“…The model approach used here has been introduced in previous work and is summarized below. The model architecture consists of three sequential steps to compute PSDs from CLDs, that is, CLD synthesis, regression models for low‐order PSD moments, and a two‐layer network defined by a generating function.…”
Section: Data‐driven Modelmentioning
confidence: 99%
“…The model architecture consists of three sequential steps to compute PSDs from CLDs, that is, CLD synthesis, regression models for low‐order PSD moments, and a two‐layer network defined by a generating function. The standard model architecture is shown in Figure and a detailed description of all model variations can be found in previous work . The inputs for this model are the measured CLD ( Q = { q 1 , …, q M }) and the corresponding solids concentration ( c ).…”
Section: Data‐driven Modelmentioning
confidence: 99%
“…In pharmaceutical crystallization, focused beam reflectance measurement (FBRM) has become a standard tool for in situ particle monitoring due to its ease of process implementation and ability to operate at high solids concentrations. However, a major limitation of this technique is that its measurement signal, that is, the chord length distribution (CLD), differs fundamentally from particle‐size distribution (PSD) data due to the FBRM measurement principle, which is explained in detail elsewhere . Thus, the measured CLD is not only a function of particle number and size, but is generally also affected by particle morphology and various process parameters, for example, probe positioning, particle concentration, and optical effects of the continuous and dispersed phase.…”
Section: Introductionmentioning
confidence: 99%
“…Thus, a single ab initio model alone cannot capture all physical phenomena and reflection properties of liquid and solid phases affecting a CLD measurement and therefore will fail to predict the PSD of the dispersed phase accurately. Generally, the measured PSD depends on the type of characterization, which is why the selection of a reference technique is also important when aiming at extracting PSD from CLD data. PSDs in the pharmaceutical industry are generated as quality control under laboratory conditions.…”
Section: Introductionmentioning
confidence: 99%
“…Although laser diffraction measurements suffer also from limitations, particularly for nonspherical particles as described in the literature, PSD data from laser diffraction will be considered as the reference data due to its importance in the quality release process during pharmaceutical production. Previously, a data‐driven modeling approach has been introduced which allowed the quantitative determination of one‐dimensional and two‐dimensional PSDs from measured CLDs, suggesting an effective solution to the above‐mentioned limitations of the FBRM . The model architecture is based on three sequential steps:First, CLD data are compressed into a small set of CLD descriptors (low‐order moments).Second, the CLD descriptors are mapped into a small number of PSD moments using a regression model.Finally, the PSD moments are expanded into a full PSD using a two‐layer network model.…”
A recently proposed model to determine particle‐size distributions (PSDs) from chord length measurements has been applied to different particle morphologies, namely compact, platelet‐ and rod‐shaped particles. To study these systems, chord length distributions (CLDs) were measured at varying particle size and solids concentration for each compound and were subsequently utilized to determine the system‐specific parameters. Each model was successfully applied to its respective compound such that the experimental PSDs and model predictions were in good agreement. Moreover, the effect of other variables such as agitation rate and solvent composition was investigated and found to be negligible for the specific systems tested. Finally, potential model optimizations of the general model construct have been studied. Two variants of the CLD compression step, namely principal component analysis and a geometric model have been considered as surrogate models. However, neither of these approaches yielded superior results than the previously proposed approach.
“…The model approach used here has been introduced in previous work and is summarized below. The model architecture consists of three sequential steps to compute PSDs from CLDs, that is, CLD synthesis, regression models for low‐order PSD moments, and a two‐layer network defined by a generating function.…”
Section: Data‐driven Modelmentioning
confidence: 99%
“…The model architecture consists of three sequential steps to compute PSDs from CLDs, that is, CLD synthesis, regression models for low‐order PSD moments, and a two‐layer network defined by a generating function. The standard model architecture is shown in Figure and a detailed description of all model variations can be found in previous work . The inputs for this model are the measured CLD ( Q = { q 1 , …, q M }) and the corresponding solids concentration ( c ).…”
Section: Data‐driven Modelmentioning
confidence: 99%
“…In pharmaceutical crystallization, focused beam reflectance measurement (FBRM) has become a standard tool for in situ particle monitoring due to its ease of process implementation and ability to operate at high solids concentrations. However, a major limitation of this technique is that its measurement signal, that is, the chord length distribution (CLD), differs fundamentally from particle‐size distribution (PSD) data due to the FBRM measurement principle, which is explained in detail elsewhere . Thus, the measured CLD is not only a function of particle number and size, but is generally also affected by particle morphology and various process parameters, for example, probe positioning, particle concentration, and optical effects of the continuous and dispersed phase.…”
Section: Introductionmentioning
confidence: 99%
“…Thus, a single ab initio model alone cannot capture all physical phenomena and reflection properties of liquid and solid phases affecting a CLD measurement and therefore will fail to predict the PSD of the dispersed phase accurately. Generally, the measured PSD depends on the type of characterization, which is why the selection of a reference technique is also important when aiming at extracting PSD from CLD data. PSDs in the pharmaceutical industry are generated as quality control under laboratory conditions.…”
Section: Introductionmentioning
confidence: 99%
“…Although laser diffraction measurements suffer also from limitations, particularly for nonspherical particles as described in the literature, PSD data from laser diffraction will be considered as the reference data due to its importance in the quality release process during pharmaceutical production. Previously, a data‐driven modeling approach has been introduced which allowed the quantitative determination of one‐dimensional and two‐dimensional PSDs from measured CLDs, suggesting an effective solution to the above‐mentioned limitations of the FBRM . The model architecture is based on three sequential steps:First, CLD data are compressed into a small set of CLD descriptors (low‐order moments).Second, the CLD descriptors are mapped into a small number of PSD moments using a regression model.Finally, the PSD moments are expanded into a full PSD using a two‐layer network model.…”
A recently proposed model to determine particle‐size distributions (PSDs) from chord length measurements has been applied to different particle morphologies, namely compact, platelet‐ and rod‐shaped particles. To study these systems, chord length distributions (CLDs) were measured at varying particle size and solids concentration for each compound and were subsequently utilized to determine the system‐specific parameters. Each model was successfully applied to its respective compound such that the experimental PSDs and model predictions were in good agreement. Moreover, the effect of other variables such as agitation rate and solvent composition was investigated and found to be negligible for the specific systems tested. Finally, potential model optimizations of the general model construct have been studied. Two variants of the CLD compression step, namely principal component analysis and a geometric model have been considered as surrogate models. However, neither of these approaches yielded superior results than the previously proposed approach.
Crystallization control can be improved through real-time monitoring technologies. Here, a workflow is demonstrated on rapid batch cooling crystallization of L-glutamic acid. First, in situ images were generated using video microscopy sensors and analyzed, by employing a single, rapid macro code to extract particle data descriptors. A binning procedure (over time) was performed, where every data point represented the counts of particles within a specific size or shape range per 100 images. This binning method was found more informative in tracking of the populations compared to whole image averages or individual particle datapoints. This study provides a step-by-step guide towards improving mechanistic modeling, control via feedback, automation, and continuous manufacturing for Industry 4.0.
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