A modelling approach for exploring muscle dynamics during cyclic contractions.
ABSTRACT: Hill-type muscle models are widely used within the field of biomechanics to predict and understand muscle behaviour, and are often essential where muscle forces cannot be directly measured. However, these models have limited accuracy, particularly during cyclic contractions at the submaximal levels of activation that typically occur during locomotion. To address this issue, recent studies have incorporated effects into Hill-type models that are oftentimes neglected, such as size-dependent, history-dependent, and activation-dependent effects. However, the contribution of these effects on muscle performance has yet to be evaluated under common contractile conditions that reflect the range of activations, strains, and strain rates that occur in vivo. The purpose of this study was to develop a modelling framework to evaluate modifications to Hill-type muscle models when they contract in cyclic loops that are typical of locomotor muscle function. Here we present a modelling framework composed of a damped harmonic oscillator in series with a Hill-type muscle actuator that consists of a contractile element and parallel elastic element. The intrinsic force-length and force-velocity properties are described using Bézier curves where we present a system to relate physiological parameters to the control points for these curves. The muscle-oscillator system can be geometrically scaled while preserving dynamic and kinematic similarity to investigate the muscle size effects while controlling for the dynamics of the harmonic oscillator. The model is driven by time-varying muscle activations that cause the muscle to cyclically contract and drive the dynamics of the harmonic oscillator. Thus, this framework provides a platform to test current and future Hill-type model formulations and explore factors affecting muscle performance in muscles of different sizes under a range of cyclic contractile conditions.
Project description:In order to perform external work, muscles must do additional internal work to deform their tissue, and in particular, to overcome the inertia due to their internal mass. However, the contribution of the internal mass within a muscle to the mechanical output of that muscle has only rarely been studied. Here, we use a dynamic, multi-element Hill-type muscle model to examine the effects of the inertial mass within muscle on its contractile performance. We find that the maximum strain-rate of muscle is slower for lower activations and larger muscle sizes. As muscle size increases, the ability of the muscle to overcome its inertial load will decrease, as muscle tension is proportional to cross-sectional area and inertial load is proportional to mass. Thus, muscles that are larger in size will have a higher inertial cost to contraction. Similarly, when muscle size and inertial load are held constant, decreasing muscle activation will increase inertial cost to contraction by reducing muscle tension. These results show that inertial loads within muscle contribute to a slowing of muscle contractile velocities (strain-rates), particularly at the submaximal activations that are typical during animal locomotion.
Project description:Hill-type models are commonly used to estimate muscle forces during human and animal movement-yet the accuracy of the forces estimated during walking, running, and other tasks remains largely unknown. Further, most Hill-type models assume a single contractile element, despite evidence that faster and slower motor units, which have different activation-deactivation dynamics, may be independently or collectively excited. This study evaluated a novel, two-element Hill-type model with "differential" activation of fast and slow contractile elements. Model performance was assessed using a comprehensive data set (including measures of EMG intensity, fascicle length, and tendon force) collected from the gastrocnemius muscles of goats during locomotor experiments. Muscle forces predicted by the new two-element model were compared to the forces estimated using traditional one-element models and to the forces measured in vivo using tendon buckle transducers. Overall, the two-element model resulted in the best predictions of in vivo gastrocnemius force. The coefficient of determination, r(2), was up to 26.9% higher and the root mean square error, RMSE, was up to 37.4% lower for the two-element model than for the one-element models tested. All models captured salient features of the measured muscle force during walking, trotting, and galloping (r(2)=0.26-0.51), and all exhibited some errors (RMSE=9.63-32.2% of the maximum in vivo force). These comparisons provide important insight into the accuracy of Hill-type models. The results also show that incorporation of fast and slow contractile elements within muscle models can improve estimates of time-varying, whole muscle force during locomotor tasks.
Project description:Skeletal muscle-derived stem cells (MDSCs) are able to differentiate into cardiomyocytes (CMs). However, it remains to be investigated whether differentiated CMs contract similar to native CMs. Here, we developed a three-dimensional collagen gel bioreactor (3DGB) that induces a working CM phenotype from MDSCs, and the contractile properties are directly measured as an engineered cardiac tissue. Neonate rat MDSCs were isolated from hind-leg muscles via the preplate technique. Isolated MDSCs were approximately 60% positive to Sca-1 and negative to CD34, CD45, or c-kit antigens. We sorted Sca-1(-) MDSCs and constructed MDSC-3DGBs by mixing MDSCs with acid soluble rat tail collagen type-I and matrix factors. MDSC-3DGB exhibited spontaneous cyclic contraction by culture day 7. MDSC-3DGB expressed cardiac-specific genes and proteins. Histological assessment revealed that cardiac-specific troponin-T and -I expressed in a typical striation pattern and connexin-43 was expressed similar to the native fetal ventricular papillary muscle. beta-Adrenergic stimulation increased MDSC-3DGB spontaneous beat frequency. MDSC-3DGB generated contractile force and intracellular calcium ion transients similar to engineered cardiac tissue from native cardiac cells. Results suggest that MDSC-3DGB induces a working CM phenotype in MDSCs and is a useful 3D culture system to directly assess the contractile properties of differentiated CMs in vitro.
Project description:We perform third harmonic spectroscopy of dolmen-type nanostructures, which exhibit plasmonic Fano resonances in the near-infrared. Strong third harmonic emission is predominantly radiated close to the low energy peak of the Fano resonance. Furthermore, we find that the third harmonic polarization of the subradiant mode interferes destructively and diminishes the nonlinear signal in the far-field. By comparing the experimental third harmonic spectra with finite element simulations and an anharmonic oscillator model, we find strong indications that the source of the third harmonic is the optical nonlinearity of the bare gold enhanced by the resonant plasmonic polarization.
Project description:Activation of airway smooth muscle (ASM) cells plays a central role in the pathophysiology of asthma. Because ASM is an important therapeutic target in asthma, it is beneficial to develop bioengineered ASM models available for assessing physiological and biophysical properties of ASM cells. In the physiological condition in vivo, ASM cells are surrounded by extracellular matrix (ECM) and exposed to mechanical stresses such as cyclic stretch. We utilized a 3-D culture model of human ASM cells embedded in type-I collagen gel. We further examined the effects of cyclic mechanical stretch, which mimics tidal breathing, on cell orientation and expression of contractile proteins of ASM cells within the 3-D gel. ASM cells in type-I collagen exhibited a tissue-like structure with actin stress fiber formation and intracellular Ca2+ mobilization in response to methacholine. Uniaxial cyclic stretching enhanced alignment of nuclei and actin stress fibers of ASM cells. Moreover, expression of mRNAs for contractile proteins such as ?-smooth muscle actin, calponin, myosin heavy chain 11, and transgelin of stretched ASM cells was significantly higher than that under the static condition. Our findings suggest that mechanical force and interaction with ECM affects development of the ASM tissue-like construct and differentiation to the contractile phenotype in a 3-D culture model.
Project description:Existing in vitro models of human skeletal muscle cannot recapitulate the organization and function of native muscle, limiting their use in physiological and pharmacological studies. Here, we demonstrate engineering of electrically and chemically responsive, contractile human muscle tissues ('myobundles') using primary myogenic cells. These biomimetic constructs exhibit aligned architecture, multinucleated and striated myofibers, and a Pax7(+) cell pool. They contract spontaneously and respond to electrical stimuli with twitch and tetanic contractions. Positive correlation between contractile force and GCaMP6-reported calcium responses enables non-invasive tracking of myobundle function and drug response. During culture, myobundles maintain functional acetylcholine receptors and structurally and functionally mature, evidenced by increased myofiber diameter and improved calcium handling and contractile strength. In response to diversely acting drugs, myobundles undergo dose-dependent hypertrophy or toxic myopathy similar to clinical outcomes. Human myobundles provide an enabling platform for predictive drug and toxicology screening and development of novel therapeutics for muscle-related disorders.
Project description:The accurate prediction of vibrational wavenumbers for functional groups involved in hydrogen-bonded bridges remains an important challenge for computational spectroscopy. For the specific case of the C=O and N-H stretching modes of nucleobases and their oligomers, the paucity of experimental reference values needs to be compensated by reliable computational data, which require the use of approaches going beyond the standard harmonic oscillator model. Test computations performed for model systems (formamide, acetamide and their cyclic homodimers) in the framework of the second order vibrational perturbation theory (VPT2) confirmed that anharmonic corrections can be safely computed by global hybrid (GHF) or double hybrid (DHF) functionals, whereas the harmonic part is particularly challenging. As a matter of fact, GHFs perform quite poorly and even DHFs, while fully satisfactory for C=O stretchings, face unexpected difficulties when dealing with N-H stretchings. On these grounds, a linear regression for N-H stretchings has been obtained and validated for the heterodimers formed by 4-aminopyrimidine with 6-methyl-4-pyrimidinone (4APM-M4PMN) and by uracil with water. In view of the good performance of this computational model, we have built a training set of B2PLYP-D3/maug-cc-pVTZ harmonic wavenumbers (including linear regression scaling for N-H) for six-different uracil dimers and a validation set including 4APM-M4PMN, one of the most stable hydrogen-bonded adenine homodimers, as well as the adenine-uracil, adenine-thymine, guanine-cytosine and adenine-4-thiouracil heterodimers. Because of the unfavourable scaling of DHF harmonic wavenumbers with the dimensions of the investigated systems, we have optimized a linear regression of B3LYP-D3/N07D harmonic wavenumbers for the training set, which has been next checked against the validation set. This relatively cheap model, which shows very good agreement with experimental data (average errors of about 10 cm(-1)), paves the route toward a reliable analysis of spectroscopic signatures for larger polynucleotides.
Project description:Traditional Hill-type muscle models, parameterized using high-quality experimental data, are often "too weak" to reproduce the joint torques generated by healthy adults during rapid, high force tasks. This study investigated whether the failure of these models to account for different types of motor units contributes to this apparent weakness; if so, muscle-driven simulations may rely on excessively high muscle excitations to generate a given force. We ran a series of forward simulations that reproduced measured ankle mechanics during cycling at five cadences ranging from 60 to 140 RPM. We generated both "nominal" simulations, in which an abstract ankle model was actuated by a 1-element Hill-type plantar flexor with a single contractile element (CE), and "test" simulations, in which the same model was actuated by a 2-element plantar flexor with two CEs that accounted for the force-generating properties of slower and faster motor units. We varied the total excitation applied to the 2-element plantar flexor between 60 and 105% of the excitation from each nominal simulation, and we varied the amount distributed to each CE between 0 and 100% of the total. Within this test space, we identified the excitation level and distribution, at each cadence, that best reproduced the plantar flexor forces generated in the nominal simulations. Our comparisons revealed that the 2-element model required substantially less total excitation than the 1-element model to generate comparable forces, especially at higher cadences. For instance, at 140 RPM, the required excitation was reduced by 23%. These results suggest that a 2-element model, in which contractile properties are "tuned" to represent slower and faster motor units, can increase the apparent strength and perhaps improve the fidelity of simulations of tasks with varying mechanical demands.
Project description:Whether glucocorticoids (GC) can directly affect human testicular functions is not well understood. A predominant site of GC receptor (GR; NR3C1) expression in the adult testis are peritubular smooth muscle-like cells, which express smooth muscle actin (ACTA2), contract and thereby are involved in sperm transport. In contrast to the adult, neither GR nor ACTA2, or elastin (ELN) were detected in the peritubular compartment before puberty in non-human primate testes. In isolated human testicular peritubular cells (HTPCs), activation of GR by dexamethasone (Dex) caused the translocation of GR to the nucleus and stimulated expression of ACTA2 and ELN, without affecting the expression of collagens. Cytoskeletal ACTA2-rearrangements were observed and were associated with an increased ability to contract. Our results indicate post-pubertal testicular roles of GC in the maintenance of the contractile, smooth muscle-like phenotype of peritubular cells.
Project description:This a model from the article:
Nonlinearities make a difference: comparison of two common Hill-type models with
Siebert T, Rode C, Herzog W, Till O, Blickhan R. Biol Cybern
2008 Feb;98(2):133-43 18049823
Compared to complex structural Huxley-type models, Hill-type models
phenomenologically describe muscle contraction using only few state variables.
The Hill-type models dominate in the ever expanding field of musculoskeletal
simulations for simplicity and low computational cost. Reasonable parameters are
required to gain insight into mechanics of movement. The two most common
Hill-type muscle models used contain three components. The series elastic
component is connected in series to the contractile component. A parallel
elastic component is either connected in parallel to both the contractile and
the series elastic component (model [CC+SEC]), or is connected in parallel only
with the contractile component (model [CC]). As soon as at least one of the
components exhibits substantial nonlinearities, as, e.g., the contractile
component by the ability to turn on and off, the two models are mechanically
different. We tested which model ([CC+SEC] or [CC]) represents the cat soleus
better. Ramp experiments consisting of an isometric and an isokinetic part were
performed with an in situ cat soleus preparation using supramaximal nerve
stimulation. Hill-type models containing force-length and force-velocity
relationship, excitation-contraction coupling and series and parallel elastic
force-elongation relations were fitted to the data. To test which model might
represent the muscle better, the obtained parameters were compared with
experimentally determined parameters. Determined in situations with negligible
passive force, the force-velocity relation and the series elastic component
relation are independent of the chosen model. In contrast to model [CC+SEC],
these relations predicted by model [CC] were in accordance with experimental
relations. In conclusion model [CC] seemed to better represent the cat soleus
contraction dynamics and should be preferred in the nonlinear regression of
muscle parameters and in musculoskeletal modeling.
This model was taken from the CellML repository
and automatically converted to SBML.
The original model was:
Siebert T, Rode C, Herzog W, Till O, Blickhan R. (2008) - version=1.0
The original CellML model was created by:
The University of Auckland
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