Normal tissue complication probability models for severe acute radiological lung injury after radiotherapy for lung cancer

PurposeTo derive Normal Tissue Complication Probability (NTCP) models for severe patterns of early radiological radiation-induced lung injury (RRLI) in patients treated with radiotherapy (RT) for lung tumors. Second, derive threshold doses and optimal doses for prediction of RRLI to be used in differential diagnosis of tumor recurrence from RRLI during follow-up.Methods and materialsLyman-EUD (LEUD), Logit-EUD (LogEUD), relative seriality (RS) and critical volume (CV) NTCP models, with DVH corrected for fraction size, were used to model the presence of severe early RRLI in follow-up CTs. The models parameters, including α/β, were determined by fitting data from forty-five patients treated with IMRT for lung cancer. Models were assessed using Akaike information criterion (AIC) and area under receiver operating characteristic curve (AUC). Threshold doses for risk of RRLI and doses corresponding to the optimal point of the receiver operating characteristic (ROC) curve were determined.ResultsThe α/βs obtained with different models were 2.7–3.2 Gy. The thresholds and optimal doses curves were EUDs of 3.2–7.8 Gy and 15.2–18.1 Gy with LEUD, LogEUD and RS models, and μ_d of 0.013 and 0.071 with the CV model. NTCP models had AUCs significantly higher than 0.5. Occurrence and severity of RRLI were correlated with patients’ values of EUD and μ_d.ConclusionsThe models and dose levels derived can be used in differential diagnosis of tumor recurrence from RRLI in patients treated with RT. Cross validation is needed to prove prediction performance of the model outside the dataset from which it was derived.     

Complication probability model for subcutaneous fibrosis based on published data of partial and whole breast irradiation

PurposeTo extend the application of current radiation therapy (RT) based normal tissue complication probability (NTCP) models of radiation-induced fibrosis (RIF) of the breast to include the effects of fractionation, inhomogeneous dose, incomplete recovery, and time after the end of radiotherapy in partial breast irradiation (PBI).Materials and methodsAn NTCP Lyman model with biologically effective uniform dose (BEUD) with and without a correction for the effect of incomplete repair was used. The time to occurrence of RIF was also taken into account. The radiobiological parameters were determined by fitting incidences of moderate/severe RIF in published randomized studies on RT of the breast. The NTCP model was used to calculate the risk of toxicity in 35 patients treated with intensity modulated, non-accelerated PBI and the result was compared with observed incidence of RIF.ResultsWith α/β fixed at 3Gy the parameters of the model without correction for incomplete repair extracted from fitting were: 50% complication probability biologically effective dose BEUD₅₀ = 107.2 Gy (95%CI = 95.9–118.6 Gy), volume parameter n = 0.06 (95%CI = 0–0.23), and slope of dose response m = 0.22, (95%CI = 0.20–0.23). After including the correction for incomplete repair with repair halftime for subcutaneous tissue of τ = 4.4 h we obtained BEUD₅₀ = 105.8 Gy (95%CI = 96.9–114.6Gy), n = 0.15 (95%CI = 0–0.33), m = 0.22 (95%CI = 0.20–0.23). Average NTCP predicted by these models, 4.3% and 2.0% respectively, offered a good agreement with RIF incidence in our patients, 5.7%, after an average follow-up of 12 months.ConclusionThe NTCP models of RIF, incorporating the effects of fractionation, volume effect, and latency of toxicity look promising to model PBI. Clinical validation from a prospective PBI treatment study is under development and will help test this preliminary result.     

Normal lung tissue complication probability in MR-Linac and conventional radiotherapy

PurposeTo study normal lung tissue (NLT) complications in magnetic resonance (MR) image based linac and conventional radiotherapy (RT) techniques.Materials and MethodsThe Geant4 toolkit was used to simulate a 6 MV photon beam. A homogenous magnetic field of 1.5 Tesla (T) was applied in both perpendicular and parallel directions relative to the radiation beam.Analysis of the NLT complications was assessed according to the normal lung tissue complication probability (NTCP), the mean lung dose (MLD), and percentage of the lung volume receiving doses greater than 20 Gy (V₂₀), using a sample set of CT images generated from a commercially available 4D-XCAT digital phantom.ResultsThe results show that the MLD and V₂₀ were lower for MR-linac RT. The largest reduction of MLD and V₂₀ for MR-linac RT configurations were 5 Gy and 29.3%, respectively.ConclusionMR-linac RT may result in lower NLT complications when compared to conventional RT.     

Two-dimensional imaging of tumour control probabilities and normal tissue complication probabilities

Aim

To create a presentation method of TCP and NTCP distributions calculated based on dose distribution for a selected CT slice.

Materials and methods

Three 24-bit colour maps – of dose distribution, delineated structures and CT information – were converted into m-by-n-by-3 data arrays, containing intensities of red, green, and blue colour components for each pixel. All calculations were performed with Matlab v.6.5. The transformation function, which consists of five linear functions, was prepared to translate the colour map into a one-dimensional data array of dose values. A menu-driven application based on the transformation function and mathematical models of complication risk (NTCP) and treatment control probability (TCP) was designed to allow pixel-by-pixel translation of colour maps into one-dimensional arrays of TCP and NTCP values.

Results

The result of this work is an application created to visualize the TCP and NTCP distribution for a single CT scan based on the spatial dose distribution calculated in the treatment planning system. The application allows 10 targets (PTV) and 10 organs at risks (OaR) to be defined. The interface allows alpha/beta values to be inserted for each delineated structure. The application computes TCP and NTCP matrices, which are presented as colour maps superimposed on the corresponding CT slice. There is a set of parameters used for TCP/NTCP calculations which can be defined by the user.

Conclusion

Our application is a prototype of an evaluation tool. Although limited to a single plane of the treatment plan, it is believed to be a starting point for further development.     

Radiobiological comparison of two radiotherapy treatment techniques for high-risk prostate cancer

Background

To make a radiobiological comparison, for high risk prostate cancer (T3a, PSA > 20 ng/ml or Gleason > 7) of two radiotherapy treatment techniques. One technique consists of a treatment in three phases of the pelvic nodes, vesicles and prostate using a conventional fractionation scheme of 2 Gy/fraction (SIMRT). The other technique consists of a treatment in two phases that gives simultaneously different dose levels in each phase, 2 Gy/fraction, 2.25 Gy/fraction and 2.5 Gy/fraction to the pelvic nodes, vesicles and prostate, respectively (SIBIMRT).

Materials and methods

The equivalent dose at fractionation of 2 Gy (EQD₂), calculated using the linear quadratic model with α/β_prostate = 1.5 Gy, was the same for both treatment strategies. For comparison the parameters employed were D95, mean dose and Tumour Control Probabilities for prostate PTV and D15, D25, D35, D50, mean dose and Normal Tissue Complication Probabilities for the rectum and bladder, with physical doses converted to EQD₂. Parameters were obtained for α/β_prostate = 1.5, 3 and 10 Gy and for α/β_oar = 1, 2, 3, 4, 6 and 8.

Results

For prostate PTV, both treatment strategies are equivalent for α/β_prostate = 1.5 Gy but for higher α/β_prostate, EQD₂ and TCP, decrease for the SIBIMRT technique. For the rectum and bladder when α/β_oar ≤ 2 Gy, EQD₂ and NTCP are lower for the SIMRT technique or equal in both techniques. For α/β_oar ≥ 2–3 Gy, EQD₂ and NTCP increase for the SIMRT treatment.

Conclusions

A comparison between two radiotherapy techniques is presented. The SIBIMRT technique reduces EQD₂ and NTCP for α/β_oar from 2 to 8 Gy.     

Fluctuations and Noise in Kinetic Systems: Application to K+ Channels in the Squid Axon

We consider the equilibrium or steady-state noise power density spectrum in the quantity N = Σ^x_i=0 a_iN_i for an ensemble of independent and equivalent systems each of which can exist in the discrete set of states i = 0, 1, ···, x. N_i is the number of systems of the ensemble in state i and the a_i's are constants. There is a transition rate constant α_ij for an arbitrary transition i → j; the kinetic equations are linear. There are possible applications to enzyme and biochemical kinetics generally, to membrane transport, muscle contraction, binding on macromolecules, etc. In each case, noise measurements would provide information about the kinetic scheme. The particular application considered here is to K⁺ channels or gates (one channel = one system) in the squid axon membrane: a_iK is the K⁺ conductance of a channel in state i and the kinetic scheme is of the Hodgkin-Huxley type (HH). Here we allow an arbitrary set of a_i's. This is a generalization of our treatment of K⁺ channel noise in an earlier paper. The theory is discussed and some calculations made using Fishman's recent experimental results on K⁺ channel noise as a guide. Preliminary indications are that the HH choice of a_i's may be oversimplified and that a₀ 0, a₁ ≠ a₀, a_x ≠ a_x-1. Quite possibly the a_i's increase from a₀ to a_x, though the early a_i's must be relatively small to give the observed induction behavior in g_K(t). An increase in equal steps is unsatisfactory because this is essentially HH with x = 1 (no induction). More refined experiments may modify these tentative conclusions. In any case, it appears from Fishman's work that noise measurements will probably be very useful in distinguishing between rival models of K⁺ channels.     

Relations between doses cumulated in bone marrow and dose delivery techniques during radiation therapy of cervical and endometrial cancer

PurposeTo compare normal tissue complication probability (NTCP) and average doses in the bone marrow (BM), obtained for five different radiotherapy delivery and planning strategies of cervical and endometrial cancer.Material/methods50 patients were taken to analysis. For each case, 3 different dose delivery techniques were used: 4-field, X15MV, 3DCRT; 7-field, X6MV, IMRT; and 2-arc, X6MV, VMAT. Two optimization scenarios were used for the IMRT and VMAT plans generation: with (+) and without (−) the inclusion of the BM as an optimized structure. Average doses and dose-volume histogram parameters for the PTV, BM, bladder, rectum, bowels and femoral heads were compared. In addition, the BM doses were analyzed with respect to the PTV and/or volume of the BM, and NTCP for the BM were computed.ResultsThe dose in PTV for evaluated plans was similar. The worst doses in organs at risk were obtained for 3DCRT. Using the BM during the optimization of IMRT and VMAT reduces an average dose in BM without increasing the doses in the bladder, rectum and bowels. Differences between doses in BM for IMRT(+) and VMAT(+) plans were similar while NTCP was lower for VMAT(+). A correlation between average dose in BM and the volume ratio of BM and PTV was found for each technique.ConclusionUsing the BM during the optimization of the IMRT and VMAT plans effectively reduces the dose in BM without increasing the dose in the bladder, rectum and bowels. The VMAT(+) plans were characterized by the lowest NTCP.     

Design,synthesis and biological evaluation of benzamide derivatives as novel NTCP inhibitors that induce apoptosis in HepG2 cells

Sodium taurocholate cotransport polypeptide (NTCP) plays an important role in the development of hepatitis and acts as a switch to allow hepatitis virus to enter hepatic cells. As the entry receptor protein of hepatitis virus, NTCP is also an effective target for the treatment of hepatocellular carcinoma. Herein, twenty-five benzamide analogues were synthesized based on the virtual screening design and their anti-proliferative activities against HepG2 cells were evaluated in vitro. Compound 35 was found to be promising, with an IC₅₀ value of 2.8 μM. The apoptosis induced by 35 was characterized by the regulation of markers, including an increase in Bax, cleaved-caspase 3, and cleaved-PARP proteins, and a decrease in Bcl-2 protein. Molecular docking and molecular dynamics (MD) simulation confirmed that compound 35 can bind tightly to NTCP. Western blot analysis also showed that NTCP was inhibited. Altogether, these results indicate that compound 35 acts as a novel NTCP inhibitor to induce apoptosis in HepG2 cells.     

Bacterial cleavage of nitrogen to sulfone bonds in sulfamide and 1H-2,1,3-benzothiadiazin-4(3H)-one 2,2-dioxide: formation of 2-nitrobenzamide by Gordonia sp.

Pure cultures of aerobic bacteria were isolated which could utilize sulfamate, sulfamide or 1H-2,1,3-benzothiadiazin-4(3H)-one 2,2-dioxide (BTDD) as sole source of sulfur for growth and thus cleave a N–S(O)_x bond. The molar growth yields indicated that each source of sulfur was utilized quantitatively. This was confirmed directly for Gordonia sp. strain BT2 utilizing BTDD, which was converted quantitatively via an unidentified intermediate to 2-nitrobenzamide. Another isolate, strain BT1, could utilize saccharin to yield salicylamide, thus cleaving both the N–S(O)_x and C–S(O)_x bonds.     

Image guidance in clinical practice – Influence of positioning inaccuracy on the dose distribution for prostate cancer

BackgroundIn order to consider potential positioning errors there are different recipes for safety-margins for CTV-to-PTV expansion. The aim of this study is to simulate the effect of positioning inaccuracy with clinically realistic patient treatment plans.MethodsFor a collective of 40 prostate patients, the isocenter was shifted back appropriately to the applied table shifts after positioning verification, simulating that no positioning correction had been performed and the treatment plans were recalculated. All the treatment fractions with the appropriate isocenter-shifts were added to yield a new plan considering two scenarios:

• 1)Extreme scenario: summation of only shifted plans.
• 2)Realistic scenario: consideration of the original treatment plan for the fractions with verification imaging.

Afterwards all plans were analysed and compared with each other regarding target coverage, sparing of organs at risk (OAR) and normal tissue complication probability (NTCP).ResultsDose distributions and especially DVH show a deterioration of the target-coverage caused by the positioning inaccuracy. Deviations in dose at a single point can reach values of over 10 Gy. In single cases minimum plan agreement only achieved 66% pass within 3% local dose for the realistic case. Organs at risk and NTCP analysis result in a slightly better sparing of the rectum. Measures of quality like homogeneity and conformity differ just minimally regarding the different scenarios.ConclusionPTV-coverage suffers markedly by the positioning uncertainties, the shifted plans are in large parts clinically not acceptable. Surprisingly sparing of the OAR is not negatively affected by potential positioning errors for this prostate collective.     

Applying radiobiological plan ranking methodology to VMAT prostate SBRT

The impact of a rectal spacer and an increased near maximum target dose in VMAT prostate SBRT is studied.For a group of 11 patients (35 Gy-in-five-fractions VMAT prostate SBRT) a set of 4 plans were generated, namely two VMAT plans, with D2% ⩽ 37.5 Gy (Hom) and with D2% ⩽ 40.2 Gy (Het), were created for each of two CT scans taken before (NoSpc) and after (Spc) transperineal spacer insertion. Consequently the methodology for parameter invariant TCP (tumor control probability) plan ranking was applied for comparison of the plans in terms of tumor control. NTCPs (normal tissue complication probabilities) were calculated for rectum and bladder using Lyman’s model.For all 11 patients the TCP plan ranking has shown that the Het plans would perform considerably better in TCP terms than the Hom ones. The plans without rectal spacer were ranked worse compared to those with rectal spacer except for one set of Hom plans. The calculated NTCPs for rectum produced by the Het plans were quite similar to the NTCPs of the Hom ones. The rectal NTCPs of the Hom Spc plans were always lower than the NTCPs of the Hom NoSpc plans. The NTCP values for bladder were extremely low in all cases.The use of rectal spacer leads in general to lower risk of rectal complications, as expected, and even to better tumor control. Plans with increased near maximum target dose (D2% ⩽ 40.2 Gy) are expected to perform much better in terms of tumor control than those with D2% ⩽ 37.5 Gy.     

Body temperature and respiratory dynamics in un-shaded beef cattle

In this study body temperature (BT, °C) and panting score (PS, 0–4.5; where 0?=?no panting/no stress and 4.5?=?catastrophic stress) data were obtained from 30 Angus steers housed outside over 120 days Steers were implanted with a BT transmitter on day ?31, BT was recorded at 30-min intervals to a data logger and downloaded each day to a database. The cattle were housed in ten outdoor un-shaded pens with an earthen floor, eight of which had a pen floor area of 144 m² (three transmitter steers plus five non-transmitter steers; 18 m²/steer) and two had an area of 168 m² (three transmitter steers and six non-transmitter steers; 18.7 m²/steer). Only data from the transmitter steers were used in this study. The PS of the steers was obtained daily (± 15 min) at 0600 hours (AM), 1200 hours (MD) and 1600 hours (PM). At the same times climate variables (ambient temperature, black globe temperature, solar radiation, relative humidity, wind speed and rainfall) were obtained from an on-site weather station. PS observations were made from outside the pens so as not to influence cattle responses. The two closest BT values to the time when PS was obtained were downloaded retrospectively from a logger and averaged. A total of 8,352 observations were used to generate second order polynomial response curves: (AM) y?=?39.08?+?0.009?x +?0.137x ² (R ²?=?0.94; P? y?=?39.09?+?0.914x ? 0.080x ² (R ²?=?0.89; P? y?=?39.52?+?0.790x ? 0.068x ² (R ²?=?0.83; P?x?PS. These data suggest that PS is a good indicator of body temperature. The BT at MD corresponded to slightly lower PS compared with PM, e.g., for PS 1; BT at MD?=?39.1?±?0.05 °C whereas BT at PM?=?39.5?±?0.05 °C. However during AM, BT was lower (P?相似文献   

The rate of convergence of a generalized stable population

In an age-structured population that grows exponentially, each age groupP _i(t) at periodt is asymptotically equivalent tox ₀ ^t for some positive number x₀. In this paper we show that the speed at which the ith age group reaches its exponential state of equilibrium can be measured by the rate at which the ratio v_i(t)=P_i(t)/p_i(t–1) converges tox ₀. The age specific rate of convergence is determined by considering a quantityr satisfyingv _i(t)-x ₀ ¦ r ^t whent is large;R _i=Infr (over all initial populations,r satisfying the above inequality) is the R-factor used in numerical analysis to measure the rate at which the sequencev _i (t) converges tox ₀;S _i =- In R_i is then defined as the rate of convergence to stability of the ith age group. The case of constant net maternity rates is studied in detail; in this contextS ₀ is compared to the population entropyH, which was proposed by Tuljapurkar (1982) as a measure of the rate of convergence to stability.     

Optimal Fixing of the Bandwidth-Parameter for the Empirical Regression1,2

The estimator ?₀(x) of the regression r(x) = E (Y | × = x) from measured points (x_i, y_i), i = 1(1) n, of a continuous two-dimensional random variable (X, Y) with unknown continuous density function f(x, y) and with moments up to the second order can be made with the help of a density estimation f?₀(x, y) (see e.g. SCHMERLING and PEIL, 1980). Here f?₀(x, y) still contains free parameters (so-called band-width-parameters), the values of which have to be optimally fixed in the concrete case. This fixing can be done by using a modification of the maximum-likelihood principle including jackknife techniques. The parameter values can be also found from the estimators for r(x). Here the cross-validation principle can be applied. Some numerical aspects of these possibilities for optimally fixing the bandwidth-parameter are discussed by means of examples. If ?₀(x) is used as a smoothing operator for time series the optimal choice of the parameter values is dependent on the purpose of application of the smoothed time series. The fixing will then be done by considering the so-called filter-characteristic of ?C₀(x).     

Syntheses and spectroscopic and structural characterization of silver(I) complexes containing tris(isobutyl)phosphine and poly(azol-1-yl)borates

Silver(I) derivatives [Ag(L)(PⁱBu₃)] (L = H₂B(tz)₂ (dihydrobis(1H-1,2,4-triazol-1-yl)borate), HB(tz)₃ (hydrotris(1H-1,2,4-triazol-1-yl)borate), Tp (hydrotris(1H-pyrazol-1-yl)borate), Tp∗ (hydrotris(3,5-dimethyl-1H-pyrazol-1-yl)borate), Tp^Me (hydrotris(3-methyl-1H-pyrazol-1-yl)borate), Tp^CF3 (hydrotris(3-trifluoromethyl-1H-pyrazol-1-yl)borate), Tp^4Br (hydrotris(4-bromo-1H-pyrazol-1-yl)borate), HB(btz)₃ (hydrotris(1H-1,2,4-benzotriazol-1-yl)borate), Tm (hydrotris(3-methy-1-imidazolyl-2-thione)borate), pzTp (tetrakis(1H-pyrazol-1-yl)borate), pz⁰Tp^Me (tetrakis(3-methyl-1H-pyrazol-1-yl)borate) have been synthesized from the reaction of [Ag(NO₃)(PⁱBu₃)₂] with ML (M = Na or K) and characterized both in solution (¹H- and ³¹P{¹H} NMR, ESI MS spectroscopy, conductivity) and in the solid state (IR, single crystal X-ray structure analysis). These complexes are air-stable and light-sensitive and non-electrolytes in CH₂Cl₂ and acetone in which they slowly decompose, even with the strict exclusion of oxygen and light, yielding metallic silver and/or azolate (Az) species of formula [Ag(Az)(PⁱBu₃)_x] upon breaking of the bridging B-N_(azole) bond. The solid state structures of [Ag(Tp)(PⁱBu₃)], [Ag(Tp^Me)(PⁱBu₃)], [Ag(Tp^CF3)(PⁱBu₃)], [Ag{HB(btz)₃}(PⁱBu₃)], and [Ag(Tm)(PⁱBu₃)] show that the silver atom adopts a distorted tetrahedral coordination geometry. [Ag(L)(PPh₃)] can be easily obtained from the reaction of [Ag(L)(PⁱBu₃)] with excess PPh₃, whereas from the reverse reaction of [Ag(L)(PPh₃)] with PⁱBu₃a mixture of [Ag(L)(PⁱBu₃)] and [Ag(L)]₂ and [Ag(L)(PPh₃)] was recovered. ³¹P{¹H} NMR variable temperature NMR studies showed that in the pz⁰Tp^x derivatives the scorpionate ligand acts as a bidentate donor, whereas tridentate coordination is found for all tris(azolyl)borate derivatives, both in solution and in the solid state. ESI MS data suggest the existence in solution of species such as [Ag(PⁱBu₃)₂]⁺ upon dissociation of the L ligand, and also the formation of dimeric species of the form [Ag₂(L)(PⁱBu₃)₂]⁺.     

Chemical implantation of Group 4 cations on silica via cyclopentadienyl- and N,N-dialkylcarbamato derivatives

Chemical implantation of Group 4 cations [Ti(III), Ti(IV), Zr(IV), Hf(IV)] has been carried out under mild conditions by the reaction of polycyclopentadienyl- (MCp_n; M = Ti, n = 3, 4; M = Zr, Hf, n = 4), mixed cyclopentadienyl/N,N-dialkylcarbamato (ML_x(O₂CNEt₂)_y; M = Ti, L = Cp, C₅Me₅ (Cp*), x = 2, y = 1; M = Hf, L = Cp, x = 1, y = 3), and N,N-dialkylcarbamato (M(O₂CNR₂)_n, M = Ti, n = 3, R = ⁱPr; M = Ti, Hf, n = 4, R = Et; M = Zr, n = 4, R = ⁱPr) derivatives, with the silanol groups of amorphous silica. Cyclopentadiene/pentamethylcyclopentadiene and/or carbon dioxide and the secondary amine are released in the process. The amount of implanted cations depends on the metal and on the ligands, the pentamethylcyclopentadienyl complex being less reactive than the unsubstituted congener. The starting complexes and the final products have been characterized by EPR or by ¹³C CP-MAS NMR spectroscopy.     

Dipole moments of random coil polypeptides

The Rotational Isomeric States model is applied to calculate dipole moments of polypeptides of the twenty natural α-amino acids in the random coil state. Dipole moments of each repeat unit (μ_i), are evaluated using a quantum mechanics procedure. Dipole moment ratios ($\text{D}{}_{\mathrm{x}}\text{=}\text{〈μ}{}^2\text{〉}\text{x}\text{μ}{}_{\mathrm{i}}{}^2\text{,}\text{x = number of repeat units}$) of homopolypeptides are calculated and extrapolated to x →?. With a few exceptions, D_? = 0.36 ± 0.1. Ten actual proteins and three enzymes are also studied; their dipole ratios (D_x′ =〈μ〉/x) range from 7.34 to 10.57 in 10^?59 C² m² (6.6–9.5 D²). Diffferences in the values of D_x′ are due mainly to the different contributions, μ_i, of the amino acid residues contained in each polymer, whereas the sequence of amino acids has a very minor effect.     

Metaplastic breast cancer: Treatment and prognosis by molecular subtype

BackgroundMetaplastic breast cancer (MBC) is a rare and aggressive subtype of breast. However, the effect of molecular subtype on treatment and prognosis of MBC remains unclear.Patients and methodsThe Surveillance, Epidemiology, and End Results database was used to analyze patients with MBC between 2010 and 2016. Molecular subtype was stratified to TN group (ER and PR-/HER2-), HER2 group (ER and PR-/HER2+, ER/PR+ and HER2+), and HR group (ER/PR+ and HER2-). The breast cancer-specific survival (BCSS) differences were estimated using multivariate Cox regression model and Kaplan-Meier curves.ResultsWe included 1665 patients with median follow-up time of 27 months (range 0–83 months). 1154 (69.3%), 65 (3.9%), and 446 (26.8%) patients presented in TN group, HER2 group, and HR group, respectively. On multivariate Cox analysis, the prognosis was related to age, tumor size, regional node metastasis, and surgery. Molecular subtype remained no impact on BCSS. Radiotherapy (RT) was associated with better prognosis. Patients cannot benefit from chemotherapy. In Kaplan-Meier curve, triple-negative (P = 0.047) and HR-positive (P = 0.006) patients receiving RT had a superior BCSS than that not RT. HER2-positive patients cannot benefit from RT. However, adjusted Kaplan-Meier survival model showed that triple-negative (P = 0.019) but not HER2-positive (P = 0.575) or HR-positive (P = 0.574) patients receiving RT had a superior BCSS than that not RT.ConclusionsMolecular subtype is not associated with the better prognosis of MBC. Patients could benefit from RT. However, triple-negative but not HR-positive or HER2-positive patients have superior survival after receiving RT.     

Modelling of a single-staged bioseparation process for simultaneous removal of iron(III) and chromium(VI) by using Chlorella vulgaris

In this study, the competitive biosorption of iron(III) and chromium(VI) to Chlorella vulgaris from a binary metal mixture was investigated in a single-staged batch reactor as a function of V₀/X₀ (volume of solution containing heavy metal mixture/quantity of biosorbent) ratio and second metal ion concentration at pH 2. The obtained results showed that the increase in biomass quantity (or the decrease of V₀/X₀ ratio) with the addition of second metal ion affected the removed quantities of iron(III) or chromium(VI). The sorption phenomenon was expressed by the competitive, multi-component Langmuir adsorption isotherm and this expression was used for calculating each residual or adsorbed metal ion concentration at equilibrium (C_eq,i or C_ad,eq,i) at a constant V₀/X₀ ratio for a given combination of heavy metal ions in a single-staged batch reactor. Experimental C_eq,i and C_ad,eq,i values were compared to those calculated and graphically determined.