Mechanical cell-matrix feedback explains pairwise and collective endothelial cell behavior in vitro.

In vitro cultures of endothelial cells are a widely used model system of the collective behavior of endothelial cells during vasculogenesis and angiogenesis. When seeded in an extracellular matrix, endothelial cells can form blood vessel-like structures, including vascular networks and sprouts. Endothelial morphogenesis depends on a large number of chemical and mechanical factors, including the compliancy of the extracellular matrix, the available growth factors, the adhesion of cells to the extracellular matrix, cell-cell signaling, etc. Although various computational models have been proposed to explain the role of each of these biochemical and biomechanical effects, the understanding of the mechanisms underlying in vitro angiogenesis is still incomplete. Most explanations focus on predicting the whole vascular network or sprout from the underlying cell behavior, and do not check if the same model also correctly captures the intermediate scale: the pairwise cell-cell interactions or single cell responses to ECM mechanics. Here we show, using a hybrid cellular Potts and finite element computational model, that a single set of biologically plausible rules describing (a) the contractile forces that endothelial cells exert on the ECM, (b) the resulting strains in the extracellular matrix, and (c) the cellular response to the strains, suffices for reproducing the behavior of individual endothelial cells and the interactions of endothelial cell pairs in compliant matrices. With the same set of rules, the model also reproduces network formation from scattered cells, and sprouting from endothelial spheroids. Combining the present mechanical model with aspects of previously proposed mechanical and chemical models may lead to a more complete understanding of in vitro angiogenesis.

Osteocyte shape and mechanical loading.

There is considerable variation in the shape of osteocyte lacunae, which is likely to influence the function of osteocytes as the professional mechanosensors of bone. In this review, we first discussed how mechanical loading could affect the shape of osteocyte lacunae. Recent studies show that osteocyte lacunae are aligned to collagen. Since collagen fiber orientation is affected by loading mode, this alignment may help to understand how mechanical loading shapes the osteocyte lacuna. Secondly, we discussed how the shape of osteocytes could influence their mechanosensation. In vitro, round osteocytes are more mechanosensitive than flat osteocytes. Altered lacunar morphology has been associated with bone pathology. It is important to know whether osteocyte shape is part of the etiology.

Abutment-to-fixture load transfer and peri-implant bone stress.

PURPOSE: To uncover design principles for the abutment-fixture complex that reduce the stress concentration on the bone. METHODS: A 3-dimensional finite element model was used to vary shape, elasticity, and connectivity of the abutment-fixture complex. We compared peri-implant bone stress of these designs. RESULTS: Peri-implant bone stress was increased when the abutment could slide frictionless along the rim of the fixture, allowing the abutment to "lean into" the fixture rim and transfer loads near the bone crest. Conversely, bone stress was reduced when no motion was allowed (or no contact was made at all) between the abutment and the fixture rim. Bone stress was also reduced when the fixture was stiffer and thus more resistant to deformation, or when the fixture was wider.

A unified theory for osteonal and hemi-osteonal remodeling.

The process of bone remodeling is carried out by 'basic multicellular units' of osteoclasts and osteoblasts. Osteoclasts excavate a resorption space that is subsequently filled with new bone by osteoblasts. In cortical bone osteoclasts dig tunnels through solid bone, in cancellous bone they dig trenches across the trabecular surface. Osteoblasts fill these tunnels and trenches, creating osteons and hemi-osteons, respectively. Both the osteons of cortical bone and the trabeculae of cancellous bone are aligned to the dominant loading direction, indicating that BMU's are mechanically regulated. How mechanical forces guide these cells is still uncertain. We hypothesize that strain-induced osteocyte signals inhibit osteoclast activity and stimulate osteoblast activity. This hypothesis was implemented in a finite element-based bone adaptation model, that was extended with a cell simulation model. This allowed us to examine tunneling and trenching by osteoclasts. We found that our simulations capture key features of BMU-based remodeling: (1) cortical BMU's create load-aligned osteons; (2) cancellous BMU's move across the surface of trabeculae instead of piercing them; (3) resorption-formation coupling occurs in response to strains around resorption sites; and (4) resorbing osteoclasts target nearby regions of osteocyte death, thus providing a mechanism for bone repair.

Relating osteon diameter to strain.

Osteon diameter is generally smaller in bone regions that experience larger strains. A mechanism relating osteon diameter to strain is as yet unknown. We propose that strain-induced osteocyte signals inhibit osteoclastic bone resorption. This mechanism was previously shown to produce load-aligned osteons in computer simulations. Now we find that it also predicts smaller osteon diameter for higher loads. Additionally, we find that our model predicts osteon development with two cutting cones, one moving up and one moving down the loading axis. Such 'double-ended osteons' were reported in literature as a common type of osteon development. Further, we find that a steep gradient in strain magnitude can result in an osteonal tunnel with continuous resorption along the less strained side, which corresponds to 'drifting osteons' reported in literature.

Osteocyte morphology and orientation in relation to strain in the jaw bone.

Bone mass is important for dental implant success and is regulated by mechanoresponsive osteocytes. We aimed to investigate the relationship between the levels and orientation of tensile strain and morphology and orientation of osteocytes at different dental implant positions in the maxillary bone. Bone biopsies were retrieved from eight patients who underwent maxillary sinus-floor elevation with ß-tricalcium phosphate prior to implant placement. Gap versus free-ending locations were compared using 1) a three-dimensional finite-element model of the maxilla to predict the tensile strain magnitude and direction and 2) histology and histomorphometric analyses. The finite-element model predicted larger, differently directed tensile strains in the gap versus free-ending locations. The mean percentage of mineralised residual native-tissue volume, osteocyte number (mean ± standard deviations: 97 ± 40/region-of-interest), and osteocyte shape (~90% elongated, ~10% round) were similar for both locations. However, the osteocyte surface area was 1.5-times larger in the gap than in the free-ending locations, and the elongated osteocytes in these locations were more cranially caudally oriented. In conclusion, significant differences in the osteocyte surface area and orientation seem to exist locally in the maxillary bone, which may be related to the tensile strain magnitude and orientation. This might reflect local differences in the osteocyte mechanosensitivity and bone quality, suggesting differences in dental implant success based on the location in the maxilla.

Virtual patient 3D dose reconstruction using in air EPID measurements and a back-projection algorithm for IMRT and VMAT treatments.

PURPOSE: At our institute, a transit back-projection algorithm is used clinically to reconstruct in vivo patient and in phantom 3D dose distributions using EPID measurements behind a patient or a polystyrene slab phantom, respectively. In this study, an extension to this algorithm is presented whereby in air EPID measurements are used in combination with CT data to reconstruct 'virtual' 3D dose distributions. By combining virtual and in vivo patient verification data for the same treatment, patient-related errors can be separated from machine, planning and model errors. METHODS AND MATERIALS: The virtual back-projection algorithm is described and verified against the transit algorithm with measurements made behind a slab phantom, against dose measurements made with an ionization chamber and with the OCTAVIUS 4D system, as well as against TPS patient data. Virtual and in vivo patient dose verification results are also compared. RESULTS: Virtual dose reconstructions agree within 1% with ionization chamber measurements. The average γ-pass rate values (3% global dose/3mm) in the 3D dose comparison with the OCTAVIUS 4D system and the TPS patient data are 98.5±1.9%(1SD) and 97.1±2.9%(1SD), respectively. For virtual patient dose reconstructions, the differences with the TPS in median dose to the PTV remain within 4%. CONCLUSIONS: Virtual patient dose reconstruction makes pre-treatment verification based on deviations of DVH parameters feasible and eliminates the need for phantom positioning and re-planning. Virtual patient dose reconstructions have additional value in the inspection of in vivo deviations, particularly in situations where CBCT data is not available (or not conclusive).

Comparison of gamma- and DVH-based in vivo dosimetric plan evaluation for pelvic VMAT treatments.

BACKGROUND AND PURPOSE: To compare DVH-based quality assurance to a multi-parametric γ-based methodology for in vivo EPID dosimetry for VMAT to the pelvis. MATERIALS AND METHODS: For 47 rectum, 37 prostate, and 44 bladder VMAT treatments we reconstructed the 3D dose distributions of 387 fractions from in vivo EPID dosimetry. The difference between planned and measured dose was evaluated using γ analysis (3%/3mm) in the 50% isodose volume (IDV) and DVH differences (ΔD2, ΔD50 and ΔD98) of targets and organs at risk. The γ-indicators mean γ, γ pass rate and γ1% were compared to DVH-differences and their correlations were studied. DVH-based alerts on PTV and IDV were compared to γ-based alerts. RESULTS: Average PTV D50 and D98 dose differences were 0.0±2.2% (1SD) and -1.4±2.9% (1SD). Alert criteria of |ΔD50|<3.5-4.5% corresponded to an alert rate of about 10%. Strong correlations between mean γ and γ pass rate and difference in PTV ΔD50 were observed for all sites. DVH- and γ-based alerts agreed on >80% of the fractions for the majority of compared alert thresholds and methods. This agreement is >90% for the larger deviations. CONCLUSIONS: Strong correlations between some γ- and DVH indicators were found. Our comparison of multi-parametric alert strategies showed clinical equivalence for γ- and DVH-based methods.

Bone cell mechanosensitivity, estrogen deficiency, and osteoporosis.

Adaptation of bone to mechanical stresses normally produces a bone architecture that combines a proper resistance against failure with a minimal use of material. This adaptive process is governed by mechanosensitive osteocytes that transduce the mechanical signals into chemical responses, i.e. the osteocytes release signaling molecules, which orchestrate the recruitment and activity of bone forming osteoblasts and/or bone resorbing osteoclasts. Computer models have shown that the maintenance of a mechanically-efficient bone architecture depends on the intensity and spatial distribution of the mechanical stimulus as well as on the osteocyte response. Osteoporosis is a condition characterized by a reduced bone mass and a compromized resistance of bone against mechanical loads, which has led us to hypothesize that mechanotransduction by osteocytes is altered in osteoporosis. One of the major causal factors for osteoporosis is the loss of estrogen, the major hormonal regulator of bone metabolism. Loss of estrogen may increase osteocyte-mediated activation of bone remodeling, resulting in impaired bone mass and architecture. In this review we highlight current insights on how osteocytes perceive mechanical stimuli placed on whole bones. Particular emphasis is placed on the role of estrogen in signaling pathway activation by mechanical stimuli, and on computer simulation in combination with cell biology to unravel biological processes contributing to bone strength.

Osteocyte-viability-based simulations of trabecular bone loss and recovery in disuse and reloading.

Osteocyte apoptosis is known to trigger targeted bone resorption. In the present study, we developed an osteocyte-viability-based trabecular bone remodeling (OVBR) model. This novel remodeling model, combined with recent advanced simulation methods and analysis techniques, such as the element-by-element 3D finite element method and the ITS technique, was used to quantitatively study the dynamic evolution of bone mass and trabecular microstructure in response to various loading and unloading conditions. Different levels of unloading simulated the disuse condition of bed rest or microgravity in space. The amount of bone loss and microstructural deterioration correlated with the magnitude of unloading. The restoration of bone mass upon the reloading condition was achieved by thickening the remaining trabecular architecture, while the lost trabecular plates and rods could not be recovered by reloading. Compared to previous models, the predictions of bone resorption of the OVBR model are more consistent with physiological values reported from previous experiments. Whereas osteocytes suffer a lack of loading during disuse, they may suffer overloading during the reloading phase, which hampers recovery. The OVBR model is promising for quantitative studies of trabecular bone loss and microstructural deterioration of patients or astronauts during long-term bed rest or space flight and thereafter bone recovery.

A sclerostin-based theory for strain-induced bone formation.

Bone formation responds to mechanical loading, which is believed to be mediated by osteocytes. Previous theories assumed that loading stimulates osteocytes to secrete signals that stimulate bone formation. In computer simulations this 'stimulatory' theory successfully produced load-aligned trabecular structures. In recent years, however, it was discovered that osteocytes inhibit bone formation via the protein sclerostin. To reconcile this with strain-induced bone formation, one must assume that sclerostin secretion decreases with mechanical loading. This leads to a new 'inhibitory' theory in which loading inhibits osteocytes from inhibiting bone formation. Here we used computer simulations to show that a sclerostin-based model is able to produce a load-aligned trabecular architecture. An important difference appeared when we compared the response of the stimulatory and inhibitory models to loss of osteocytes, and found that the inhibitory pathway prevents the loss of trabeculae that is seen with the stimulatory model. Further, we demonstrated with combined stimulatory/inhibitory models that the two pathways can work side-by-side to achieve a load-adapted bone architecture.

Simulations of trabecular remodeling and fatigue: is remodeling helpful or harmful?

Microdamage-targeted resorption is paradoxal, because it entails the removal of bone from a region that was already overloaded. Under continued intense loading, resorption spaces could potentially cause more damage than they remove. To investigate this problem, we incorporated damage algorithms in a computer-simulation model for trabecular remodeling. We simulated damage accumulation and bone remodeling in a trabecular architecture, for two fatigue regimens, a 'moderate' regimen, and an 'intense' regimen with a higher number of loading cycles per day. Both simulations were also performed without bone remodeling to investigate if remodeling removed or exacerbated the damage. We found that remodeling tends to remove damage under the 'moderate' fatigue regimen, but it exacerbates damage under the 'intense' regimen. This harmful effect of remodeling may play a role in the development of stress fractures.