed for the water phase. In both figures, the cyan-colored isosurface corresponds to the highest molecular orbital, which is localized at the interface. To the best of our knowledge, our simulations represent the first of their kind where the electronic structures of thousands of atoms of the air and oil–water interfaces are treated.The top left and right panels of Fig. 26, although the reported charge densities were too small compared with those obtained from electrophoretic experiments. The essential idea is that asymmetries in hydrogen bonding between water molecules at an interface leads to a subsequent imbalance in the charge transfer along donating versus accepting hydrogen bonds. We begin by showing in Fig. 32, which characterizes the instantaneous density fluctuations of the interface. The zero on the x axes of Fig. The possibility that a charge transfer mechanism could rationalize the negative charge at hydrophobic surfaces has been suggested in previous theoretical studies−3; immediately below this, there is a compensating negative layer of ~1.5 Å thickness (2nd layer) but with a larger charge density of ~−0.41 e nm−3; and finally, below 2–5 Å from the interface, there is another positively charged layer  after which, charge neutrality develops (the 4th layer). The presence of the triple layer is essentially caused by the asymmetry in the magnitude of the first two charged layers where the negative branch is about twice as large than that of its positive counterpart closer to the interface. The charge density shown can be integrated from the vacuum to the bulk to give a better description of the cumulative surface charge. The dashed-blue curve shows the integrated surface charge density—between 1 and 2 Å from the WCI interface, there is a substantial negative charge density of ~−0.015 e nm−2, which is about an order of magnitude larger than previous findings26.The left panel of Fig. x axis corresponds to the position of the WCI surface. In stark contrast to the surface of water, there is a sharp peak of positive charge in the water phase just below the interface with a charge density of ~0.39 e nm−3. This layer is followed by a negatively charge region of water with a lower charge density of ~−0.18 e nm−3. The complementary charge distributions of the dodecane molecules forms one of our central findings in this report, namely that the oil phase is negatively charged. We observe a large negative surface charge density of ~−0.016 e nm−2 in the oil phase. These results are striking as they show that there is a net charge transfer of ~0.4 electron charge from the water to the oil. Furthermore, the magnitude of this surface charge is very similar to what is observed at the air–water interface, which is also consistent with the similarity in the zeta-potentials obtained from air and oil droplets33.How does the behavior change near the oil–water interface? Rather unexpectedly, the oil phase is not a passive spectator in the charging mechanism. The right panel of Fig. 24 and at surface35 create local coordination defects, which have asymmetries in the number of donated versus accepted hydrogen bonds. The bottom panel of Fig. In order to dissect the microscopic origins of the charge gradients observed at the interface, we turn next to examining how the charge is modulated by differences in topological defects. It is well appreciated that fluctuations in liquid water both in the bulkUsing the four layers previously defined to describe the different charged layers, we determined how the relative concentration of different water molecules change as one moves from the interface to the bulk, as well as their relative contribution to the total charge . Interestingly, Bonn and co-workers compare a whole class of empirical water models including mB-POL—the percentage of our dangling O–H bonds is consistent with these results. As we have also pointed out from our work, one of the key ingredients of observing the charge asymmetries is the apparent higher concentration of 1in-2out defects versus 2in-1out defects. This feature is not just exclusive to the interface but also in the bulk. In a previous study35, we have compared, exhaustively, the concentration of defects in different water models ranging from classical empirical to DFT based and finally, of course mb-POL. Again, the conclusion is that the higher concentration of 1in-2out water molecules compared with 2in-1out is found in all water models including mb-POL. Having understood the origins of the charge oscillations at the surface of water, we move next to examining how these properties behave near oil. In order to adequately compare the two interfaces, we repeated the charge and population analysis previously done for the water–air system as a function of different layers see Fig. a. For thWe begin by first showing the qualitative behavior involving the intra and inter-fragment electron reorganization in the clusters. Fig. −1—for the clusters, this implies a binding energy of slightly under thermal energy per water molecule. As result of these charge transfer and polarization effects that render the oil-phase negative and the water one positive, the electrostatic component of the energy is also attractive . Our findings in the previous section strongly suggest that these effects are likely to be enhanced and also critical driving force in enhancing the negative surface charge observed at extended oil–water interfaces.A more quantitative measure of these effects at the oil–water interface can be explicated by examining the distributions associated with the various components of the interaction energy. Fig. 41 and the iterative Hirshfield (IH)42 and stockholder (ISA)43 approaches. The DDEC method combines the strengths of the ISA and IH methods with the additional trait of giving a more faithful representation of the potential 44. To assess the reliability of our results with respect to the charge partitioning adopted, we compared the results obtained with the DDEC scheme to the ones obtained using two different charge representations: natural bond orbital (NBO), iterative Hirshfiled (IH). These test were constructed by averaging over 20 and 10 frames for the air/water and oil/water interface, respectively, instead of the full 250 and 200 used in the original sets . The results depicted in Fig. The use of net atomic charges is widely used in the area of chemical sciences, as they provide a practical and convenient way to partition the electron density distribution into atomic or molecular contributions. The method of choice in this work was the DDEC charge partitioning. In the DDEC method, the net atomic charges are assigned as a functional of the electron density, hence are not sensitive to the choice of basis set. There are of course many charge schemes to partition the electron density with similar traits such as Bader2O molecule (WATC) and various geometrical descriptors which are visually depicted in Fig. In order to understand how the charge fluctuations are modulated by the local environment, we determined the correlation between the total charge on each H45  for the effect of charge transfer on electrophoretic mobility. In this scenario, the slip plane resides several Angstroms from the oil surface and the role of fluctuations of water topologies is not considered. For the oil–water interface, our findings suggest that the slip plane will be pinned right near the oil droplet, as it is negatively charged, whereas the water in close proximity is positively charged. On the other hand for the air bubbles, the slip plane must reside somewhere in between the boundary of the second and third charged layers  spectroscopy experiments of bulk liquid water, indicate the presence of short-time oscillatory behavior on the sub-picosecond timescale49. Our current models do not account for the possible binding of protons or hydroxide ions to the interface. Inserting the hydronium and hydroxide ion into the calculations and examining how it affects the charge transfer mechanisms will be the subject of a forthcoming study. At this point, we can only make speculations about what the presence of a proton would do to the charge at the air–water interface. Assuming that the proton exists as a local ionic defect, namely on a single water molecule as an Eigen or on two water molecules as a Zundel, we do not expect it to change the concentration of hydrogen bond topologies significantly. However, the presence of the ions will likely also change the extent of charge transfer between the water molecules at the interface as observed in previous studies51. The details of the charge profile in the presence of the proton will also depend a lot on whether it is pinned above the Willard–Chandler interface or if it lies below it. If the proton lies within the second layer, we estimate that one would need a single proton per ~10 nm2 to neutralize the negative charge caused by the topological defects in that layer. Of course, another important ingredient would be the role of counterions. Previous studies have shown that while charge transfer does not affect the binding affinity of ions to the surface of water, ions can have long-range effects on surface charge51. More specific answers to these questions will the subject of a forthcoming study.The mechanism associated with the response of the electronic degrees of freedom, as revealed by an EDA, involve a combination of both polarization and charge transfer. The coupling between the electronic reorganization and nuclear coordinates, such as local topology, opens up some very interesting perspectives and questions for future lines of research. An obvious one centers around the generality of our results to other extended hydrophobic interfaces or more heterogeneous surfaces such as metal oxides or even biological systems. In addition, the patchiness of surface charge at different interfaces deserves further investigationz direction. This system comprises of a total of 6540 atoms (2180 water molecules). The second system studied a water–oil interface where the oil phase was composed of 200 dodecane molecules, whereas the water phase was made up of 1960 water molecules, leading to a total of 13,479 atoms. The cell dimensions for this system are 46.269 Å × 46.269 Å × 62.768 Å Our strategy for performing the analysis involved two steps: first, classical empirical molecular dynamics simulations were performed in order to allow for large and long timescale fluctuations that would not be possible using ab initio molecular dynamics; second, configurations from these simulations were sampled from which the electronic structure calculations were performed. The classical MD simulations were run using the GROMACS software52. The water phase was modeled using the TIP4P/200553 force field in both cases. The dodecane molecules were simulated using the modified OPLS-AA (L-OPLS) potential developed by Böckmann et al.54. This potential has been parameterized on the basis of high level ab initio calculations, densities, and heats of vaporization of both short- and long-chain alkanes and on the phase transition temperature of pentadecane in order to extend the OPLS-AA validity to long hydrocarbon chains and recover a more precise description of their phase transition temperatures and ordering. The air–water system was equilibrated for 10 ns using the NPT ensemble using the Parrinello-Rahaman barostat55 for the first half of the run for bulk water, followed thereafter by an NVT simulation at 300 K, opening up a gap in the z direction, which separated the two water surfaces by 160 Å for the remainder of the simulation. The production simulations were run for 20 ns. The surface tension computed from the classical simulations is 68.2 mN m−1 in agreement with previous studies56. From these simulations a total of 250 configurations were randomly selected to perform the electronic structure calculations. The oil–water interfaces were equilibrated first 20 ns via NVT simulations. The production calculations were then run for 40 ns using the isothermal–isobaric ensemble. In all, 200 frames were randomly selected for the electronic structure calculations.Most of our results rely on simulations of two different systems that serve as prototypical models for water near hydrophobic surfaces: the surface of water and water near oil. The air–water interface was modeled building a water slab with dimension 40 Å × 40 Å × 40 Å and adding a vacuum padding of 80 Å on each side of the slab along the 57. This technique allowed us to extend the system sizes in our study to thousands of atoms and to model electronic effects of extended hydrophobic interfaces on the nanometer length scale. For a more detailed and technical summary of the underlying theory the reader is referred to relevant literature58. Here, we briefly summarize the essential ideas. LS-DFT as implemented in ONETEP makes use of the nearsightedness59 inherent to quantum many-body systems by exploiting the single-particle density matrix, r, r′)61 representation of the system of interest. Within ONETEP, r, r′), is expressed in a separable form63 via atom-centered functions , 65. Such truncation leads to a sparse density matrix 70 norm-conserving pseudopotentials constructed with the Opium code71 were used.In order to extend the scope of our electronic structure calculations, we employed a LS-DFT approach as implemented in the ONETEP code72 scheme implementation in ONETEP73. DDEC3 is an atom in molecules approach where the total QM electron density . In addition, we compared the results recovered using BLYP+D2 on smaller clusters with the ones obtained considering both hybrid functionals such as B3LYP as well as wavefunction approaches such as MP276. The use of smaller clusters was forced by the heavy computational cost that such methods require. Besides the quality of the electronic structure, we also examined the sensitivity of the charge transfer to sampling configurations of the air–water interface sampled from mb-POL. The mb-POL potential reproduces many structural and dynamical properties of water across the phase diagram, and although we could not simulate a system as big as the one with TIP4P/2005, this test provide a useful comparison with respect to our results. More details about these benchmark simulations are expanded upon in the Supporting Information.In order to characterize any possible charge gradients developing at our simulated interfaces, atomic point charges are then derived from the electron density. The atomic charges reported in this work were calculated using the DDEC3Supplementary InformationPeer Review File