The Impact of Elastic Deformations of the Extracellular Matrix on Cell Migration.

The mechanical properties of the extracellular matrix, in particular its stiffness, are known to impact cell migration. In this paper, we develop a mathematical model of a single cell migrating on an elastic matrix, which accounts for the deformation of the matrix induced by forces exerted by the cell, and investigate how the stiffness impacts the direction and speed of migration. We model a cell in 1D as a nucleus connected to a number of adhesion sites through elastic springs. The cell migrates by randomly updating the position of its adhesion sites. We start by investigating the case where the cell springs are constant, and then go on to assuming that they depend on the matrix stiffness, on matrices of both uniform stiffness as well as those with a stiffness gradient. We find that the assumption that cell springs depend on the substrate stiffness is necessary and sufficient for an efficient durotactic response. We compare simulations to recent experimental observations of human cancer cells exhibiting durotaxis, which show good qualitative agreement.

Radiation pneumonitis and pulmonary function with lung dose-volume constraints in breast cancer irradiation.

PURPOSE: We studied symptomatic radiation pneumonitis (RP) and changes in pulmonary function tests (PFTs) after loco-regional radiotherapy (LRRT) with V20 lung constraints in breast cancer (BC). PATIENTS AND METHODS: Sixty-four women underwent PFTs before and 5 months after 3D planned LRRT for BC. The incidentally irradiated ipsilateral lung V20 was minimised to <30%. Patients were monitored for symptoms of RP 1, 4 and 7 months after radiotherapy (RT) and data on covariates were collected prospectively. The outcome was compared with previous treatment series. RESULTS: Pneumonitis was less frequent with the applied constraint, that is, four mild and one moderate case, than in our previous report (p < 0·001). In multivariate analyses, neither dosimetric data nor covariates appeared to influence mean changes in vital capacity [-0·11L, standard error of the mean (SEM) 0·03] or diffusing capacity of the lung for carbon monoxide (DLCO) (-0·20 mmol/kPa/min, SEM 0·01), except for pre-RT chemotherapy, which diminished the change in DLCO 5 months post-RT. CONCLUSIONS: The used constraint and 3D planning lowered the rate of RP and short-term changes in PFTs compared with our previous treatment series. Pre-RT chemotherapy affects DLCO baseline levels. Rates of side effects should be continuously studied when new target definitions or therapies are introduced in LRRT of BC.

Increased migration in host-pathogen metapopulations can cause host extinction.

There are at least two potentially counteracting effects of migration in host-pathogen metapopulations. On the one hand increased migration leads to increased colonization of empty habitats by healthy hosts; on the other hand migrants can carry infectious diseases to susceptible populations. Earlier metapopulation models have found that the beneficial effects of increasing migration (reduced infection) are likely to dominate, and a general recommendation for managers of endangered metapopulations has been to increase connectivity between habitat patches. We extend the model framework to simultaneously allow for (1) Allee effects in host colonization rate, (2) spillover of pathogens from a second host species, and (3) differential colonization success by infected and healthy hosts. We find that the dynamics of a host-pathogen system can be highly sensitive to increased migration rates. Allee effects make host populations vulnerable to spillover of pathogens from other hosts, and metapopulation extinction can emerge from seemingly stable situations of endemic coexistence. Increasing connectivity in endangered metapopulations can be a risky management action unless the details of the biology of the host-pathogen system are known.

Breathing-motion induced interplay effects for stereotactic body radiotherapy of liver tumours using flattening-filter free volumetric modulated arc therapy.

The purpose of this study was to investigate breathing-motion induced interplay effects for stereotactic body radiotherapy (SBRT) of liver tumours treated with flattening-filter free (FFF) volumetric modulated arc therapy (VMAT). Ten patients previously treated with liver SBRT were included in this study. All patients had four-dimensional computed tomography (4DCT) scans acquired prior to treatment. The 4DCT was sorted into 8-10 phases covering an equal time interval. A FFF VMAT plan was created for one fraction in the mid-ventilation phase for each patient. To generate dose distributions including both interplay effects and dose blurring, a sub-plan was calculated for each phase. The total dose distributions were accumulated to the mid-ventilation phase using the deformed vector fields (DVF) from deformable image registration between the corresponding CT and the mid-ventilation phase CT. A blurred dose distribution, not including interplay effects, was also obtained by distributing the delivery of the whole plan uniformly on all phases, and was similarly accumulated to the mid-ventilation phase. To isolate interplay effects, this blurred dose distribution was subtracted from the total dose distribution with interplay effects. The near minimum dose (D 98%), mean dose (D mean), heterogeneity index (HI), and the near minimum dose difference (ΔD 98%) between the accumulated dose distributions with and without interplay effects were calculated within the gross tumour volume (GTV) for each patient. Comparing the accumulated dose distributions with and without interplay effects, the D 98% decreased for nine of the ten patients and the HI increased for all patients. The median and minimum differences in D 98% were -2.1% and -5.0% (p = 0.006), respectively, and the median HI significantly increased from 6.2% to 12.2% (p = 0.002). The median ΔD 98% was -4.0% (range -7% to -1.5%). In conclusion, statistically significant breathing-induced interplay effects were observed for a single fraction of FFF VMAT liver SBRT, resulting in heterogeneous dose distributions within the GTV.

Impact of anticipation in dynamical systems.

Many animals, including humans, have predictive capabilities and, presumably, base their behavioral decisions-at least partially-upon an anticipated state of their environment. We explore a minimal version of this idea in the context of particles that interact according to a pairwise potential. Anticipation enters the picture by calculating the interparticle forces from linear extrapolations of the particle positions some time τ in the future. Simulations show that for intermediate values of τ, compared to a transient time scale defined by the potential and the initial conditions, the particles form rotating clusters in which the particles are arranged in a hexagonal pattern. Analysis of the system shows that anticipation induces energy dissipation and we show that the kinetic energy asymptotically decays as 1/t. Furthermore, we show that the angular momentum is not necessarily conserved for τ>0, and that asymmetries in the initial condition therefore can cause rotational movement. These results suggest that anticipation could play an important role in collective behavior, since it may induce pattern formation and stabilizes the dynamics of the system.

Pulmonary function following adjuvant chemotherapy and radiotherapy for breast cancer and the issue of three-dimensional treatment planning.

BACKGROUND AND PURPOSE: The frequency and grade of pulmonary complications following adjuvant radiotherapy for breast cancer are still debated. This study focuses on loss of pulmonary function. MATERIALS AND METHODS: We have measured the reduction of pulmonary function 5 months following radiotherapy in 144 node-positive stage II breast cancer patients by using pulmonary function tests. RESULTS: No deterioration of pulmonary function was detected among the patients who were treated with local radiotherapy. On the contrary, there was a mean increase in diffusion capacity by 7% (P = 0.004) following radiotherapy, which most likely was explained by the adjuvant chemotherapy administered prior to the baseline pulmonary function tests. Patients undergoing loco-regional radiotherapy showed a mean reduction in diffusion capacity by 5% (P < 0.001) and in vital capacity by 3% (P = 0.001). The subset of patients (9%) who were diagnosed with severe pulmonary complications needing cortisone treatment had significantly larger mean paired differences in vital capacity (-0.446 L, -15% (equivalent to 15 years of normal ageing or the loss of 3/4 of a lung lobe)) compared to the patients who were asymptomatic (-0.084 L) (P < 0.05). When the effects of potential confounding factors and different radiotherapy techniques were tested on the reduction of pulmonary function by stepwise multiple regression analysis, a significant correlation was found only to locoregional radiotherapy including the lower internal mammary lymph nodes. CONCLUSIONS: We conclude that a clinically important reduction of pulmonary function is seen in the subset of patients who are diagnosed with severe pulmonary complication following loco-regional radiotherapy for breast cancer. The results of this study warrant further studies based on individual lung dose volume histograms.

Conservation laws and unidentifiability of rate expressions in biochemical models.

New experimental techniques in bioscience provide us with high-quality data allowing quantitative mathematical modelling. Parameter estimation is often necessary and, in connection with this, it is important to know whether all parameters can be uniquely estimated from available data, (i.e. whether the model is identifiable). Dealing essentially with models for metabolism, we show how the assumption of an algebraic relation between concentrations may cause parameters to be unidentifiable. If a sufficient data set is available, the problem with unidentifiability arises locally in individual rate expressions. A general method for reparameterisation to identifiable rate expressions is provided, together with a Mathematica code to help with the calculations. The general results are exemplified by four well-cited models for glycolysis.

Pulmonary complications following different radiotherapy techniques for breast cancer, and the association to irradiated lung volume and dose.

PURPOSE: This study investigates the incidence of short-term pulmonary complications following radiotherapy (RT) for breast cancer (BC) with different treatment techniques/incidentally irradiated lung volumes and the importance of confounding factors on RT-induced pulmonary complications. PATIENTS AND METHODS: Prospectively, 475 patients with BC were followed for pulmonary complications 1, 4 and 7 months post-RT. Mean lung dose volume histograms (MDVH) were constructed and compared for the different RT-techniques. Among a subset of the mastectomized patients treated with loco-regional (LR-) RT, who had undergone complete three-dimensional (3-D) dose planning (n = 43), MDVH for asymptomatic patients was compared with MDVH for patients experiencing both radiological and clinical pulmonary side-effects. RESULTS: Moderate pulmonary complications, that is requiring treatment with corticosteroids, were rare following local RT (< 1%), but were diagnosed among 11% of the patients treated with LR-RT. A correlation between increasing irradiated lung volumes at the >20 Gy-level (V20), based on MDVH for the RT-techniques, and pulmonary complications was found (P < 0.001). Furthermore, increasing age and reduced pre-RT functional level were independently associated with a higher rate of pulmonary complications (P = 0.005 and P = 0.018). Among the subgroup of mastectomized patients treated with LR-RT, who had undergone complete 3-D dose planning, a difference in mean V20 was found between patients experiencing both clinical and radiological pulmonary side-effects compared to patients experiencing neither of the two side-effects (P = 0.007). CONCLUSION: Moderate pulmonary complications following local RT for BC are rare. The incidence of short-term moderate pulmonary complications in LR-RT is, however, clinically significant and to define quality assurance guidelines for these RT-techniques, 3-D RT planning can be used.

A descriptive study of pulmonary complications after postoperative radiation therapy in node-positive stage II breast cancer.

This study was conducted to assess the frequencies of symptomatic pulmonary complications following adjuvant postoperative radiotherapy using different treatment techniques in patients with Stage II node-positive breast cancer. During 1991-1993, 177 patients were referred to the Radiotherapy Department of Stockholm Söder Hospital; 144 after modified radical mastectomy and 33 after partial mastectomy. The records of these patients were studied retrospectively for clinically diagnosed radiotherapy-induced lung complications 1-7 months after treatment. Thirty-three of 138 patients (24%) irradiated after modified radical mastectomy developed pulmonary complications and 20 (14%) of these were diagnosed as severe, i.e. needing medical treatment with corticosteroids. No statistically significant difference could be found between the different electron energies used for treating the chest wall and the frequency of respiratory side-effects. Eighteen of 33 patients completed the prescribed treatment after partial mastectomy. Nine of these 18 patients (50%) developed pulmonary complications and 4 (22%) developed severe reactions. Fifteen patients received alternative treatments. With the techniques used after partial mastectomy the median central lung distance was 32 mm among the patients who experienced respiratory side-effects compared with 25 mm among the patients who were not affected (p = 0.03). This study identifies acute/subacute pulmonary side-effects as a clinically significant problem. Prospective follow-up with lung function tests, identification of risk factors, and individual lung dose volume histograms is warranted to assess the long-term implications.

Abnormalities on chest radiographs following radiation therapy for breast cancer.

The aim of this study was to study pulmonary radiological abnormalities with chest radiography following different radiotherapy (RT) techniques for breast cancer with respect to regions and density, and their association with pulmonary complications and reduction in vital capacity (VC). Chest radiographs were performed 5 months following local or loco-regional RT in 167 breast cancer patients. The radiological abnormalities were analysed with a classification system originally proposed by Arriagada and evaluated according to increasing density (0-3) and affected lung regions (apical-lateral, basal-lateral, central-parahilar). The highest-density grades in each region were added together to form scores ranging from 0 to 9. The patients were monitored for RT-induced pulmonary complications. The VC was measured prior to and 5 months following RT. An independent evaluation of 51 patients was performed by a second radiologist to control the reproducibility of the classification system. Increasing scores were associated with loco-regional RT and pulmonary complications (P < 0.001). The mean reduction of VC for patients scoring 0-3 (-30 ml) vs 4-9 (-161 ml) was not statistically significant (P = 0.10). Scores of 4-9 were more frequently observed in older patients (P < 0.001). The independent evaluations by two radiologists revealed good agreement (P < 0.001) and no systematic inter-observer variation. Radiological abnormalities on chest radiographs, scored according to Arriagada, can be used as an objective end point for RT-induced pulmonary side effects in breast cancer.