About

Christian Franck is the Bjorn Borgen Professor in Mechanical Engineering at the University of Wisconsin-Madison and serves as the acting director of the Center for Traumatic Brain Injury. His research program within the PANTHER initiative focuses on advanced detection and prevention of traumatic brain injuries by translating basic science discoveries into solutions for civilian and warfighter protection. His lab develops innovative 2D and 3D full-field imaging and motion tracking techniques with applications in mechanobiology, biomechanics, and the mechanics of soft materials. Current research areas include investigating the mechanobiology of neurons during traumatic brain injuries, the adhesion and migration behavior of human neutrophils, and the role of non-linear material deformations in soft matter. Franck's work aims to provide insights into injury mechanisms and develop protective strategies through experimental characterization and modeling of soft tissues and cellular responses.

Research topics

• Mathematics
• Computer Science
• Physics
• Algorithm
• Cancer research
• Cell biology
• Classical mechanics
• Geology
• Genetics
• Biology
• Geodesy
• Statistics
• Computational science
• Mechanics
• Engineering
• Mathematical optimization

Selected publications

• Field Evaluation of a Wearable Instrumented Headband Designed for Measuring Head Kinematics

  Annals of Biomedical Engineering · 2026-03-13

  articleOpen access

  Abstract Purpose To study the relationship between soccer heading and the risk of mild traumatic brain injury (mTBI), we previously developed an instrumented headband and data-processing scheme to measure the angular head kinematics of soccer headers. Laboratory evaluation of the headband on an anthropomorphic test device showed good agreement with a reference sensor for soccer ball impacts to the front of the head. In this study, we evaluate the headband in measuring the full head kinematics of soccer headers in the field. Methods The headband was evaluated under typical soccer heading scenarios (throw-ins, goal-kicks, and corner-kicks) on a human subject. The measured time history and peak kinematics from the headband were compared with those from an instrumented mouthpiece, which is a widely accepted method for measuring head kinematics in the field. Results The time-history agreement (CORA scores) between the headband and the mouthpiece ranged from ‘fair’ to ‘excellent’, with the highest agreement for angular velocities (0.79 ± 0.08) and translational accelerations (0.73 ± 0.05) and lowest for angular accelerations (0.67 ± 0.06). A Bland–Altman analysis of the peak kinematics from the headband and mouthpiece found the mean bias to be 40.9 $$\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>%</mml:mo> </mml:math> (of the maximum mouthpiece reading) for the angular velocity, 16.6 $$\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>%</mml:mo> </mml:math> for the translational acceleration, and −14.1 $$\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>%</mml:mo> </mml:math> for the angular acceleration. Conclusions The field evaluation of the instrumented headband showed reasonable agreement with the mouthpiece for some kinematic measures and impact conditions. Future work should focus on improving the headband performance across all kinematic measures.

  PublisherOA PDFDOI

• An Equilibrium Constrained Genetic Algorithm (ECGA) calibration framework for isotropic hyperelastic constitutive models with application to an elastomeric foam material

  Computer Methods in Applied Mechanics and Engineering · 2026-04-16

  articleOpen access

  This work introduces a calibration framework for material parameter identification in isotropic hyperelastic constitutive models. The framework defines an objective function based on equilibrium constraints, which is then minimized using a Genetic Algorithm (GA) to facilitate automated calibration. The formulation of the objective function uses experimental displacement fields measured from Digital Image Correlation (DIC) synchronized with load cell data and can accommodate data from experiments involving homogeneous or inhomogeneous deformation fields. The framework places no restrictions on the target isotropic hyperelastic constitutive model, accommodating models with coupled dependencies on deformation invariants and specialized functional forms with a number of material parameters, and assesses material stability, eliminating sets of material parameters that potentially lead to non-physical behavior for the target hyperelastic constitutive model. To minimize the objective function, a GA is deployed as the optimization tool due to its ability to navigate the intricate landscape of material parameter space. The Equilibrium Constrained Genetic Algorithm (ECGA) framework is evaluated by applying it to a hyperelastic constitutive model for compressible elastomeric foams. The evaluation process entails a number of tests that employ both homogeneous and inhomogeneous displacement fields collected from DIC experiments on open-cell foam specimens. The results demonstrate the framework’s robust and efficient capability to handle material parameter identification for a complex hyperelastic constitutive model.

  PublisherDOI

• Toward a Unified Lexicon in Traumatic Brain Injury: Defining the Mechanism of Injury

  Neurotrauma Reports · 2026-04-01

  articleOpen accessSenior author

  In the field of traumtic brain injury (TBI) we have often witnessed miscommunication arise when articles and presentations are not adequately precise with the language describing their TBI models and/or findings. The lack of precise, consistent terminology to describe injury mechanisms across biological scales and temporal phases impedes communication. We propose that at the cellular scale, standardizing the definitions of primary and secondary injury as distinct biological mechanisms—rather than sequential stages—can help advance our understanding of TBI, facilitate interdisciplinary collaboration, and enable more effective comparisons across experimental models, ultimately leading to improved diagnosis and treatment strategies.

  PublisherDOI

• Digital Volume Correlation Challenge 2.0: A Comprehensive Dataset for Digital Volume Correlation Benchmarking

  Research Square · 2026-05-13

  preprintOpen access
  PublisherDOI

• Why do you have to wear a helmet when you’re skateboarding?

  2026-05-04

  article1st authorCorresponding
  PublisherDOI

• Laboratory evaluation of a wearable instrumented headband for rotational head kinematics measurement

  ArXiv.org · 2025-04-02

  preprintOpen access

  Mild traumatic brain injuries (mTBI) are a highly prevalent condition with heterogeneous outcomes between individuals. A key factor governing brain tissue deformation and the risk of mTBI is the rotational kinematics of the head. Instrumented mouthguards are a widely accepted method for measuring rotational head motions, owing to their robust sensor-skull coupling. However, wearing mouthguards is not feasible in all situations, especially for long-term data collection. Therefore, alternative wearable devices are needed. In this study, we present an improved design and data processing scheme for an instrumented headband. Our instrumented headband utilizes an array of inertial measurement units (IMUs) and a new data-processing scheme based on continuous wavelet transforms to address sources of error in the IMU measurements. The headband performance was evaluated in the laboratory on an anthropomorphic test device, which was impacted with a soccer ball to replicate soccer heading. When comparing the measured peak rotational velocities (PRV) and peak rotational accelerations (PRA) between the reference sensors and the headband for impacts to the front of the head, the correlation coefficients (r) were 0.80 and 0.63, and the normalized root mean square error (NRMSE) values were 0.20 and 0.28, respectively. However, when considering all impact locations, r dropped to 0.42 and 0.34 and NRMSE increased to 0.5 and 0.41 for PRV and PRA, respectively. This new instrumented headband improves upon previous headband designs in reconstructing the rotational head kinematics resulting from frontal soccer ball impacts, providing a potential alternative to instrumented mouthguards.

  PublisherOA PDFDOI

• Shear Wave Propagation as a Noninvasive Metric of Loading and Microdamage in Tendon Fascicles

  SSRN Electronic Journal · 2025-01-01

  preprintOpen access
  PublisherDOI

• Determination of high strain-rate, viscoelastic material properties of soft solids using inertial microcavitation in a thin layer

  Extreme Mechanics Letters · 2025-07-25 · 1 citations

  articleOpen access

  Determining the high strain-rate mechanical properties of soft hydrogels and biological tissues is important for a number of biological and engineering applications but remains challenging due to the high compliance of these materials. Inertial microcavitation rheometry (IMR) is a recently developed experimental technique aimed at addressing this need and requires the optical resolution of cavitation bubble kinematics via high-speed videography. While this approach works well for optically transparent samples of dimensions much larger than the typical micron to sub-millimeter bubble sizes, IMR is challenged in highly light scattering media, such as nearly opaque tissues. One remedy to decrease the light scattering within a tissue is to prepare a thinner sample, which facilitates successful recording of the cavitation bubble dynamics. However, the thickness of the required thin samples can approach the size of the microbubbles, and the resulting confinement of the soft material layer between two boundaries changes the fundamental character of the assumed nearly infinite domain of the IMR theoretical framework, leading to erroneous material property estimates. To address this issue and to facilitate successful application of IMR to thin layers of soft materials under confinement, we developed a modified, thin-layer IMR approach for the accurate determination of high strain-rate viscoelastic material properties of soft solids that utilizes axisymmetric finite-element simulations of bubble dynamics in a thin layer. The approach is applied to two transparent, benchmark gels: 6% and 14% gelatin, and the material parameters estimated using the thin-layer IMR approach are validated against experimental data for isolated, spherical bubbles and oversized bubbles in a thin layer. The thin-layer IMR approach provides a robust methodology for applying IMR to nearly opaque, soft materials, such as tissues.

  PublisherDOI

• Design of a Simple and Rugged Soft Polydimethylsiloxane‐Carbon Nanotube‐Graphene‐Based Composite Sensor

  Advanced Materials Technologies · 2025-05-19 · 2 citations

  articleOpen accessSenior authorCorresponding

  Abstract Many applications in human health screening, soft robotics, and structural health monitoring require sensors that can accommodate large deformations and highly curved geometries, while providing reliable measurements across a range of frequencies. Ideally, such sensors will also be low cost and easy to manufacture. While prior studies achieve some of these goals, it is rare to achieve them all in a holistic manner. Here, a soft sensor that is easy to manufacture, affordable, and water compatible is presented. The sensor is made of a combination of carbon nanotubes and few‐layer graphene dispersed in a polydimethylsiloxane elastomer. The sensor's ability to detect a broad range of frequencies under both uniaxial stretch and bending is demonstrated. The sensor is effective in multiple configurations, including directly stretching the sensor, adhering the sensor to a deforming compliant substrate, and operating under water. Specifically, the sensor can accurately detect vibrational frequencies with amplitudes as small as 0.1% strain and excitation frequencies covering a broad range of 50–600 Hz with an average root mean square error (RMSE) of 0.16%. Even in the presence of large (≈ 20%) deformations and aqueous environments the sensor can recover the fundamental and higher order vibrational modes within less than 2% error.

  PublisherOA PDFDOI

• Monocytes use protrusive forces to generate migration paths in viscoelastic collagen-based extracellular matrices

  Proceedings of the National Academy of Sciences · 2025-06-16 · 8 citations

  articleOpen access

  Circulating monocytes are recruited to the tumor microenvironment, where they can differentiate into macrophages that mediate tumor progression. To reach the tumor microenvironment, monocytes must first extravasate and migrate through the type-1 collagen rich stromal matrix. The viscoelastic stromal matrix around tumors not only stiffens relative to normal stromal matrix, but often exhibits enhanced viscous characteristics, as indicated by a higher loss tangent or faster stress relaxation rate. Here, we studied how changes in matrix stiffness and viscoelasticity impact the three-dimensional (3D) migration of monocytes through stromal-like matrices. Interpenetrating networks of type-1 collagen and alginate, which enable independent tunability of stiffness and stress relaxation over physiologically relevant ranges, were used as confining matrices for 3D culture of monocytes. Increased stiffness and faster stress relaxation independently enhanced the 3D migration of monocytes. Migrating monocytes have an ellipsoidal or rounded wedge-like morphology, reminiscent of amoeboid migration, with accumulation of actin at the trailing edge. Matrix adhesions were dispensable for monocyte migration in 3D, but migration did require actin polymerization and myosin contractility. Mechanistic studies indicate that actin polymerization at the leading edge generates protrusive forces that open a path for the monocytes to migrate through in the confining viscoelastic matrices. Taken together, our findings implicate matrix stiffness and stress relaxation as key mediators of monocyte migration and reveal how monocytes use pushing forces at the leading edge mediated by actin polymerization to generate migration paths in confining viscoelastic matrices.

  PublisherDOI

Recent grants

• Use of Biomimicry to Determine the Effect of Sepsis on Neutrophil Traction

  NIH · $2.1M · 2015–2021

Frequent coauthors

• Jonathan B. Estrada

  University of Michigan–Ann Arbor

  59 shared

• Mohak Patel

  53 shared

• Jonathan S. Reichner

  Rhode Island Hospital

  48 shared

• David L. Henann

  John Brown University

  41 shared

• Harry C. Cramer

  Dana-Farber Cancer Institute

  38 shared

• Eyal Bar-Kochba

  Johns Hopkins University Applied Physics Laboratory

  33 shared

• Alexander K. Landauer

  National Institute of Standards and Technology

  32 shared

• Jennet Toyjanova

  Providence College

  31 shared

Labs

• Christian Franck LabPI

Awards & honors

• American Society of Mechanical Engineers, Fellow (2025)
• Society for Experimental Mechanics, Fellow (2025)
• College of Engineering, University of Wisconsin-Madison, H.I…
• Society for Experimental Mechanics, M. Hetenyi Best Journal…
• College of Engineering, University of Wisconsin-Madison, Bjo…