Alexander M. Zöllner

On the biomechanics and mechanobiology of growing skin

Skin displays an impressive functional plasticity, which allows it to adapt gradually to environmental changes. Tissue expansion takes advantage of this adaptation, and induces a controlled in situ skin growth for defect correction in plastic and reconstructive surgery. Stretches beyond the skins physiological limit invoke several mechanotransduction pathways, which increase mitotic activity and collagen synthesis, ultimately resulting in a net gain in skin surface area. However, the interplay between mechanics and biology during tissue expansion remains unquantified. Here, we present a continuum model for skin growth that summarizes the underlying mechanotransduction pathways collectively in a single phenomenological variable, the strain-driven area growth. We illustrate the governing equations for growing biological membranes, and demonstrate their computational solution within a nonlinear finite element setting. In displacement-controlled equi-biaxial extension tests, the model accurately predicts the experimentally observed histological, mechanical, and structural features of growing skin, both qualitatively and quantitatively. Acute and chronic elastic uniaxial stretches are 25% and 10%, compared to 36% and 10% reported in the literature. Acute and chronic thickness changes are -28% and -12%, compared to -22% and -7% reported in the literature. Chronic fractional weight gain is 3.3, compared to 2.7 for wet weight and 3.3 for dry weight reported in the literature. In two clinical cases of skin expansion in pediatric forehead reconstruction, the model captures the clinically observed mechanical and structural responses, both acutely and chronically. Our results demonstrate that the field theories of continuum mechanics can reliably predict the mechanical manipulation of thin biological membranes by controlling their mechanotransduction pathways through mechanical overstretch. We anticipate that the proposed skin growth model can be generalized to arbitrary biological membranes, and that it can serve as a valuable tool to virtually manipulate living tissues, simply by means of changes in the mechanical environment.

Stretching Skeletal Muscle: Chronic Muscle Lengthening through Sarcomerogenesis

Skeletal muscle responds to passive overstretch through sarcomerogenesis, the creation and serial deposition of new sarcomere units. Sarcomerogenesis is critical to muscle function: It gradually re-positions the muscle back into its optimal operating regime. Animal models of immobilization, limb lengthening, and tendon transfer have provided significant insight into muscle adaptation in vivo. Yet, to date, there is no mathematical model that allows us to predict how skeletal muscle adapts to mechanical stretch in silico. Here we propose a novel mechanistic model for chronic longitudinal muscle growth in response to passive mechanical stretch. We characterize growth through a single scalar-valued internal variable, the serial sarcomere number. Sarcomerogenesis, the evolution of this variable, is driven by the elastic mechanical stretch. To analyze realistic three-dimensional muscle geometries, we embed our model into a nonlinear finite element framework. In a chronic limb lengthening study with a muscle stretch of 1.14, the model predicts an acute sarcomere lengthening from 3.09m to 3.51m, and a chronic gradual return to the initial sarcomere length within two weeks. Compared to the experiment, the acute model error was 0.00% by design of the model; the chronic model error was 2.13%, which lies within the rage of the experimental standard deviation. Our model explains, from a mechanistic point of view, why gradual multi-step muscle lengthening is less invasive than single-step lengthening. It also explains regional variations in sarcomere length, shorter close to and longer away from the muscle-tendon interface. Once calibrated with a richer data set, our model may help surgeons to prevent muscle overstretch and make informed decisions about optimal stretch increments, stretch timing, and stretch amplitudes. We anticipate our study to open new avenues in orthopedic and reconstructive surgery and enhance treatment for patients with ill proportioned limbs, tendon lengthening, tendon transfer, tendon tear, and chronically retracted muscles.

Segmental Aortic Stiffening Contributes to Experimental Abdominal Aortic Aneurysm Development

Background— Stiffening of the aortic wall is a phenomenon consistently observed in age and in abdominal aortic aneurysm (AAA). However, its role in AAA pathophysiology is largely undefined. Methods and Results— Using an established murine elastase-induced AAA model, we demonstrate that segmental aortic stiffening precedes aneurysm growth. Finite-element analysis reveals that early stiffening of the aneurysm-prone aortic segment leads to axial (longitudinal) wall stress generated by cyclic (systolic) tethering of adjacent, more compliant wall segments. Interventional stiffening of AAA-adjacent aortic segments (via external application of surgical adhesive) significantly reduces aneurysm growth. These changes correlate with the reduced segmental stiffness of the AAA-prone aorta (attributable to equalized stiffness in adjacent segments), reduced axial wall stress, decreased production of reactive oxygen species, attenuated elastin breakdown, and decreased expression of inflammatory cytokines and macrophage infiltration, and attenuated apoptosis within the aortic wall, as well. Cyclic pressurization of segmentally stiffened aortic segments ex vivo increases the expression of genes related to inflammation and extracellular matrix remodeling. Finally, human ultrasound studies reveal that aging, a significant AAA risk factor, is accompanied by segmental infrarenal aortic stiffening. Conclusions— The present study introduces the novel concept of segmental aortic stiffening as an early pathomechanism generating aortic wall stress and triggering aneurysmal growth, thereby delineating potential underlying molecular mechanisms and therapeutic targets. In addition, monitoring segmental aortic stiffening may aid the identification of patients at risk for AAA.

Growth on demand: Reviewing the mechanobiology of stretched skin

Skin is a highly dynamic, autoregulated, living system that responds to mechanical stretch through a net gain in skin surface area. Tissue expansion uses the concept of controlled overstretch to grow extra skin for defect repair in situ. While the short-term mechanics of stretched skin have been studied intensely by testing explanted tissue samples ex vivo, we know very little about the long-term biomechanics and mechanobiology of living skin in vivo. Here we explore the long-term effects of mechanical stretch on the characteristics of living skin using a mathematical model for skin growth. We review the molecular mechanisms by which skin responds to mechanical loading and model their effects collectively in a single scalar-valued internal variable, the surface area growth. This allows us to adopt a continuum model for growing skin based on the multiplicative decomposition of the deformation gradient into a reversible elastic and an irreversible growth part. To demonstrate the inherent modularity of this approach, we implement growth as a user-defined constitutive subroutine into the general purpose implicit finite element program Abaqus/Standard. To illustrate the features of the model, we simulate the controlled area growth of skin in response to tissue expansion with multiple filling points in time. Our results demonstrate that the field theories of continuum mechanics can reliably predict the manipulation of thin biological membranes through mechanical overstretch. Our model could serve as a valuable tool to rationalize clinical process parameters such as expander geometry, expander size, filling volume, filling pressure, and inflation timing to minimize tissue necrosis and maximize patient comfort in plastic and reconstructive surgery. While initially developed for growing skin, our model can easily be generalized to arbitrary biological structures to explore the physiology and pathology of stretch-induced growth of other living systems such as hearts, arteries, bladders, intestines, ureters, muscles, and nerves.

Growing skin: Tissue expansion in pediatric forehead reconstruction

Tissue expansion is a common surgical procedure to grow extra skin through controlled mechanical over-stretch. It creates skin that matches the color, texture, and thickness of the surrounding tissue, while minimizing scars and risk of rejection. Despite intense research in tissue expansion and skin growth, there is a clear knowledge gap between heuristic observation and mechanistic understanding of the key phenomena that drive the growth process. Here, we show that a continuum mechanics approach, embedded in a custom-designed finite element model, informed by medical imaging, provides valuable insight into the biomechanics of skin growth. In particular, we model skin growth using the concept of an incompatible growth configuration. We characterize its evolution in time using a second-order growth tensor parameterized in terms of a scalar-valued internal variable, the in-plane area growth. When stretched beyond the physiological level, new skin is created, and the in-plane area growth increases. For the first time, we simulate tissue expansion on a patient-specific geometric model, and predict stress, strain, and area gain at three expanded locations in a pediatric skull: in the scalp, in the forehead, and in the cheek. Our results may help the surgeon to prevent tissue over-stretch and make informed decisions about expander geometry, size, placement, and inflation. We anticipate our study to open new avenues in reconstructive surgery and enhance treatment for patients with birth defects, burn injuries, or breast tumor removal.

On high heels and short muscles: A multiscale model for sarcomere loss in the gastrocnemius muscle

High heels are a major source of chronic lower limb pain. Yet, more than one third of all women compromise health for looks and wear high heels on a daily basis. Changing from flat footwear to high heels induces chronic muscle shortening associated with discomfort, fatigue, reduced shock absorption, and increased injury risk. However, the long-term effects of high-heeled footwear on the musculoskeletal kinematics of the lower extremities remain poorly understood. Here we create a multiscale computational model for chronic muscle adaptation to characterize the acute and chronic effects of global muscle shortening on local sarcomere lengths. We perform a case study of a healthy female subject and show that raising the heel by 13cm shortens the gastrocnemius muscle by 5% while the Achilles tendon remains virtually unaffected. Our computational simulation indicates that muscle shortening displays significant regional variations with extreme values of 22% in the central gastrocnemius. Our model suggests that the muscle gradually adjusts to its new functional length by a chronic loss of sarcomeres in series. Sarcomere loss varies significantly across the muscle with an average loss of 9%, virtually no loss at the proximal and distal ends, and a maximum loss of 39% in the central region. These changes reposition the remaining sarcomeres back into their optimal operating regime. Computational modeling of chronic muscle shortening provides a valuable tool to shape our understanding of the underlying mechanisms of muscle adaptation. Our study could open new avenues in orthopedic surgery and enhance treatment for patients with muscle contracture caused by other conditions than high heel wear such as paralysis, muscular atrophy, and muscular dystrophy.

Passive Stretch Induces Structural and Functional Maturation of Engineered Heart Muscle as Predicted by Computational Modeling

The ability to differentiate human pluripotent stem cells (hPSCs) into cardiomyocytes (CMs) makes them an attractive source for repairing injured myocardium, disease modeling, and drug testing. Although current differentiation protocols yield hPSC‐CMs to >90% efficiency, hPSC‐CMs exhibit immature characteristics. With the goal of overcoming this limitation, we tested the effects of varying passive stretch on engineered heart muscle (EHM) structural and functional maturation, guided by computational modeling. Human embryonic stem cells (hESCs, H7 line) or human induced pluripotent stem cells (IMR‐90 line) were differentiated to hPSC‐derived cardiomyocytes (hPSC‐CMs) in vitro using a small molecule based protocol. hPSC‐CMs were characterized by troponin+ flow cytometry as well as electrophysiological measurements. Afterwards, 1.2 × 106 hPSC‐CMs were mixed with 0.4 × 106 human fibroblasts (IMR‐90 line) (3:1 ratio) and type‐I collagen. The blend was cast into custom‐made 12‐mm long polydimethylsiloxane reservoirs to vary nominal passive stretch of EHMs to 5, 7, or 9 mm. EHM characteristics were monitored for up to 50 days, with EHMs having a passive stretch of 7 mm giving the most consistent formation. Based on our initial macroscopic observations of EHM formation, we created a computational model that predicts the stress distribution throughout EHMs, which is a function of cellular composition, cellular ratio, and geometry. Based on this predictive modeling, we show cell alignment by immunohistochemistry and coordinated calcium waves by calcium imaging. Furthermore, coordinated calcium waves and mechanical contractions were apparent throughout entire EHMs. The stiffness and active forces of hPSC‐derived EHMs are comparable with rat neonatal cardiomyocyte‐derived EHMs. Three‐dimensional EHMs display increased expression of mature cardiomyocyte genes including sarcomeric protein troponin‐T, calcium and potassium ion channels, β‐adrenergic receptors, and t‐tubule protein caveolin‐3. Passive stretch affects the structural and functional maturation of EHMs. Based on our predictive computational modeling, we show how to optimize cell alignment and calcium dynamics within EHMs. These findings provide a basis for the rational design of EHMs, which enables future scale‐up productions for clinical use in cardiovascular tissue engineering. Stem Cells 2018;36:265–277

Towards an instrumented tissue expander

Tissue expansion is a surgical procedure to grow additional skin per controlled mechanical stretch. Despite the progress of this reconstructive treatment, there are still some limitations. Both, the inflation protocol and the filling volume vary for every patient. The aim of this paper is to present a first attempt of a sensor featured tissue expander. This so-called instrumented tissue expander provides the treating surgeon a sensory feedback to enhance a successful treatment. The implementation of a pressure sensor enables the display of both, the current expander pressure and the pressure over time. Based on the progress of the pressure curve, the inflation time points are triggered. The skin growth is maximized and adjustable to each individual patient. This new way of tissue expansion is simulated with a finite element model. The skin growth is implemented as a strain-driven process. In addition, a first feasibility prototype is built. Based on the pressure-time diagram the condition of the skin can be deduced from the first derivative. Additionally the user is always enabled to observe or rather check the current pressure inside the tissue expander. Moreover, the risk of necrosis or pressure-induced ischemia is minimized. Thanks to the technical data the treatment is simplified for less experienced surgeons. Experienced doctors can train less experienced surgeons by monitoring and comparing both the appearance of the skin and the pressure data.

Finite Element Modeling of Flap Design After Skin Expansion

Tissue expansion is a common technique in reconstructive surgery used to resurface damaged areas such as burns, birth defects or after tumor removal. The procedure is characterized by the inflation of a balloon below the skin that leads to three-dimensional dome-like shapes of tissue. Skin then needs to be cut to create a flap, which is extended to cover the excised area. The latter procedure, called flap design, has been empirically studied and advantages and disadvantages of the use of one type of flap over another have been discussed [1]. However, to date, flap design has never been optimized from a mechanical point of view.Copyright

Modeling Growth in Tissue Expansion

Skin expansion enables the correction of birthmarks, burn injuries, and reconstruction of breasts after tumor removal. The astonishing properties of human skin allow us to implant and inflate a balloon expander next to a defect to grow skin with matching color, texture, hairiness, and thickness while minimizing the risk for rejection and scaring3. In order to grow skin in situ, the balloon expander is placed in a subcutaneous pocket of approximately the expander size and shape, see Figure 1. Inflating the balloon gradually between four to eight weeks after surgery triggers growth by overstretching the skin.Copyright