A particularly important case is fibrosis, a degenerative progressive disease in which connective tissue invades the intracellular matrix thus interrupting the intracellular space. Under healthy conditions during normal propagation there are no direct significant manifestations of microscopic discontinuities which would play a major role at the tissue and organ scale, however, when external electric fields are applied or when discontinuities become more pronounced as it may be the case under pathological conditions, conduction pathways at the microscopic size scale are altered to an extent which can cause noticeable effects at the macroscopic size scale as well. When viewed at a finer microscopic size scale though, cardiac tissue is a discrete medium in which electrical impulses propagate discontinuously. The validity of this assumption at a macroscopic size scale is supported by the successful application of macroscopic models such as the cardiac bidomain model, whose predictions are very well in line with experimental observations. Such models are built upon the assumption of an electric syncytium, that is, diffusive material properties of the tissue are continuous. Moreover, the method can be implemented in any standard continuous finite element code with minor effort.Ĭomputational modeling of cardiac electrophysiology at the tissue and organ scale relies mostly on continuum formulations which characterize emergent bioelectric phenomena such as wavefront propagation at a macroscopic size scale. Simulation results demonstrate that the dFE approach accounts for effects induced by microscopic size scale discontinuities, such as the formation of microscopic virtual electrodes, with vast computational savings as compared to high resolution continuous finite element models. In the dFE method this is achieved by imposing infinitely thin lines of electrical insulation along edges of finite elements which approximate the geometry of discontinuities in the intracellular matrix. In this study, a novel discontinuous finite element (dFE) approach for discretizing the bidomain equations is presented, which accounts for fine-scale structures in a computer model without the need to increase spatial resolution. Current state-of-the-art computer models built upon such datasets account for increasingly finer anatomical details, however, structural discontinuities at the paracellular level are typically discarded in the model generation process, owing to the significant costs which incur when using high resolutions for explicit representation. If you identify information that you believe to be incorrect or outdated, let us know.Advanced medical imaging technologies provide a wealth of information on cardiac anatomy and structure at a paracellular resolution, allowing to identify micro-structural discontinuities which disrupt the intracellular matrix. While CNN has attempted to clean this data, it may still contain errors. Employee totals, which the SBA refers to as “jobs retained,” refers to the number of employees as reported by the borrower and may not necessarily reflect the number of workers kept employed with PPP funds. Data for those and cancelled loans is not included in this database.īecause the SBA released loan amounts in ranges, date, business type, industry, state and county totals represent minimum estimates. Dollar amounts represent loan amounts approved by lenders and not necessarily the amount of money disbursed to businesses.įor loans worth less than $150,000, the SBA released anonymized data by state. This data represents about 13% of the 4.8 million loans and about 73% of the $521 billion approved under the PPP to date. The data in this database was published by the Small Business Administration (SBA) on Jand includes all approved, active Paycheck Protection Program (PPP) loans worth $150,000 or more. Email or, if you need to reach us securely, visit cnn.com/tips. Do you have information about the Paycheck Protection Program or any of the businesses or loans in this database? We’d like to hear from you.
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