Finite mixture distributions, sequential likelihood and the EM algorithm

A popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution. A barrier to using finite mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive separability of the log-likelihood function. We show, however, that an extension of the EM algorithm reintroduces additive separability, thus allowing one to estimate parameters sequentially during each maximization step. In establishing this result, we develop a broad class of estimators for mixture models. Returning to the likelihood problem, we show that, relative to full information maximum likelihood, our sequential estimator can generate large computational savings with little loss of efficiency.

Chondrogenesis of adult stem cells from adipose tissue and bone marrow: induction by growth factors and cartilage-derived matrix.

OBJECTIVES: Adipose-derived stem cells (ASCs) and bone marrow-derived mesenchymal stem cells (MSCs) are multipotent adult stem cells with potential for use in cartilage tissue engineering. We hypothesized that these cells show distinct responses to different chondrogenic culture conditions and extracellular matrices, illustrating important differences between cell types. METHODS: Human ASCs and MSCs were chondrogenically differentiated in alginate beads or a novel scaffold of reconstituted native cartilage-derived matrix with a range of growth factors, including dexamethasone, transforming growth factor beta3, and bone morphogenetic protein 6. Constructs were analyzed for gene expression and matrix synthesis. RESULTS: Chondrogenic growth factors induced a chondrocytic phenotype in both ASCs and MSCs in alginate beads or cartilage-derived matrix. MSCs demonstrated enhanced type II collagen gene expression and matrix synthesis as well as a greater propensity for the hypertrophic chondrocyte phenotype. ASCs had higher upregulation of aggrecan gene expression in response to bone morphogenetic protein 6 (857-fold), while MSCs responded more favorably to transforming growth factor beta3 (573-fold increase). CONCLUSIONS: ASCs and MSCs are distinct cell types as illustrated by their unique responses to growth factor-based chondrogenic induction. This chondrogenic induction is affected by the composition of the scaffold and the presence of serum.

Functional properties of cell-seeded three-dimensionally woven poly(epsilon-caprolactone) scaffolds for cartilage tissue engineering.

Articular cartilage possesses complex mechanical properties that provide healthy joints the ability to bear repeated loads and maintain smooth articulating surfaces over an entire lifetime. In this study, we utilized a fiber-reinforced composite scaffold designed to mimic the anisotropic, nonlinear, and viscoelastic biomechanical characteristics of native cartilage as the basis for developing functional tissue-engineered constructs. Three-dimensionally woven poly(epsilon-caprolactone) (PCL) scaffolds were encapsulated with a fibrin hydrogel, seeded with human adipose-derived stem cells, and cultured for 28 days in chondrogenic culture conditions. Biomechanical testing showed that PCL-based constructs exhibited baseline compressive and shear properties similar to those of native cartilage and maintained these properties throughout the culture period, while supporting the synthesis of a collagen-rich extracellular matrix. Further, constructs displayed an equilibrium coefficient of friction similar to that of native articular cartilage (mu(eq) approximately 0.1-0.3) over the prescribed culture period. Our findings show that three-dimensionally woven PCL-fibrin composite scaffolds can be produced with cartilage-like mechanical properties, and that these engineered properties can be maintained in culture while seeded stem cells regenerate a new, functional tissue construct.

Analysis of soil carbon transit times and age distributions using network theories

The long-term soil carbon dynamics may be approximated by networks of linear compartments, permitting theoretical analysis of transit time (i.e., the total time spent by a molecule in the system) and age (the time elapsed since the molecule entered the system) distributions. We compute and compare these distributions for different network. configurations, ranging from the simple individual compartment, to series and parallel linear compartments, feedback systems, and models assuming a continuous distribution of decay constants. We also derive the transit time and age distributions of some complex, widely used soil carbon models (the compartmental models CENTURY and Rothamsted, and the continuous-quality Q-Model), and discuss them in the context of long-term carbon sequestration in soils. We show how complex models including feedback loops and slow compartments have distributions with heavier tails than simpler models. Power law tails emerge when using continuous-quality models, indicating long retention times for an important fraction of soil carbon. The responsiveness of the soil system to changes in decay constants due to altered climatic conditions or plant species composition is found to be stronger when all compartments respond equally to the environmental change, and when the slower compartments are more sensitive than the faster ones or lose more carbon through microbial respiration. Copyright 2009 by the American Geophysical Union.

Hand-held spectroscopic device for in vivo and intraoperative tumor detection: contrast enhancement, detection sensitivity, and tissue penetration.

Surgery is one of the most effective and widely used procedures in treating human cancers, but a major problem is that the surgeon often fails to remove the entire tumor, leaving behind tumor-positive margins, metastatic lymph nodes, and/or satellite tumor nodules. Here we report the use of a hand-held spectroscopic pen device (termed SpectroPen) and near-infrared contrast agents for intraoperative detection of malignant tumors, based on wavelength-resolved measurements of fluorescence and surface-enhanced Raman scattering (SERS) signals. The SpectroPen utilizes a near-infrared diode laser (emitting at 785 nm) coupled to a compact head unit for light excitation and collection. This pen-shaped device effectively removes silica Raman peaks from the fiber optics and attenuates the reflected excitation light, allowing sensitive analysis of both fluorescence and Raman signals. Its overall performance has been evaluated by using a fluorescent contrast agent (indocyanine green, or ICG) as well as a surface-enhanced Raman scattering (SERS) contrast agent (pegylated colloidal gold). Under in vitro conditions, the detection limits are approximately 2-5 × 10(-11) M for the indocyanine dye and 0.5-1 × 10(-13) M for the SERS contrast agent. Ex vivo tissue penetration data show attenuated but resolvable fluorescence and Raman signals when the contrast agents are buried 5-10 mm deep in fresh animal tissues. In vivo studies using mice bearing bioluminescent 4T1 breast tumors further demonstrate that the tumor borders can be precisely detected preoperatively and intraoperatively, and that the contrast signals are strongly correlated with tumor bioluminescence. After surgery, the SpectroPen device permits further evaluation of both positive and negative tumor margins around the surgical cavity, raising new possibilities for real-time tumor detection and image-guided surgery.

Use of an insulating mask for controlling anisotropy in multilayer electrospun scaffolds for tissue engineering.

Tissue engineering of various musculoskeletal or cardiovascular tissues requires scaffolds with controllable mechanical anisotropy. However, native tissues also exhibit significant inhomogeneity in their mechanical properties, and the principal axes of anisotropy may vary with site or depth from the tissue surface. Thus, techniques to produce multilayered biomaterial scaffolds with controllable anisotropy may provide improved biomimetic properties for functional tissue replacements. In this study, poly(ε-caprolactone) scaffolds were electrospun onto a collecting electrode that was partially covered by rectangular or square shaped insulating masks. The use of a rectangular mask resulted in aligned scaffolds that were significantly stiffer in tension in the axial direction than the transverse direction at 0 strain (22.9 ± 1.3 MPa axial, 16.1 ± 0.9 MPa transverse), and at 0.1 strain (4.8 ± 0.3 MPa axial, 3.5 ± 0.2 MPa transverse). The unaligned scaffolds, produced using a square mask, did not show this anisotropy, with similar stiffness in the axial and transverse directions at 0 strain (19.7 ± 1.4 MPa axial, 20.8 ± 1.3 MPa transverse) and 0.1 strain (4.4 ± 0.2 MPa axial, 4.6 ± 0.3 MPa, transverse). Aligned scaffolds also induced alignment of adipose stem cells near the expected axis on aligned scaffolds (0.015 ± 0.056 rad), while on the unaligned scaffolds, their orientation showed more variation and was not along the expected axis (1.005 ± 0.225 rad). This method provides a novel means of creating multilayered electrospun scaffolds with controlled anisotropy for each layer, potentially providing a means to mimic the complex mechanical properties of various native tissues.

Animal models of soft-tissue sarcoma.

Soft-tissue sarcomas (STSs) are rare mesenchymal tumors that arise from muscle, fat and connective tissue. Currently, over 75 subtypes of STS are recognized. The rarity and heterogeneity of patient samples complicate clinical investigations into sarcoma biology. Model organisms might provide traction to our understanding and treatment of the disease. Over the past 10 years, many successful animal models of STS have been developed, primarily genetically engineered mice and zebrafish. These models are useful for studying the relevant oncogenes, signaling pathways and other cell changes involved in generating STSs. Recently, these model systems have become preclinical platforms in which to evaluate new drugs and treatment regimens. Thus, animal models are useful surrogates for understanding STS disease susceptibility and pathogenesis as well as for testing potential therapeutic strategies.

Noninvasive monitoring of tissue hemoglobin using UV-VIS diffuse reflectance spectroscopy: a pilot study.

We conducted a pilot study on 10 patients undergoing general surgery to test the feasibility of diffuse reflectance spectroscopy in the visible wavelength range as a noninvasive monitoring tool for blood loss during surgery. Ratios of raw diffuse reflectance at wavelength pairs were tested as a first-pass for estimating hemoglobin concentration. Ratios can be calculated easily and rapidly with limited post-processing, and so this can be considered a near real-time monitoring device. We found the best hemoglobin correlations were when ratios at isosbestic points of oxy- and deoxyhemoglobin were used, specifically 529/500 nm. Baseline subtraction improved correlations, specifically at 520/509 nm. These results demonstrate proof-of-concept for the ability of this noninvasive device to monitor hemoglobin concentration changes due to surgical blood loss. The 529/500 nm ratio also appears to account for variations in probe pressure, as determined from measurements on two volunteers.

Effect of different jump distributions on the dynamics of jump processes

The paper investigates stochastic processes forced by independent and identically distributed jumps occurring according to a Poisson process. The impact of different distributions of the jump amplitudes are analyzed for processes with linear drift. Exact expressions of the probability density functions are derived when jump amplitudes are distributed as exponential, gamma, and mixture of exponential distributions for both natural and reflecting boundary conditions. The mean level-crossing properties are studied in relation to the different jump amplitudes. As an example of application of the previous theoretical derivations, the role of different rainfall-depth distributions on an existing stochastic soil water balance model is analyzed. It is shown how the shape of distribution of daily rainfall depths plays a more relevant role on the soil moisture probability distribution as the rainfall frequency decreases, as predicted by future climatic scenarios. © 2010 The American Physical Society.

Magnetic resonance water proton relaxation in protein solutions and tissue: T(1rho) dispersion characterization.

BACKGROUND: Image contrast in clinical MRI is often determined by differences in tissue water proton relaxation behavior. However, many aspects of water proton relaxation in complex biological media, such as protein solutions and tissue are not well understood, perhaps due to the limited empirical data. PRINCIPAL FINDINGS: Water proton T(1), T(2), and T(1rho) of protein solutions and tissue were measured systematically under multiple conditions. Crosslinking or aggregation of protein decreased T(2) and T(1rho), but did not change high-field T(1). T(1rho) dispersion profiles were similar for crosslinked protein solutions, myocardial tissue, and cartilage, and exhibited power law behavior with T(1rho)(0) values that closely approximated T(2). The T(1rho) dispersion of mobile protein solutions was flat above 5 kHz, but showed a steep curve below 5 kHz that was sensitive to changes in pH. The T(1rho) dispersion of crosslinked BSA and cartilage in DMSO solvent closely resembled that of water solvent above 5 kHz but showed decreased dispersion below 5 kHz. CONCLUSIONS: Proton exchange is a minor pathway for tissue T(1) and T(1rho) relaxation above 5 kHz. Potential models for relaxation are discussed, however the same molecular mechanism appears to be responsible across 5 decades of frequencies from T(1rho) to T(1).

Utility of telomerase-pot1 fusion protein in vascular tissue engineering.

While advances in regenerative medicine and vascular tissue engineering have been substantial in recent years, important stumbling blocks remain. In particular, the limited life span of differentiated cells that are harvested from elderly human donors is an important limitation in many areas of regenerative medicine. Recently, a mutant of the human telomerase reverse transcriptase enzyme (TERT) was described, which is highly processive and elongates telomeres more rapidly than conventional telomerase. This mutant, called pot1-TERT, is a chimeric fusion between the DNA binding protein pot1 and TERT. Because pot1-TERT is highly processive, it is possible that transient delivery of this transgene to cells that are utilized in regenerative medicine applications may elongate telomeres and extend cellular life span while avoiding risks that are associated with retroviral or lentiviral vectors. In the present study, adenoviral delivery of pot1-TERT resulted in transient reconstitution of telomerase activity in human smooth muscle cells, as demonstrated by telomeric repeat amplification protocol (TRAP). In addition, human engineered vessels that were cultured using pot1-TERT-expressing cells had greater collagen content and somewhat better performance in vivo than control grafts. Hence, transient delivery of pot1-TERT to elderly human cells may be useful for increasing cellular life span and improving the functional characteristics of resultant tissue-engineered constructs.

Portable, Fiber-Based, Diffuse Reflection Spectroscopy (DRS) Systems for Estimating Tissue Optical Properties.

Steady-state diffuse reflection spectroscopy is a well-studied optical technique that can provide a noninvasive and quantitative method for characterizing the absorption and scattering properties of biological tissues. Here, we compare three fiber-based diffuse reflection spectroscopy systems that were assembled to create a light-weight, portable, and robust optical spectrometer that could be easily translated for repeated and reliable use in mobile settings. The three systems were built using a broadband light source and a compact, commercially available spectrograph. We tested two different light sources and two spectrographs (manufactured by two different vendors). The assembled systems were characterized by their signal-to-noise ratios, the source-intensity drifts, and detector linearity. We quantified the performance of these instruments in extracting optical properties from diffuse reflectance spectra in tissue-mimicking liquid phantoms with well-controlled optical absorption and scattering coefficients. We show that all assembled systems were able to extract the optical absorption and scattering properties with errors less than 10%, while providing greater than ten-fold decrease in footprint and cost (relative to a previously well-characterized and widely used commercial system). Finally, we demonstrate the use of these small systems to measure optical biomarkers in vivo in a small-animal model cancer therapy study. We show that optical measurements from the simple portable system provide estimates of tumor oxygen saturation similar to those detected using the commercial system in murine tumor models of head and neck cancer.

Ambient aerosol size distributions and number concentrations measured during the Pittsburgh Air Quality Study (PAQS)

Twelve months of aerosol size distributions from 3 to 560nm, measured using scanning mobility particle sizers are presented with an emphasis on average number, surface, and volume distributions, and seasonal and diurnal variation. The measurements were made at the main sampling site of the Pittsburgh Air Quality Study from July 2001 to June 2002. These are supplemented with 5 months of size distribution data from 0.5 to 2.5μm measured with a TSI aerosol particle sizer and 2 months of size distributions measured at an upwind rural sampling site. Measurements at the main site were made continuously under both low and ambient relative humidity. The average Pittsburgh number concentration (3-500nm) is 22,000cm-3 with an average mode size of 40nm. Strong diurnal patterns in number concentrations are evident as a direct effect of the sources of particles (atmospheric nucleation, traffic, and other combustion sources). New particle formation from homogeneous nucleation is significant on 30-50% of study days and over a wide area (at least a hundred kilometers). Rural number concentrations are a factor of 2-3 lower (on average) than the urban values. Average measured distributions are different from model literature urban and rural size distributions. © 2004 Elsevier Ltd. All rights reserved.

Diet-induced obesity alters the differentiation potential of stem cells isolated from bone marrow, adipose tissue and infrapatellar fat pad: the effects of free fatty acids.

INTRODUCTION: Obesity is a major risk factor for several musculoskeletal conditions that are characterized by an imbalance of tissue remodeling. Adult stem cells are closely associated with the remodeling and potential repair of several mesodermally derived tissues such as fat, bone and cartilage. We hypothesized that obesity would alter the frequency, proliferation, multipotency and immunophenotype of adult stem cells from a variety of tissues. MATERIALS AND METHODS: Bone marrow-derived mesenchymal stem cells (MSCs), subcutaneous adipose-derived stem cells (sqASCs) and infrapatellar fat pad-derived stem cells (IFP cells) were isolated from lean and high-fat diet-induced obese mice, and their cellular properties were examined. To test the hypothesis that changes in stem cell properties were due to the increased systemic levels of free fatty acids (FFAs), we further investigated the effects of FFAs on lean stem cells in vitro. RESULTS: Obese mice showed a trend toward increased prevalence of MSCs and sqASCs in the stromal tissues. While no significant differences in cell proliferation were observed in vitro, the differentiation potential of all types of stem cells was altered by obesity. MSCs from obese mice demonstrated decreased adipogenic, osteogenic and chondrogenic potential. Obese sqASCs and IFP cells showed increased adipogenic and osteogenic differentiation, but decreased chondrogenic ability. Obese MSCs also showed decreased CD105 and increased platelet-derived growth factor receptor α expression, consistent with decreased chondrogenic potential. FFA treatment of lean stem cells significantly altered their multipotency but did not completely recapitulate the properties of obese stem cells. CONCLUSIONS: These findings support the hypothesis that obesity alters the properties of adult stem cells in a manner that depends on the cell source. These effects may be regulated in part by increased levels of FFAs, but may involve other obesity-associated cytokines. These findings contribute to our understanding of mesenchymal tissue remodeling with obesity, as well as the development of autologous stem cell therapies for obese patients.

Convergent Surface Water Distributions in U.S. Cities

Earth's surface is rapidly urbanizing, resulting in dramatic changes in the abundance, distribution and character of surface water features in urban landscapes. However, the scope and consequences of surface water redistribution at broad spatial scales are not well understood. We hypothesized that urbanization would lead to convergent surface water abundance and distribution: in other words, cities will gain or lose water such that they become more similar to each other than are their surrounding natural landscapes. Using a database of more than 1 million water bodies and 1 million km of streams, we compared the surface water of 100 US cities with their surrounding undeveloped land. We evaluated differences in areal (A WB) and numeric densities (N WB) of water bodies (lakes, wetlands, and so on), the morphological characteristics of water bodies (size), and the density (D C) of surface flow channels (that is, streams and rivers). The variance of urban A WB, N WB, and D C across the 100 MSAs decreased, by 89, 25, and 71%, respectively, compared to undeveloped land. These data show that many cities are surface water poor relative to undeveloped land; however, in drier landscapes urbanization increases the occurrence of surface water. This convergence pattern strengthened with development intensity, such that high intensity urban development had an areal water body density 98% less than undeveloped lands. Urbanization appears to drive the convergence of hydrological features across the US, such that surface water distributions of cities are more similar to each other than to their surrounding landscapes. © 2014 The Author(s).