Finite Elasticity of the Vertex Model and its Role in Rigidity of Curved Cellular Tissues

Using a mean field approach and simulation, we study the non-linear mechanical response of the vertex model (VM) of biological tissue under compression and dilation. The VM is known to exhibit a transition between rigid and fluid-like, or floppy, states driven by geometric incompatibility. Target perimeter and area set a target shape which may not be geometrically achievable, thereby engendering frustration. Previously, an asymmetry in the linear elastic response was identified at the rigidity transition between compression and dilation. Here we show and characterize how the asymmetry extends away from the transition point for finite strains. Under finite compression, an initially solid VM can totally relax perimeter tension, and thereby have reduced bulk and shear modulus. Conversely, an initially floppy VM under dilation can rigidify and have a higher bulk and shear modulus. These observations imply that re-scaling of cell area shifts the transition between rigid and floppy states. Based on this insight, we calculate the re-scaling of cell area engendered by intrinsic curvature and write a prediction for the rigidity transition in the presence of curvature. The shift of the rigidity transition in the presence of curvature for the VM provides a new metric for predicting tissue rigidity from image data for curved tissues in a manner analogous to the flat case.Comment: 10 pages, 3 figure

Anomalous elasticity of cellular tissue vertex model

Vertex Models, as used to describe cellular tissue, have an energy controlled by deviations of each cell area and perimeter from target values. The constrained nonlinear relation between area and perimeter leads to new mechanical response. Here we provide a mean-field treatment of a highly simplified model: a uniform network of regular polygons with no topological rearrangements. Since all polygons deform in the same way, we only need to analyze the ground states and the response to deformations of a single polygon (cell). The model exhibits the known transition between a fluid/compatible state, where the cell can accommodate both target area and perimeter, and a rigid/incompatible state. %The rigid solid-like state has a single gapped ground state. We calculate and measure the mechanical resistance to various deformation protocols and discover that at the onset of rigidity, where a single zero-energy ground-state exists, %We show that in the incompatible state, where a single frustrated ground-state exists, linear elasticity fails to describe the mechanical response to even infinitesimal deformations. In particular we identify a breakdown of reciprocity expressed via different moduli for compressive and tensile loads, implying non-analyticity of the energy functional. We give a pictorial representation in configuration space that reveals that the complex elastic response of the Vertex Model arises from the presence of two distinct sets of reference states (associated with target area and target perimeter)

The role of non-affine deformations in the elastic behavior of the cellular vertex model

The vertex model of epithelia describes the apical surface of a tissue as a tiling of polygonal cells, with a mechanical energy governed by deviations in cell shape from preferred, or target, area, $A_0$, and perimeter, $P_0$. The model exhibits a rigidity transition driven by geometric incompatibility as tuned by the target shape index, $p_0 = P_0 / \sqrt{A_0}$. For $p_0 > p_*(6) = \sqrt{8 \sqrt{3}} \approx 3.72$, with $p_*(6)$ the perimeter of a regular hexagon of unit area, a cell can simultaneously attain both the preferred area and preferred perimeter. As a result, the tissue is in a mechanically soft compatible state, with zero shear and Young's moduli. For $p_0 < p_*(6)$, it is geometrically impossible for any cell to realize the preferred area and perimeter simultaneously, and the tissue is in an incompatible rigid solid state. Using a mean-field approach, we present a complete analytical calculation of the linear elastic moduli of an ordered vertex model. We analyze a relaxation step that includes non-affine deformations, leading to a softer response than previously reported. The origin of the vanishing shear and Young's moduli in the compatible state is the presence of zero-energy deformations of cell shape. The bulk modulus exhibits a jump discontinuity at the transition and can be lower in the rigid state than in the fluid-like state. The Poisson's ratio can become negative which lowers the bulk and Young's moduli. Our work provides a unified treatment of linear elasticity for the vertex model and demonstrates that this linear response is protocol-dependent

Quality of Life and Utility in Patients with Metastatic Soft Tissue and Bone Sarcoma: The Sarcoma Treatment and Burden of Illness in North America and Europe (SABINE) Study

The aim of the study was to assess health-related quality of life (HRQoL) among metastatic soft tissue (mSTS) or bone sarcoma (mBS) patients who had attained a favourable response to chemotherapy. We employed the EORTC QLQ-C30, the 3-item Cancer-Related Symptoms Questionnaire, and the EQ-5D instrument. HRQoL was evaluated overall and by health state in 120 mSTS/mBS patients enrolled in the SABINE study across nine countries in Europe and North America. Utility was estimated from responses to the EQ-5D instrument using UK population-based weights. The mean EQ-5D utility score was 0.69 for the pooled patient sample with little variation across health states. However, patients with progressive disease reported a clinically significant lower utility (0.56). Among disease symptoms, pain and respiratory symptoms are common. This study showed that mSTS/mBS is associated with reduced HRQoL and utility among patients with metastatic disease

Randomised phase III trial of trabectedin versus doxorubicin-based chemotherapy as first-line therapy in translocation-related sarcomas

Abstract Aim This randomised phase III trial evaluated first-line trabectedin versus doxorubicin-based chemotherapy (DXCT) in patients with advanced/metastatic translocation-related sarcomas (TRS). Methods Patients were randomly assigned (1:1) to receive trabectedin 1.5mg/m 2 24-h intravenous (i.v.) infusion every 3weeks (q3wk) ( Arm A ), or doxorubicin 75mg/m 2 i.v. q3wk, or doxorubicin 60mg/m 2 i.v. plus ifosfamide (range, 6–9g/m 2 ) i.v. q3wk ( Arm B ). Progression-free survival (PFS) by independent review was the primary efficacy end-point. Results One hundred and twenty-one patients were randomised; 88 of them had TRS confirmed by central pathology review (efficacy population). Twenty-nine PFS events were assessed by independent review (16 with trabectedin; 13 with DXCT). PFS showed non-significant difference between arms (stratified log rank test, p =0.9573; hazard ratio=0.86, p =0.6992). At the time of this analysis, 63.9% and 58.3% of patients were alive in trabectedin and DXCT arms, respectively. There was no statistically significant difference in survival curves. Response rate according to Response Evaluation Criteria in Solid Tumours (RECIST) v.1.0 was significantly higher in DXCT arm (27.0% versus 5.9%), but response according to Choi criteria showed fewer differences between treatment arms (45.9% versus 37.3%). Safety profile was as expected for both arms, with higher incidence of severe neutropenia, alopecia and mucositis in the DXCT arm. Conclusion Neither trabectedin nor doxorubicin-based chemotherapy showed significant superiority in the first-line treatment of patients with advanced translocation-related sarcoma

Clinical Study Quality of Life and Utility in Patients with Metastatic Soft Tissue and Bone Sarcoma: The Sarcoma Treatment and Burden of Illness in North America and Europe (SABINE) Study

The aim of the study was to assess health-related quality of life (HRQoL) among metastatic soft tissue (mSTS) or bone sarcoma (mBS) patients who had attained a favourable response to chemotherapy. We employed the EORTC QLQ-C30, the 3-item CancerRelated Symptoms Questionnaire, and the EQ-5D instrument. HRQoL was evaluated overall and by health state in 120 mSTS/mBS patients enrolled in the SABINE study across nine countries in Europe and North America. Utility was estimated from responses to the EQ-5D instrument using UK population-based weights. The mean EQ-5D utility score was 0.69 for the pooled patient sample with little variation across health states. However, patients with progressive disease reported a clinically significant lower utility (0.56). Among disease symptoms, pain and respiratory symptoms are common. This study showed that mSTS/mBS is associated with reduced HRQoL and utility among patients with metastatic disease

Denosumab in patients with giant-cell tumour of bone: an open-label, phase 2 study

Background: Giant-cell tumour (GCT) of bone is a primary osteolytic bone tumour with low metastatic potential and is associated with substantial skeletal morbidity. GCT is rich in osteoclast-like giant cells and contains mononuclear (stromal) cells that express RANK ligand (RANKL), a key mediator of osteoclast activation. We investigated the potential therapeutic effect of denosumab, a fully human monoclonal antibody against RANKL, on tumour-cell survival and growth in patients with GCT. Methods: In this open-label, single-group study, 37 patients with recurrent or unresectable GCT were enrolled and received subcutaneous denosumab 120 mg monthly (every 28 days), with loading doses on days 8 and 15 of month 1. The primary endpoint was tumour response, defined as elimination of at least 90% of giant cells or no radiological progression of the target lesion up to week 25. Study recruitment is closed; patient treatment and follow-up are ongoing. The study is registered with Clinical Trials.gov, NCT00396279. Findings: Two patients had insufficient histology or radiology data for efficacy assessment. 30 of 35 (86%; 95% CI 70-95) of evaluable patients had a tumour response: 20 of 20 assessed by histology and 10 of 15 assessed by radiology. Adverse events were reported in 33 of 37 patients; the most common being pain in an extremity (n=7), back pain (n=4), and headache (n=4). Five patients had grade 3-5 adverse events, only one of which (grade 3 increase in human chorionic gonadotropin concentration not related to pregnancy) was deemed to be possibly treatment related. Five serious adverse events were reported although none were deemed treatment related. Interpretation: Further investigation of denosumab as a therapy for GCT is warranted. Funding: Amgen, Inc. © 2010 Elsevier Ltd. All rights reserved