Lorenz Holzer is a senior scientist at the Zurich University of Applied Sciences (ZHAW), Switzerland, and head of the research group Microstructure Analysis and Property prediction (MAP). His research focuses on digital materials design (DMD/ICME), which combines methods of imaging/tomography, 3D image analysis, microstructure modeling and multiphysics simulations. These methods serve as a basis for optimization of engineered porous and composite materials (e.g., electrodes of fuel cells and batteries). Lorenz Holzer has published more than 150 scientific papers. He has organized several international conferences on the topics of 3D imaging and microstructure analysis. For his pioneering work in FIB-SEM tomography he received the Purdy award (American Ceramic Society) in 2007.  Philip Marmet obtained his Master of Science in Engineering in Industrial Technologies from Bern University of Applied Sciences in 2013 and his Master of Science in Physics from University of Fribourg (Switzerland) in 2016. He is a specialist in modelling and simulation of industrial systems, with strong experience in applied research with partners form academia and private sector. During his PhD thesis (2019 to 2023, Uni Fribourg and ZHAW), Philip Marmet was developing new models for digital materials design of Solid Oxide Fuell Cell electrodes. Since 2023, Philip Marmet is employed as a research associate at the Institute of Computational Physics (ICP), Zurich University of Applied Sciences (ZHAW), Switzerland. Mathias Fingerle received his PhD in experimental physics from TU Kaiserslautern in 2014. He has conducted academic teaching and research in the field of energy materials and led the group Electrochemical Interfaces at the Institute of Surface Science at TU Darmstadt. Presently, as Head of Consulting & Projects at Math2Market GmbH, he is coordinating scientific consulting and application engineering for digital material design mainly in the fields of batteries, fuel cells, digital rock physics, air and oil filtration and composites. Andreas Wiegmann is CEO and founder of Math2Market, an engineering software company that specializes in digital mesoscale materials characterization and materials design. He has a PhD in mathematics from the University of Washington in Seattle and then worked at the University of California at Berkeley, LBNL and Fraunhofer ITWM. He specializes in numerics of interfaces between high contrast materials, stochastic 3D material models, and the analysis of 3D scans and published more than 150 articles in areas ranging from machine learning to computational physics, textile engineering, fuel cell modelling, battery material research, petroleum engineering and structural topology optimization. Matthias Neumann is Post-doc at the Institute of Stochastics of Ulm University (UU), where he received his PhD in 2020. He was awarded with the PhD price of UU and received start-up funding by the Graduate & Professional Training Center Ulm. Since 2021, he is member of the Cluster of Excellence POLiS (Post Lithium Storage). The focus of his research is on microstructure characterization by statistical image analysis and machine learning, the development of stochastic models for generating digital twins, and the quantification of microstructure-property relationships. He published 33 research papers in peer-reviewed international journals and 3 contributions in conference proceedings.Volker Schmidt is Professor at the Institute of Stochastics of Ulm University. He received his PhD from the Technical University Bergakademie Freiberg. His research activities are focused on spatial stochastic modeling of highly resolved image data in 2D, 3D and 4D, using methods of statistical image processing, machine learning and stochastic geometry. Prof. Schmidt is co-author of three books and more than two hundred research papers in peer-reviewedinternational journals. He supervised more than one hundred Bachelor and Master students, and 23 PhD students who have completed their dissertation theses so far. Currently, 11 PhD students are preparing their PhD theses under his supervision.

• Chapter 1. Introduction.- Chapter 2. Review of theories and a classification of tortuosity types.- Chapter 3. Review of empirical data from literature - tortuosity-porosity relationships.- Chapter 4. Methodologies, workflows and calculation approaches.- Chapter 5. Towards a quantitative understanding of microstructure - property relationships.- Chapter 6. Summary and Conclusions.

Lorenz Holzer is a senior scientist at the Zurich University of Applied Sciences (ZHAW), Switzerland, and head of the research group Microstructure Analysis and Property prediction (MAP). His research focuses on digital materials design (DMD/ICME), which combines methods of imaging/tomography, 3D image analysis, microstructure modeling and multiphysics simulations. These methods serve as a basis for optimization of engineered porous and composite materials (e.g., electrodes of fuel cells and batteries). Lorenz Holzer has published more than 150 scientific papers. He has organized several international conferences on the topics of 3D imaging and microstructure analysis. For his pioneering work in FIB-SEM tomography he received the Purdy award (American Ceramic Society) in 2007.  Philip Marmet obtained his Master of Science in Engineering in Industrial Technologies from Bern University of Applied Sciences in 2013 and his Master of Science in Physics from University of Fribourg (Switzerland) in 2016. He is a specialist in modelling and simulation of industrial systems, with strong experience in applied research with partners form academia and private sector. During his PhD thesis (2019 to 2023, Uni Fribourg and ZHAW), Philip Marmet was developing new models for digital materials design of Solid Oxide Fuell Cell electrodes. Since 2023, Philip Marmet is employed as a research associate at the Institute of Computational Physics (ICP), Zurich University of Applied Sciences (ZHAW), Switzerland. Mathias Fingerle received his PhD in experimental physics from TU Kaiserslautern in 2014. He has conducted academic teaching and research in the field of energy materials and led the group Electrochemical Interfaces at the Institute of Surface Science at TU Darmstadt. Presently, as Head of Consulting & Projects at Math2Market GmbH, he is coordinating scientific consulting and application engineering for digital material design mainly in the fields of batteries, fuel cells, digital rock physics, air and oil filtration and composites. Andreas Wiegmann is CEO and founder of Math2Market, an engineering software company that specializes in digital mesoscale materials characterization and materials design. He has a PhD in mathematics from the University of Washington in Seattle and then worked at the University of California at Berkeley, LBNL and Fraunhofer ITWM. He specializes in numerics of interfaces between high contrast materials, stochastic 3D material models, and the analysis of 3D scans and published more than 150 articles in areas ranging from machine learning to computational physics, textile engineering, fuel cell modelling, battery material research, petroleum engineering and structural topology optimization. Matthias Neumann is Post-doc at the Institute of Stochastics of Ulm University (UU), where he received his PhD in 2020. He was awarded with the PhD price of UU and received start-up funding by the Graduate & Professional Training Center Ulm. Since 2021, he is member of the Cluster of Excellence POLiS (Post Lithium Storage). The focus of his research is on microstructure characterization by statistical image analysis and machine learning, the development of stochastic models for generating digital twins, and the quantification of microstructure-property relationships. He published 33 research papers in peer-reviewed international journals and 3 contributions in conference proceedings.Volker Schmidt is Professor at the Institute of Stochastics of Ulm University. He received his PhD from the Technical University Bergakademie Freiberg. His research activities are focused on spatial stochastic modeling of highly resolved image data in 2D, 3D and 4D, using methods of statistical image processing, machine learning and stochastic geometry. Prof. Schmidt is co-author of three books and more than two hundred research papers in peer-reviewedinternational journals. He supervised more than one hundred Bachelor and Master students, and 23 PhD students who have completed their dissertation theses so far. Currently, 11 PhD students are preparing their PhD theses under his supervision.

• Chapter 1. Introduction.- Chapter 2. Review of theories and a classification of tortuosity types.- Chapter 3. Review of empirical data from literature - tortuosity-porosity relationships.- Chapter 4. Methodologies, workflows and calculation approaches.- Chapter 5. Towards a quantitative understanding of microstructure - property relationships.- Chapter 6. Summary and Conclusions.

Lorenz Holzer is a senior scientist at the Zurich University of Applied Sciences (ZHAW), Switzerland, and head of the research group Microstructure Analysis and Property prediction (MAP). His research focuses on digital materials design (DMD/ICME), which combines methods of imaging/tomography, 3D image analysis, microstructure modeling and multiphysics simulations. These methods serve as a basis for optimization of engineered porous and composite materials (e.g., electrodes of fuel cells and batteries). Lorenz Holzer has published more than 150 scientific papers. He has organized several international conferences on the topics of 3D imaging and microstructure analysis. For his pioneering work in FIB-SEM tomography he received the Purdy award (American Ceramic Society) in 2007.  Philip Marmet obtained his Master of Science in Engineering in Industrial Technologies from Bern University of Applied Sciences in 2013 and his Master of Science in Physics from University of Fribourg (Switzerland) in 2016. He is a specialist in modelling and simulation of industrial systems, with strong experience in applied research with partners form academia and private sector. During his PhD thesis (2019 to 2023, Uni Fribourg and ZHAW), Philip Marmet was developing new models for digital materials design of Solid Oxide Fuell Cell electrodes. Since 2023, Philip Marmet is employed as a research associate at the Institute of Computational Physics (ICP), Zurich University of Applied Sciences (ZHAW), Switzerland. Mathias Fingerle received his PhD in experimental physics from TU Kaiserslautern in 2014. He has conducted academic teaching and research in the field of energy materials and led the group Electrochemical Interfaces at the Institute of Surface Science at TU Darmstadt. Presently, as Head of Consulting & Projects at Math2Market GmbH, he is coordinating scientific consulting and application engineering for digital material design mainly in the fields of batteries, fuel cells, digital rock physics, air and oil filtration and composites. Andreas Wiegmann is CEO and founder of Math2Market, an engineering software company that specializes in digital mesoscale materials characterization and materials design. He has a PhD in mathematics from the University of Washington in Seattle and then worked at the University of California at Berkeley, LBNL and Fraunhofer ITWM. He specializes in numerics of interfaces between high contrast materials, stochastic 3D material models, and the analysis of 3D scans and published more than 150 articles in areas ranging from machine learning to computational physics, textile engineering, fuel cell modelling, battery material research, petroleum engineering and structural topology optimization. Matthias Neumann is Post-doc at the Institute of Stochastics of Ulm University (UU), where he received his PhD in 2020. He was awarded with the PhD price of UU and received start-up funding by the Graduate & Professional Training Center Ulm. Since 2021, he is member of the Cluster of Excellence POLiS (Post Lithium Storage). The focus of his research is on microstructure characterization by statistical image analysis and machine learning, the development of stochastic models for generating digital twins, and the quantification of microstructure-property relationships. He published 33 research papers in peer-reviewed international journals and 3 contributions in conference proceedings.Volker Schmidt is Professor at the Institute of Stochastics of Ulm University. He received his PhD from the Technical University Bergakademie Freiberg. His research activities are focused on spatial stochastic modeling of highly resolved image data in 2D, 3D and 4D, using methods of statistical image processing, machine learning and stochastic geometry. Prof. Schmidt is co-author of three books and more than two hundred research papers in peer-reviewedinternational journals. He supervised more than one hundred Bachelor and Master students, and 23 PhD students who have completed their dissertation theses so far. Currently, 11 PhD students are preparing their PhD theses under his supervision.

• Chapter 1. Introduction.- Chapter 2. Review of theories and a classification of tortuosity types.- Chapter 3. Review of empirical data from literature - tortuosity-porosity relationships.- Chapter 4. Methodologies, workflows and calculation approaches.- Chapter 5. Towards a quantitative understanding of microstructure - property relationships.- Chapter 6. Summary and Conclusions.