On the biomechanics and mechanobiology of growing skin

Sustained Physiological Stretch Induces Abdominal Skin Growth in Pregnancy

Supraphysiological stretches are exploited in skin expanders to induce tissue growth for autologous implants. As pregnancy is associated with large levels of sustained stretch, we investigated whether skin growth occurs in pregnancy. Therefore, we combined a mechanical model of skin and the observations from suction experiments on several body locations of five pregnant women at different gestational ages. The measurements show a continuous increase in stiffness, with the largest change observed during the last trimester. A comparison with numerical simulations indicates that the measured increase in skin stiffness is far below the level expected for the corresponding deformation of abdominal skin. A new set of simulations accounting for growth could rationalize all observations. The predicted amount of tissue growth corresponds to approximately 40% area increase before delivery. The results of the simulations also offered the opportunity to investigate the biophysical cues present in abdominal skin along gestation and to compare them with those arising in skin expanders. Alterations of the skin mechanome were quantified, including tissue stiffness, hydrostatic and osmotic pressure of the interstitial fluid, its flow velocity and electrical potential. The comparison between pregnancy and skin expansion highlights similarities as well as differences possibly influencing growth and remodeling.

Advancements in 3D-printable polysaccharides, proteins, and synthetic polymers for wound dressing and skin scaffolding - A review

This review investigates the most recent advances in personalized 3D-printed wound dressings and skin scaffolding. Skin is the largest and most vulnerable organ in the human body. The human body has natural mechanisms to restore damaged skin through several overlapping stages. However, the natural wound healing process can be rendered insufficient due to severe wounds or disturbances in the healing process. Wound dressings are crucial in providing a protective barrier against the external environment, accelerating healing. Although used for many years, conventional wound dressings are neither tailored to individual circumstances nor specific to wound conditions. To address the shortcomings of conventional dressings, skin scaffolding can be used for skin regeneration and wound healing. This review thoroughly investigates polysaccharides (e.g., chitosan, Hyaluronic acid (HA)), proteins (e.g., collagen, silk), synthetic polymers (e.g., Polycaprolactone (PCL), Poly lactide-co-glycolic acid (PLGA), Polylactic acid (PLA)), as well as nanocomposites (e.g., silver nano particles and clay materials) for wound healing applications and successfully 3D printed wound dressings. It discusses the importance of combining various biomaterials to enhance their beneficial characteristics and mitigate their drawbacks. Different 3D printing fabrication techniques used in developing personalized wound dressings are reviewed, highlighting the advantages and limitations of each method. This paper emphasizes the exceptional versatility of 3D printing techniques in advancing wound healing treatments. Finally, the review provides recommendations and future directions for further research in wound dressings.

An Overview of Scaffolds and Biomaterials for Skin Expansion and Soft Tissue Regeneration: Insights on Zinc and Magnesium as New Potential Key Elements

The utilization of materials in medical implants, serving as substitutes for non-functional biological structures, supporting damaged tissues, or reinforcing active organs, holds significant importance in modern healthcare, positively impacting the quality of life for millions of individuals worldwide. However, certain implants may only be required temporarily to aid in the healing process of diseased or injured tissues and tissue expansion. Biodegradable metals, including zinc (Zn), magnesium (Mg), iron, and others, present a new paradigm in the realm of implant materials. Ongoing research focuses on developing optimized materials that meet medical standards, encompassing controllable corrosion rates, sustained mechanical stability, and favorable biocompatibility. Achieving these objectives involves refining alloy compositions and tailoring processing techniques to carefully control microstructures and mechanical properties. Among the materials under investigation, Mg- and Zn-based biodegradable materials and their alloys demonstrate the ability to provide necessary support during tissue regeneration while gradually degrading over time. Furthermore, as essential elements in the human body, Mg and Zn offer additional benefits, including promoting wound healing, facilitating cell growth, and participating in gene generation while interacting with various vital biological functions. This review provides an overview of the physiological function and significance for human health of Mg and Zn and their usage as implants in tissue regeneration using tissue scaffolds. The scaffold qualities, such as biodegradation, mechanical characteristics, and biocompatibility, are also discussed.

Multi-Fidelity Gaussian Process Surrogate Modeling of Pediatric Tissue Expansion

Growth of skin in response to stretch is the basis for tissue expansion (TE), a procedure to gain new skin area for reconstruction of large defects. Unfortunately, complications and suboptimal outcomes persist because TE is planned and executed based on physician's experience and trial and error instead of predictive quantitative tools. Recently, we calibrated computational models of TE to a porcine animal model of tissue expansion, showing that skin growth is proportional to stretch with a characteristic time constant. Here, we use our calibrated model to predict skin growth in cases of pediatric reconstruction. Available from the clinical setting are the expander shapes and inflation protocols. We create low fidelity semi-analytical models and finite element models for each of the clinical cases. To account for uncertainty in the response expected from translating the models from the animal experiments to the pediatric population, we create multifidelity Gaussian process surrogates to propagate uncertainty in the mechanical properties and the biological response. Predictions with uncertainty for the clinical setting are essential to bridge our knowledge from the large animal experiments to guide and improve the treatment of pediatric patients. Future calibration of the model with patient-specific data-such as estimation of mechanical properties and area growth in the operating room-will change the standard for planning and execution of TE protocols.

PDE-constrained shape registration to characterize biological growth and morphogenesis from imaging data

We propose a PDE-constrained shape registration algorithm that captures the deformation and growth of biological tissue from imaging data. Shape registration is the process of evaluating optimum alignment between pairs of geometries through a spatial transformation function. We start from our previously reported work, which uses 3D tensor product B-spline basis functions to interpolate 3D space. Here, the movement of the B-spline control points, composed with an implicit function describing the shape of the tissue, yields the total deformation gradient field. The deformation gradient is then split into growth and elastic contributions. The growth tensor captures addition of mass, i.e. growth, and evolves according to a constitutive equation which is usually a function of the elastic deformation. Stress is generated in the material due to the elastic component of the deformation alone. The result of the registration is obtained by minimizing a total energy functional which includes: a distance measure reflecting similarity between the shapes, and the total elastic energy accounting for the growth of the tissue. We apply the proposed shape registration framework to study zebrafish embryo epiboly process and tissue expansion during skin reconstruction surgery. We anticipate that our PDE-constrained shape registration method will improve our understanding of biological and medical problems in which tissues undergo extreme deformations over time.

Multiscale Computational Model Predicts Mouse Skin Kinematics Under Tensile Loading

Skin is a complex tissue whose biomechanical properties are generally understood in terms of an incompressible material whose microstructure undergoes affine deformations. A growing number of experiments, however, have demonstrated that skin has a high Poisson's ratio, substantially decreases in volume during uniaxial tensile loading, and demonstrates collagen fiber kinematics that are not affine with local deformation. In order to better understand the mechanical basis for these properties, we constructed multiscale mechanical models (MSM) of mouse skin based on microstructural multiphoton microscopy imaging of the dermal microstructure acquired during mechanical testing. Three models that spanned the cases of highly aligned, moderately aligned, and nearly random fiber networks were examined and compared to the data acquired from uniaxially stretched skin. Our results demonstrate that MSMs consisting of networks of matched fiber organization can predict the biomechanical behavior of mouse skin, including the large decrease in tissue volume and nonaffine fiber kinematics observed under uniaxial tension.

Mechanical stretching can modify the papillary dermis pattern and papillary fibroblast characteristics during skin regeneration

Clinical application of mechanical stretching is a reconstructive method for skin repair. Although studies have reported dermal fibroblast heterogeneity, whether stretching affects individual fibroblast subpopulations equally remains unclear. Here, we show the changes in dermal structure and papillary fibroblast (Fp) in regenerated human skin. Exhausted skin regeneration caused dermal-epidermal junction (DEJ) flattening, papillary dermis thinning, and an increase in the type III collagen (COL3)/type I collagen (COL1) ratio with upregulated hallmarks of aging. Well-regenerated skin displayed a notable increase in the Fp population. Consistent changes were observed in the rat expansion model. Moreover, we found that TGFβ1 expression was especially increased in skin showing good regeneration. Activation of the TGFβ1/Smad2/3 pathway improved exhausted skin regeneration and resulted in increased collagen content and Fp proliferation, while pharmacological inhibition of TGFβ1 action impacted well-regenerated skin. Short-term mechanical stretching that promoted skin regeneration enhanced Fp proliferation, extracellular matrix (ECM) synthesis, and increased TGFβ1 expression, leading to good regeneration. Conversely, long-term stretching induced premature Fp senescence, leading to poor regeneration. This work shows the mechanism of mechanical stretching in well skin regeneration that enhances Fp proliferation and ECM synthesis via the TGFβ1/Smad2/3 pathway, and highlights a crucial role of Fps in stretching-induced skin regeneration.

A biphasic multilayer computational model of human skin

The present study investigates the layer-specific mechanical behavior of human skin. Motivated by skin’s histology, a biphasic model is proposed which differentiates between epidermis, papillary and reticular dermis, and hypodermis. Inverse analysis of ex vivo tensile and in vivo suction experiments yields mechanical parameters for each layer and predicts a stiff reticular dermis and successively softer papillary dermis, epidermis and hypodermis. Layer-specific analysis of simulations underlines the dominating role of the reticular dermis in tensile loading. Furthermore, it shows that the observed out-of-plane deflection in ex vivo tensile tests is a direct consequence of the layered structure of skin. In in vivo suction experiments, the softer upper layers strongly influence the mechanical response, whose dissipative part is determined by interstitial fluid redistribution within the tissue. Magnetic resonance imaging-based visualization of skin deformation in suction experiments confirms the deformation pattern predicted by the multilayer model, showing a consistent decrease in dermal thickness for large probe opening diameters.

How stiff is skin?

The measurement of the mechanical properties of skin (such as stiffness, extensibility and strength) is a key step in characterisation of both dermal ageing and disease mechanisms and in the assessment of tissue-engineered skin replacements. However, the biomechanical terminology and plethora of mathematical analysis approaches can be daunting to those outside the field. As a consequence, mechanical studies are often inaccessible to a significant proportion of the intended audience. Furthermore, devices for the measurement of skin function in vivo generate relative values rather than formal mechanical measures, therefore limiting the ability to compare studies. In this viewpoint essay, we discuss key biomechanical concepts and the influence of technical and biological factors (including the nature of the testing apparatus, length scale, donor age and anatomical site) on measured mechanical properties such as stiffness. Having discussed the current state-of-the-art in macro-mechanical and micromechanical measuring techniques and in mathematical and computational modelling methods, we then make suggestions as to how these approaches, in combination with 3D X-ray imaging and mechanics methods, may be adopted into a single strategy to characterise the mechanical behaviour of skin.

Application of a pre-filled tissue expander for preventing soft tissue incarceration during tibial distraction osteogenesis

BACKGROUND

Bone transport and distraction osteogenesis has been widely used to treat bone defects after traumatic surgery, but, skin and soft tissue incarceration can be as high as 27.6%.

AIM

To investigate the efficacy of inserting a tissue expander to prevent soft tissue incarceration.

METHODS

Between January 2016 and December 2018, 12 patients underwent implantation of a tissue expander in the subcutaneous layer in the vicinity of a tibial defect to maintain the soft tissue in position. A certain amount of normal saline was injected into the tissue expander during surgery and was then gradually extracted to shrink the expander during the course of transport distraction osteogenesis. The tissue expander was removed when the two ends of the tibial defect were close enough.

RESULTS

In all 12 patients, the expanders remained intact in the subcutaneous layer of the bone defect area during the course of transport distraction osteogenesis. When bone transport was adequate, the expander was removed and the bone transport process was completed. During the whole process, there was no incarceration of skin and soft tissue in the bone defect area. Complications occurred in one patient, who experienced poor wound healing.

CONCLUSION

The pre-filled expander technique can effectively avoid soft tissue incarceration. The authors’ primary success with this method indicates that it may be a valuable tool in the management of incarcerated soft tissue.

Quantitative Assessment of Keloids Using Ultrasound Shear Wave Elastography

This study was aimed at investigating the value of shear wave elastography (SWE) in quantitative evaluation of keloids. A total of 87 patients with 139 keloids were enrolled. Vancouver scar scale (VSS) scores were recorded. Thickness and blood flow grade were evaluated using high-frequency ultrasound. Skin stiffness (mean speed of shear wave, C_mean) was evaluated using SWE in both transverse and longitudinal sections. All measurements were performed in both keloids and site-matched unaffected skin (normal controls). The reliability of measurements was evaluated using intra- and inter-class correlation coefficients by two observers. Inter- and intra-observer repeatability was excellent (correlation coefficient > 0.99, p < 0.01). The SWE results revealed a significant increase in C_mean in keloids (p < 0.001) compared with the normal controls. C_mean in the longitudinal section was greater than that in the transverse section for keloids (p < 0.001). C_mean was highly positively correlated with VSS score (r = 0.904, p < 0.001), moderately positively correlated with thickness (r = 0.490, p < 0.001) and less positively correlated with blood flow (r = 0.231, p < 0.01). This non-invasive, tolerable and convenient imaging technique could be an effective tool for objectively evaluating keloid stiffness in the future, thus laying a foundation for the treatment and evaluation of keloids.

Growth and remodelling of living tissues: perspectives, challenges and opportunities

One of the most remarkable differences between classical engineering materials and living matter is the ability of the latter to grow and remodel in response to diverse stimuli. The mechanical behaviour of living matter is governed not only by an elastic or viscoelastic response to loading on short time scales up to several minutes, but also by often crucial growth and remodelling responses on time scales from hours to months. Phenomena of growth and remodelling play important roles, for example during morphogenesis in early life as well as in homeostasis and pathogenesis in adult tissues, which often adapt to changes in their chemo-mechanical environment as a result of ageing, diseases, injury or surgical intervention. Mechano-regulated growth and remodelling are observed in various soft tissues, ranging from tendons and arteries to the eye and brain, but also in bone, lower organisms and plants. Understanding and predicting growth and remodelling of living systems is one of the most important challenges in biomechanics and mechanobiology. This article reviews the current state of growth and remodelling as it applies primarily to soft tissues, and provides a perspective on critical challenges and future directions.

Influences of sodium and glycosaminoglycans on skin oedema and the potential for ulceration: a finite-element approach

Venous ulcers are chronic transcutaneous wounds common in the lower legs. They are resistant to healing and have a 78% chance of recurrence within 2 years. It is commonly accepted that venous ulcers are caused by the insufficiency of the calf muscle pump, leading to blood pooling in the lower legs, resulting in inflammation, skin oedema, tissue necrosis and eventually skin ulceration. However, the detailed physiological events by which inflammation contributes to wound formation are poorly understood. We therefore sought to develop a model that simulated the inflammation, using it to determine the internal stresses and pressure on the skin that contribute to venous ulcer formation. A three-layer finite-element skin model (epidermis, dermis and hypodermis) was developed to explore the roles in wound formation of two inflammation identifiers: glycosaminoglycans (GAG) and sodium. A series of parametric studies showed that increased GAG and sodium content led to oedema and increased tissue stresses of 1.5 MPa, which was within the reported range of skin tissue ultimate tensile stress (0.1-40 MPa). These results suggested that both the oedema and increased fluid pressure could reach a threshold for tissue damage and eventual ulcer formation. The models presented here provide insights to the pathological events associated with venous insufficiency, including inflammation, oedema and skin ulceration.

Tissue expanders; review of indications, results and outcome during 15 years' experience

BACKGROUND

Tissue expanders (TE) are frequently used worldwide. In this study we surveyed outcome of our patients retrospectively during 15 years.

MATERIALS AND METHODS

We had 1105 patients for whom 3059 TEs have been used. Demographic data, age, sex, indications, type of tissue expander devices, volume of devices, site of scar and site TE insertion, our technique for tissue expander insertion and flap design, complications and outcome were gathered. A complete and through technical points and tips will be discussed.

RESULTS

In 91% of patients overexpansion was done. (Expansion ratio=2.1-4.5). Re-expansion has been done in about 12% of patients. Complications were perforation of skin of pocket (11%) or exposure, infection (6%), dehiscence of the wound (1.5%), perforation of the port or disconnection of the tubes (2.1%), expansion of the scar itself (1%), saggy flap (3%), dog ear (5%), lack of adhesions of flap to its new site (4%).

OUTCOME

In 93% of the patients we could totally remove the scar. Around 9.1% of our patients had two sessions of expansion in the same area and 2.9% had three sessions of expansion. 51% of our patients were highly satisfied and 42% were satisfied of the results of expansion.

CONCLUSION

Our patients were satisfied with the results. In 12% cases we have done re-expansion. Re-expansion is possible as long as you have enough thickness of dermis in the skin. More than 50% of our patients were optimistic for 2nd or 3rd session of re-expansion.

Kinetics of surface growth with coupled diffusion and the emergence of a universal growth path

Surface growth by association or dissociation of material on the boundary of a body is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a single cell, and is increasingly applied in engineering processes for fabrication and self-assembly. A significant challenge in modelling such processes arises due to the inherent coupled interaction between the growth kinetics, the local stresses and the diffusing constituents needed to sustain the growth. Moreover, the volume of the body changes not only due to surface growth but also by variation in solvent concentration within the bulk. In this paper, we present a general theoretical framework that captures these phenomena and describes the kinetics of surface growth while accounting for coupled diffusion. Then, by the combination of analytical and numerical tools, applied to a simple growth geometry, we show that the evolution of such growth processes tends towards a universal path that is independent of initial conditions. This path, on which surface growth and diffusion act harmoniously, can be extended to analytically portray the evolution of a body from inception up to a treadmilling state, in which addition and removal of material are balanced.

On skin microrelief and the emergence of expression micro-wrinkles

Over the course of a life time, as a result of adaptive mechanobiological processes (e.g. ageing), or the action of external physical factors such as mechanical loading, the human skin is subjected to, and hosts complex biophysical processes. These phenomena typically operate through a complex interplay, that, ultimately, is responsible for the evolutive geometrical characteristics of the skin surface. Wrinkles are a manifestation of these effects. Although numerous theoretical models of wrinkles arising in multi-layered structures have been proposed, they typically apply to idealised geometries. In the case of skin, which can be viewed as a geometrically complex multi-layer assembly, it is pertinent to question whether the natural skin microrelief could play a significant role in conditioning the characteristics of compression-induced micro-wrinkles by acting as an array of geometrical imperfections. Here, we explore this question through the development of an anatomically-based finite strain parametric finite element model of the skin, represented as a stratum corneum layer on top of a thicker and softer substrate. Our study suggests that skin microrelief could be the dominant factor conditioning micro-wrinkle characteristics for moderate elastic modulus ratios between the two layers. Beyond stiffness ratios of 100, other factors tend to overwrite the effects of skin microrelief. Such stiffness ratio fluctuations can be induced by changes in relative humidity or particular skin conditions and can therefore have important implications for skin tribology.

THE SIMULATION STUDY ON THE DEFORMATION OF RABBIT CORNEA AFTER REFRACTIVE SURGERY WITH DIFFERENT CUTTING THICKNESS

Based on the inflation tests data of rabbit cornea, finite element analysis has been applied to determine the material parameters, simulate corneal refractive surgery and study postoperative corneal deformations. The corneal profile and apical displacement data were recorded during the inflation experiment of five rabbit corneas. Inverse finite element method was applied to determine the material parameters from the corneal apical displacements. Based on the determined material parameters and the corneal profile information, we established five corneal geometry models that simulate refractive surgery with different cutting amounts. We analyzed displacements at corneal apex and cutting edge, corneal surface curvatures under different pressures. Both Ogden model ([Formula: see text]) and Yeoh model ([Formula: see text]) gave good fits to the experiment data. The maximum of error square sum between the calculated value and the experimental value of the displacements per point at the corneal profile was less than 0.06[Formula: see text]mm. For each model with the increase of pressure, the displacement at cutting edge was larger than that at corneal apex, both of them increased, and curvature radius of anterior and posterior corneal surface increased slowly, but the refractive power decreased slowly and tended to be a stable value. Under the same pressure, the larger the cutting amount, the larger the displacements at corneal apex and cutting edge with a cutting edge displacement of about 1.10 (less ablation model) and 1.02 (larger ablation model) times the corneal vertex displacement. Both Ogden model and Yeoh model can be used to describe corneal mechanical responses of inflation experiment. After refractive surgery, the displacement at cutting edge is larger than that at corneal apex, the curvature radius of anterior (posterior) corneal surface increases (decreases), and the refractive power decreases.

Recent advances in studying single bacteria and biofilm mechanics

Bacterial biofilms correspond to surface-associated bacterial communities embedded in hydrogel-like matrix, in which high cell density, reduced diffusion and physico-chemical heterogeneity play a protective role and induce novel behaviors. In this review, we present recent advances on the understanding of how bacterial mechanical properties, from single cell to high-cell density community, determine biofilm tri-dimensional growth and eventual dispersion and we attempt to draw a parallel between these properties and the mechanical properties of other well-studied hydrogels and living systems.

Mathematical and computational modelling of skin biophysics: a review

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas.

On the biomechanical analysis of the calories expended in a straight boxing jab

Boxing and related sports activities have become a standard workout regime at many fitness studios worldwide. Oftentimes, people are interested in the calories expended during these workouts. This note focuses on determining the calories in a boxer's jab, using kinematic vector-loop relations and basic work-energy principles. Numerical simulations are undertaken to illustrate the basic model. Multi-limb extensions of the model are also discussed.

Quantifying the relationship between cell division angle and morphogenesis through computational modeling

When biological cells divide, they divide on a given angle. It has been shown experimentally that the orientation of cell division angle for a single cell can be described by a probability density function. However, the way in which the probability density function underlying cell division orientation influences population or tissue scale morphogenesis is unknown. Here we show that a computational approach, with thousands of stochastic simulations modeling growth and division of a population of cells, can be used to investigate this unknown. In this paper we examine two potential forms of the probability density function: a wrapped normal distribution and a binomial distribution. Our results demonstrate that for the wrapped normal distribution the standard deviation of the division angle, potentially interpreted as biological noise, controls the degree of tissue scale anisotropy. For the binomial distribution, we demonstrate a mechanism by which direction and degree of tissue scale anisotropy can be tuned via the probability of each division angle. We anticipate that the method presented in this paper and the results of these simulations will be a starting point for further investigation of this topic.

The global mechanical properties and multi-scale failure mechanics of heterogeneous human stratum corneum

The outermost layer of skin, or stratum corneum, regulates water loss and protects underlying living tissue from environmental pathogens and insults. With cracking, chapping or the formation of exudative lesions, this functionality is lost. While stratum corneum exhibits well defined global mechanical properties, macroscopic mechanical testing techniques used to measure them ignore the structural heterogeneity of the tissue and cannot provide any mechanistic insight into tissue fracture. As such, a mechanistic understanding of failure in this soft tissue is lacking. This insight is critical to predicting fracture risk associated with age or disease. In this study, we first quantify previously unreported global mechanical properties of isolated stratum corneum including the Poisson's ratio and mechanical toughness. African American breast stratum corneum is used for all assessments. We show these parameters are highly dependent on the ambient humidity to which samples are equilibrated. A multi-scale investigation assessing the influence of structural heterogeneities on the microscale nucleation and propagation of cracks is then performed. At the mesoscale, spatially resolved equivalent strain fields within uniaxially stretched stratum corneum samples exhibit a striking heterogeneity, with localized peaks correlating closely with crack nucleation sites. Subsequent crack propagation pathways follow inherent topographical features in the tissue and lengthen with increased tissue hydration. At the microscale, intact corneocytes and polygonal shaped voids at crack interfaces highlight that cracks propagate in superficial cell layers primarily along intercellular junctions. Cellular fracture does occur however, but is uncommon.

STATEMENT OF SIGNIFICANCE

Human stratum corneum protects the body against harmful environmental pathogens and insults. Upon mechanical failure, this barrier function is lost. Previous studies characterizing the mechanics of stratum corneum have used macroscopic testing equipment designed for homogenous materials. Such measurements ignore the tissue's rich topography and heterogeneous structure, and cannot describe the underlying mechanistic process of tissue failure. For the first time, we establish a mechanistic insight into the failure mechanics of soft heterogeneous tissues by investigating how cracks nucleate and propagate in stratum corneum. We further quantify previously unreported values of the tissue's Poisson's ratio and toughness, and their dramatic variation with ambient humidity. To date, skin models examining drug delivery, wound healing, and ageing continue to estimate these parameters.

Surface and interfacial creases in a bilayer tubular soft tissue

Surface and interfacial creases induced by biological growth are common types of instability in soft biological tissues. This study focuses on the criteria for the onset of surface and interfacial creases as well as their morphological evolution in a growing bilayer soft tube within a confined environment. Critical growth ratios for triggering surface and interfacial creases are investigated both analytically and numerically. Analytical interpretations provide preliminary insights into critical stretches and growth ratios for the onset of instability and formation of both surface and interfacial creases. However, the analytical approach cannot predict the evolution pattern of the model after instability; therefore nonlinear finite element simulations are carried out to replicate the poststability morphological patterns of the structure. Analytical and computational simulation results demonstrate that the initial geometry, growth ratio, and shear modulus ratio of the layers are the most influential factors to control surface and interfacial crease formation in this soft tubular bilayer. The competition between the stretch ratios in the free and interfacial surfaces is one of the key driving factors to determine the location of the first crease initiation. These findings may provide some fundamental understanding in the growth modeling of tubular biological tissues such as esophagi and airways as well as offering useful clues into normal and pathological functions of these tissues.

Molecular Mechanisms of Stress-Responsive Changes in Collagen and Elastin Networks in Skin

Collagen and elastin networks make up the majority of the extracellular matrix in many organs, such as the skin. The mechanisms which are involved in the maintenance of homeostatic equilibrium of these networks are numerous, involving the regulation of genetic expression, growth factor secretion, signalling pathways, secondary messaging systems, and ion channel activity. However, many factors are capable of disrupting these pathways, which leads to an imbalance of homeostatic equilibrium. Ultimately, this leads to changes in the physical nature of skin, both functionally and cosmetically. Although various factors have been identified, including carcinogenesis, ultraviolet exposure, and mechanical stretching of skin, it was discovered that many of them affect similar components of regulatory pathways, such as fibroblasts, lysyl oxidase, and fibronectin. Additionally, it was discovered that the various regulatory pathways intersect with each other at various stages instead of working independently of each other. This review paper proposes a model which elucidates how these molecular pathways intersect with one another, and how various internal and external factors can disrupt these pathways, ultimately leading to a disruption in collagen and elastin networks.

Elastosis during airway wall remodeling explains multiple co-existing instability patterns

Living structures can undergo morphological changes in response to growth and alterations in microstructural properties in response to remodeling. From a biological perspective, airway wall inflammation and airway elastosis are classical hallmarks of growth and remodeling during chronic lung disease. From a mechanical point of view, growth and remodeling trigger mechanical instabilities that result in inward folding and airway obstruction. While previous analytical and computational studies have focused on identifying the critical parameters at the onset of folding, few have considered the post-buckling behavior. All prior studies assume constant microstructural properties during the folding process; yet, clinical studies now reveal progressive airway elastosis, the degeneration of elastic fibers associated with a gradual stiffening of the inner layer. Here, we explore the influence of temporally evolving material properties on the post-bifurcation behavior of the airway wall. We show that a growing and stiffening inner layer triggers an additional subsequent bifurcation after the first instability occurs. Evolving material stiffnesses provoke failure modes with multiple co-existing wavelengths, associated with the superposition of larger folds evolving on top of the initial smaller folds. This phenomenon is exclusive to material stiffening and conceptually different from the phenomenon of period doubling observed in constant-stiffness growth. Our study suggests that the clinically observed multiple wavelengths in diseased airways are a result of gradual airway wall stiffening. While our evolving material properties are inspired by the clinical phenomenon of airway elastosis, the underlying concept is broadly applicable to other types of remodeling including aneurysm formation or brain folding.

One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes

The framework of incompressible nonlinear hyperelasticity and viscoelasticity is applied to the derivation of one-dimensional models of nonlinear wave propagation in fiber-reinforced elastic solids. Equivalence transformations are used to simplify the resulting wave equations and to reduce the number of parameters. Local conservation laws and global conserved quantities of the models are systematically computed and discussed, along with other related mathematical properties. Sample numerical solutions are presented. The models considered in the paper are appropriate for the mathematical description of certain aspects of the behavior of biological membranes and similar structures.

The Incompatibility of Living Systems: Characterizing Growth-Induced Incompatibilities in Expanded Skin

Skin expansion is a common surgical technique to correct large cutaneous defects. Selecting a successful expansion protocol is solely based on the experience and personal preference of the operating surgeon. Skin expansion could be improved by predictive computational simulations. Towards this goal, we model skin expansion using the continuum framework of finite growth. This approach crucially relies on the concept of incompatible configurations. However, aside from the classical opening angle experiment, our current understanding of growth-induced incompatibilities remains rather vague. Here we visualize and characterize incompatibilities in living systems using skin expansion in a porcine model: We implanted and inflated two expanders, crescent, and spherical, and filled them to 225 cc throughout a period of 21 days. To quantify the residual strains developed during this period, we excised the expanded skin patches and subdivided them into smaller pieces. Skin growth averaged 1.17 times the original area for the spherical and 1.10 for the crescent expander, and displayed significant regional variations. When subdivided into smaller pieces, the grown skin patches retracted heterogeneously and confirmed the existence of incompatibilities. Understanding skin growth through mechanical stretch will allow surgeons to improve-and ultimately personalize-preoperative treatment planning in plastic and reconstructive surgery.

Isogeometric Kirchhoff-Love shell formulations for biological membranes

Computational modeling of thin biological membranes can aid the design of better medical devices. Remarkable biological membranes include skin, alveoli, blood vessels, and heart valves. Isogeometric analysis is ideally suited for biological membranes since it inherently satisfies the C¹-requirement for Kirchhoff-Love kinematics. Yet, current isogeometric shell formulations are mainly focused on linear isotropic materials, while biological tissues are characterized by a nonlinear anisotropic stress-strain response. Here we present a thin shell formulation for thin biological membranes. We derive the equilibrium equations using curvilinear convective coordinates on NURBS tensor product surface patches. We linearize the weak form of the generic linear momentum balance without a particular choice of a constitutive law. We then incorporate the constitutive equations that have been designed specifically for collagenous tissues. We explore three common anisotropic material models: Mooney-Rivlin, May Newmann-Yin, and Gasser-Ogden-Holzapfel. Our work will allow scientists in biomechanics and mechanobiology to adopt the constitutive equations that have been developed for solid three-dimensional soft tissues within the framework of isogeometric thin shell analysis.

Isogeometric Kirchhoff-Love shell formulations for biological membranes

Computational modeling of thin biological membranes can aid the design of better medical devices. Remarkable biological membranes include skin, alveoli, blood vessels, and heart valves. Isogeometric analysis is ideally suited for biological membranes since it inherently satisfies the C¹-requirement for Kirchhoff-Love kinematics. Yet, current isogeometric shell formulations are mainly focused on linear isotropic materials, while biological tissues are characterized by a nonlinear anisotropic stress-strain response. Here we present a thin shell formulation for thin biological membranes. We derive the equilibrium equations using curvilinear convective coordinates on NURBS tensor product surface patches. We linearize the weak form of the generic linear momentum balance without a particular choice of a constitutive law. We then incorporate the constitutive equations that have been designed specifically for collagenous tissues. We explore three common anisotropic material models: Mooney-Rivlin, May Newmann-Yin, and Gasser-Ogden-Holzapfel. Our work will allow scientists in biomechanics and mechanobiology to adopt the constitutive equations that have been developed for solid three-dimensional soft tissues within the framework of isogeometric thin shell analysis.

Multi-view stereo analysis reveals anisotropy of prestrain, deformation, and growth in living skin

Skin expansion delivers newly grown skin that maintains histological and mechanical features of the original tissue. Although it is the gold standard for cutaneous defect correction today, the underlying mechanisms remain poorly understood. Here we present a novel technique to quantify anisotropic prestrain, deformation, and growth in a porcine skin expansion model. Building on our recently proposed method, we combine two novel technologies, multi-view stereo and isogeometric analysis, to characterize skin kinematics: Upon explantation, a unit square retracts ex vivo to a square of average dimensions of [Formula: see text]. Upon expansion, the unit square deforms in vivo into a rectangle of average dimensions of [Formula: see text]. Deformations are larger parallel than perpendicular to the dorsal midline suggesting that skin responds anisotropically with smaller deformations along the skin tension lines. Upon expansion, the patch grows in vivo by [Formula: see text] with respect to the explanted, unexpanded state. Growth is larger parallel than perpendicular to the midline, suggesting that elevated stretch activates mechanotransduction pathways to stimulate tissue growth. The proposed method provides a powerful tool to characterize the kinematics of living skin. Our results shed light on the mechanobiology of skin and help us to better understand and optimize clinically relevant procedures in plastic and reconstructive surgery.

Application of finite element modeling to optimize flap design with tissue expansion

BACKGROUND

Tissue expansion is a widely used technique to create skin flaps for the correction of sizable defects in reconstructive plastic surgery. Major complications following the inset of expanded flaps include breakdown and uncontrolled scarring secondary to excessive tissue tension. Although it is recognized that mechanical forces may significantly impact the success of defect repair with tissue expansion, a mechanical analysis of tissue stresses has not previously been attempted. Such analyses have the potential to optimize flap design preoperatively.

METHODS

The authors establish computer-aided design as a tool with which to explore stress profiles for two commonly used flap designs, the direct advancement flap and the double back-cut flap. The authors advanced both flaps parallel and perpendicular to the relaxed skin tension lines to quantify the impact of tissue anisotropy on stress distribution profiles.

RESULTS

Stress profiles were highly sensitive to flap design and orientation of relaxed skin tension lines, with stress minimized when flaps were advanced perpendicular to relaxed skin tension lines. Maximum stresses in advancement flaps occurred at the distal end of the flap, followed by the base. The double back-cut design increased stress at the lateral edges of the flap.

CONCLUSIONS

The authors conclude that finite element modeling may be used to effectively predict areas of increased flap tension. Performed preoperatively, such modeling can allow for the optimization of flap design and a potential reduction in complications such as flap dehiscence and hypertrophic scarring.

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.

Characterization of living skin using multi-view stereo and isogeometric analysis

Skin is our interface with the outside world. In its natural environment, it displays unique mechanical characteristics, such as prestretch and growth. While there is a general agreement on the physiological importance of these features, they remain poorly characterized, mainly because they are difficult to access with standard laboratory techniques. Here we present a new, inexpensive technique to characterize living skin using multi-view stereo and isogeometric analysis. Based on easy-to-create hand-held camera images, we quantify prestretch, deformation and growth in a controlled porcine model of chronic skin expansion. Over a period of 5 weeks, we gradually inflate an implanted tissue expander, take weekly photographs of the experimental scene, reconstruct the geometry from a tattooed surface grid and create parametric representations of the skin surface. After 5 weeks of expansion, our method reveals an average area prestretch of 1.44, an average area stretch of 1.87 and an average area growth of 2.25. Area prestretch is maximal in the ventral region with a value of 2.37, whereas area stretch and area growth are maximal above the center of the expander, with values of 4.05 and 4.81, respectively. Our study has immediate impact on understanding living skin to optimize treatment planning and decision making in plastic and reconstructive surgery. Beyond these direct implications, our experimental design has broad applications in clinical research and basic sciences: it serves as a simple, robust, low cost, easy-to-use tool to reconstruct living membranes, which are difficult to characterize in a conventional laboratory setup.

Computational modeling of skin: Using stress profiles as predictor for tissue necrosis in reconstructive surgery

Local skin flaps have revolutionized reconstructive surgery. Mechanical loading is critical for flap survival: Excessive tissue tension reduces blood supply and induces tissue necrosis. However, skin flaps have never been analyzed mechanically. Here we explore the stress profiles of two common flap designs, direct advancement flaps and double back-cut flaps. Our simulations predict a direct correlation between regions of maximum stress and tissue necrosis. This suggests that elevated stress could serve as predictor for flap failure. Our model is a promising step towards computer-guided reconstructive surgery with the goal to minimize stress, accelerate healing, minimize scarring, and optimize tissue use.

A mechanical model predicts morphological abnormalities in the developing human brain

The developing human brain remains one of the few unsolved mysteries of science. Advancements in developmental biology, neuroscience, and medical imaging have brought us closer than ever to understand brain development in health and disease. However, the precise role of mechanics throughout this process remains underestimated and poorly understood. Here we show that mechanical stretch plays a crucial role in brain development. Using the nonlinear field theories of mechanics supplemented by the theory of finite growth, we model the human brain as a living system with a morphogenetically growing outer surface and a stretch-driven growing inner core. This approach seamlessly integrates the two popular but competing hypotheses for cortical folding: axonal tension and differential growth. We calibrate our model using magnetic resonance images from very preterm neonates. Our model predicts that deviations in cortical growth and thickness induce morphological abnormalities. Using the gyrification index, the ratio between the total and exposed surface area, we demonstrate that these abnormalities agree with the classical pathologies of lissencephaly and polymicrogyria. Understanding the mechanisms of cortical folding in the developing human brain has direct implications in the diagnostics and treatment of neurological disorders, including epilepsy, schizophrenia, and autism.

Computational modeling of hypertensive growth in the human carotid artery

Arterial hypertension is a chronic medical condition associated with an elevated blood pressure. Chronic arterial hypertension initiates a series of events, which are known to collectively initiate arterial wall thickening. However, the correlation between macrostructural mechanical loading, microstructural cellular changes, and macrostructural adaptation remains unclear. Here, we present a microstructurally motivated computational model for chronic arterial hypertension through smooth muscle cell growth. To model growth, we adopt a classical concept based on the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. Motivated by clinical observations, we assume that the driving force for growth is the stretch sensed by the smooth muscle cells. We embed our model into a finite element framework, where growth is stored locally as an internal variable. First, to demonstrate the features of our model, we investigate the effects of hypertensive growth in a real human carotid artery. Our results agree nicely with experimental data reported in the literature both qualitatively and quantitatively.

Mechanically driven accumulation of microscale material at coupled solid-fluid interfaces in biological channels

The accumulation of microscale materials at solid-fluid interfaces in biological channels is often the initial stage of certain growth processes, which are present in some forms of atherosclerosis. The objective of this work is to develop a relatively simple model for such accumulation, which researchers can use to qualitatively guide their analyses. Specifically, the approach is to construct rate equations for the accumulation at the solid-fluid interface as a function of the intensity of the shear stress. The accumulation of material subsequently reduces the cross-sectional area of the channel until the fluid-induced shear stress at the solid-fluid interface reaches a critical value, which terminates the accumulation rate. Characteristics of the model are explored analytically and numerically.

On the mechanics of growing thin biological membranes

Despite their seemingly delicate appearance, thin biological membranes fulfill various crucial roles in the human body and can sustain substantial mechanical loads. Unlike engineering structures, biological membranes are able to grow and adapt to changes in their mechanical environment. Finite element modeling of biological growth holds the potential to better understand the interplay of membrane form and function and to reliably predict the effects of disease or medical intervention. However, standard continuum elements typically fail to represent thin biological membranes efficiently, accurately, and robustly. Moreover, continuum models are typically cumbersome to generate from surface-based medical imaging data. Here we propose a computational model for finite membrane growth using a classical midsurface representation compatible with standard shell elements. By assuming elastic incompressibility and membrane-only growth, the model a priori satisfies the zero-normal stress condition. To demonstrate its modular nature, we implement the membrane growth model into the general-purpose non-linear finite element package Abaqus/Standard using the concept of user subroutines. To probe efficiently and robustness, we simulate selected benchmark examples of growing biological membranes under different loading conditions. To demonstrate the clinical potential, we simulate the functional adaptation of a heart valve leaflet in ischemic cardiomyopathy. We believe that our novel approach will be widely applicable to simulate the adaptive chronic growth of thin biological structures including skin membranes, mucous membranes, fetal membranes, tympanic membranes, corneoscleral membranes, and heart valve membranes. Ultimately, our model can be used to identify diseased states, predict disease evolution, and guide the design of interventional or pharmaceutic therapies to arrest or revert disease progression.

On the Role of Mechanics in Chronic Lung Disease

Progressive airflow obstruction is a classical hallmark of chronic lung disease, affecting more than one fourth of the adult population. As the disease progresses, the inner layer of the airway wall grows, folds inwards, and narrows the lumen. The critical failure conditions for airway folding have been studied intensely for idealized circular cross-sections. However, the role of airway branching during this process is unknown. Here, we show that the geometry of the bronchial tree plays a crucial role in chronic airway obstruction and that critical failure conditions vary significantly along a branching airway segment. We perform systematic parametric studies for varying airway cross-sections using a computational model for mucosal thickening based on the theory of finite growth. Our simulations indicate that smaller airways are at a higher risk of narrowing than larger airways and that regions away from a branch narrow more drastically than regions close to a branch. These results agree with clinical observations and could help explain the underlying mechanisms of progressive airway obstruction. Understanding growth-induced instabilities in constrained geometries has immediate biomedical applications beyond asthma and chronic bronchitis in the diagnostics and treatment of chronic gastritis, obstructive sleep apnea and breast cancer.

Age-dependent biomechanical properties of the skin

The skin fulfills one of its most important functions, that is protection from mechanical injuries, due to the mechanism of reversible deformation of the structure. Human skin is a complex living material but in biomechanical tests it reveals its homogeneous nature. Biomechanical skin parameters change with time. Results of thickness measurements, where the skin was subjected to pressure, revealed that the Young's modulus increased linearly with age. The process of ageing is the reason why the skin becomes thinner, stiffer, less tense and less flexible. Skin tension measured during in vivo uniaxial load and the elasticity modulus are higher in children than in elderly adults. Furthermore, mean ultimate skin deformation before bursting is 75% for newborns and 60% for the elderly. Several types of the main lines were distinguished on the skin. The static lines, described by Langer, correspond to the lines of maximum tension, the Kraissl's lines correspond to the movements of the skin during muscle work, whereas the Borges lines are the relaxed skin tension lines. Biomechanical tests of the human skin help to quantify the effectiveness of dermatological products, detect skin diseases, schedule and plan surgical and dermatological interventions and treatments.

Growing matter: a review of growth in living systems

Living systems can grow, develop, adapt, and evolve. These phenomena are non-intuitive to traditional engineers and often difficult to understand. Yet, classical engineering tools can provide valuable insight into the mechanisms of growth in health and disease. Within the past decade, the concept of incompatible configurations has evolved as a powerful tool to model growing systems within the framework of nonlinear continuum mechanics. However, there is still a substantial disconnect between the individual disciplines, which explore the phenomenon of growth from different angles. Here we show that the nonlinear field theories of mechanics provide a unified concept to model finite growth by means of a single tensorial internal variable, the second order growth tensor. We review the literature and categorize existing growth models by means of two criteria: the microstructural appearance of growth, either isotropic or anisotropic; and the microenvironmental cues that drive the growth process, either chemical or mechanical. We demonstrate that this generic concept is applicable to a broad range of phenomena such as growing arteries, growing tumors, growing skin, growing airway walls, growing heart valve leaflets, growing skeletal muscle, growing plant stems, growing heart valve annuli, and growing cardiac muscle. The proposed approach has important biological and clinical applications in atherosclerosis, in-stent restenosis, tumor invasion, tissue expansion, chronic bronchitis, mitral regurgitation, limb lengthening, tendon tear, plant physiology, dilated and hypertrophic cardiomyopathy, and heart failure. Understanding the mechanisms of growth in these chronic conditions may open new avenues in medical device design and personalized medicine to surgically or pharmacologically manipulate development and alter, control, or revert disease progression.

A novel strategy to identify the critical conditions for growth-induced instabilities

Geometric instabilities in living structures can be critical for healthy biological function, and abnormal buckling, folding, or wrinkling patterns are often important indicators of disease. Mathematical models typically attribute these instabilities to differential growth, and characterize them using the concept of fictitious configurations. This kinematic approach toward growth-induced instabilities is based on the multiplicative decomposition of the total deformation gradient into a reversible elastic part and an irreversible growth part. While this generic concept is generally accepted and well established today, the critical conditions for the formation of growth-induced instabilities remain elusive and poorly understood. Here we propose a novel strategy for the stability analysis of growing structures motivated by the idea of replacing growth by prestress. Conceptually speaking, we kinematically map the stress-free grown configuration onto a prestressed initial configuration. This allows us to adopt a classical infinitesimal stability analysis to identify critical material parameter ranges beyond which growth-induced instabilities may occur. We illustrate the proposed concept by a series of numerical examples using the finite element method. Understanding the critical conditions for growth-induced instabilities may have immediate applications in plastic and reconstructive surgery, asthma, obstructive sleep apnoea, and brain development.

On the mechanics of thin films and growing surfaces

Many living structures are coated by thin films, which have distinct mechanical properties from the bulk. In particular, these thin layers may grow faster or slower than the inner core. Differential growth creates a balanced interplay between tension and compression and plays a critical role in enhancing structural rigidity. Typical examples with a compressive outer surface and a tensile inner core are the petioles of celery, caladium, or rhubarb. While plant physiologists have studied the impact of tissue tension on plant rigidity for more than a century, the fundamental theory of growing surfaces remains poorly understood. Here, we establish a theoretical and computational framework for continua with growing surfaces and demonstrate its application to classical phenomena in plant growth. To allow the surface to grow independently of the bulk, we equip it with its own potential energy and its own surface stress. We derive the governing equations for growing surfaces of zero thickness and obtain their spatial discretization using the finite-element method. To illustrate the features of our new surface growth model we simulate the effects of growth-induced longitudinal tissue tension in a stalk of rhubarb. Our results demonstrate that different growth rates create a mechanical environment of axial tissue tension and residual stress, which can be released by peeling off the outer layer. Our novel framework for continua with growing surfaces has immediate biomedical applications beyond these classical model problems in botany: it can be easily extended to model and predict surface growth in asthma, gastritis, obstructive sleep apnoea, brain development, and tumor invasion. Beyond biology and medicine, surface growth models are valuable tools for material scientists when designing functionalized surfaces with distinct user-defined properties.

Computational and experimental characterization of skin mechanics: identifying current challenges and future directions

The characterization of skin mechanics has many clinical implications and has been an active area of research for the past few decades. Biomechanical models have evolved from earlier empirical models to state-of-the-art structural models that provide linkage between tissue microstructure and macroscopic stress-strain response. To maximize the accuracy and predictive capabilities of such computational models, there is a need to reliably identify often a large number of unknown model parameters. This is critically dependent on the availability of experimental data that cover an extensive range of different deformation modes, and quantification of internal structural features, such as collagen orientation. To this end, future challenges should include the ongoing development of noninvasive instrumentation and imaging modalities for in vivo skin measurements. We highlight the important concept of tightly integrating computational models, instrumentation, and imaging modalities into a single platform to investigate skin biomechanics.

On the mechanics of continua with boundary energies and growing surfaces

Many biological systems are coated by thin films for protection, selective absorption, or transmembrane transport. A typical example is the mucous membrane covering the airways, the esophagus, and the intestine. Biological surfaces typically display a distinct mechanical behavior from the bulk; in particular, they may grow at different rates. Growth, morphological instabilities, and buckling of biological surfaces have been studied intensely by approximating the surface as a layer of finite thickness; however, growth has never been attributed to the surface itself. Here, we establish a theory of continua with boundary energies and growing surfaces of zero thickness in which the surface is equipped with its own potential energy and is allowed to grow independently of the bulk. In complete analogy to the kinematic equations, the balance equations, and the constitutive equations of a growing solid body, we derive the governing equations for a growing surface. We illustrate their spatial discretization using the finite element method, and discuss their consistent algorithmic linearization. To demonstrate the conceptual differences between volume and surface growth, we simulate the constrained growth of the inner layer of a cylindrical tube. Our novel approach towards continua with growing surfaces is capable of predicting extreme growth of the inner cylindrical surface, which more than doubles its initial area. The underlying algorithmic framework is robust and stable; it allows to predict morphological changes due to surface growth during the onset of buckling and beyond. The modeling of surface growth has immediate biomedical applications in the diagnosis and treatment of asthma, gastritis, obstructive sleep apnoea, and tumor invasion. Beyond biomedical applications, the scientific understanding of growth-induced morphological instabilities and surface wrinkling has important implications in material sciences, manufacturing, and microfabrication, with applications in soft lithography, metrology, and flexible electronics.