In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of a finite element model. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques. The approach relies on a high-level symbolic representation of the forward problem. In contrast to developing a model directly in Fortran or C++, high-level systems allow the developer to express the variational problems to be solved in near-mathematical notation. As such, these systems have a key advantage: since the mathematical structure of the problem is preserved, they are more amenable to automated analysis and manipulation. The framework introduced here is implemented in a freely available software package named dolfin-adjoint, based on the FEniCS Project. Our approach to automated adjoint derivation relies on run-time annotation of the temporal structure of the model and employs the FEniCS finite element form compiler to automatically generate the low-level co...

Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs

Chiari Type I Malformation in a Pediatric Population

In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of finite element models. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques. The approach relies on a high-level symbolic representation of the forward problem. In contrast to developing a model directly in Fortran or C++, high-level systems allow the developer to express the variational problems to be solved in near-mathematical notation. As such, these systems have a key advantage: since the mathematical structure of the problem is preserved, they are more amenable to automated analysis and manipulation. The framework introduced here is implemented in a freely available software package named dolfin-adjoint, based on the FEniCS Project. Our approach to automated adjoint derivation relies on run-time annotation of the temporal structure of the model, and employs the FEniCS finite element form compiler to automatically generate the low-level code for the derived models. The approach requires only trivial changes to a large class of forward models, including complicated time-dependent nonlinear models. The adjoint model automatically employs optimal checkpointing schemes to mitigate storage requirements for nonlinear models, without any user management or intervention. Furthermore, both the tangent linear and adjoint models naturally work in parallel, without any need to differentiate through calls to MPI or to parse OpenMP directives. The generality, applicability and efficiency of the approach are demonstrated with examples from a wide range of scientific applications.

Automated derivation of the adjoint of high-level transient finite element programs

OBJECT Chiari malformation Type I (CM-I) is a hindbrain disorder associated with elongation of the cerebellar tonsils, which descend below the foramen magnum into the spinal canal. It occurs in children and adults. Clinical symptoms mainly develop from alterations in CSF flow at the foramen magnum and the common subsequent development of syringomyelia. METHODS The authors reviewed English-language reports of pediatric, adult, and combined (adult and pediatric) surgical series of patients with CM-I published from 1965 through August 31, 2013, to investigate the following: 1) geographical distribution of reports; 2) demographics of patients; 3) follow-up lengths; 4) study durations; 5) spectrum and frequency of surgical techniques; 6) outcomes for neurological status, syrinx, and headache; 7) frequency and scope of complications; 8) mortality rates; and 9) differences between pediatric and adult populations. Research and inclusion criteria were defined, and all series that contained at least 4 cases and all...

Pediatric and adult Chiari malformation Type I surgical series 1965–2013: a review of demographics, operative treatment, and outcomes

The pathogenesis of syringomyelia associated with lesions at the foramen magnum: a critical review of existing theories and proposal of a new hypothesis

Object. Syringomyelia causes progressive myelopathy. Most patients with syringomyelia have a Chiari I malformation of the cerebellar tonsils. Determination of the pathophysiological mechanisms underlying the progression of syringomyelia associated with the Chiari I malformation should improve strategies to halt progression of myelopathy. Methods. The authors prospectively studied 20 adult patients with both Chiari I malformation and symptomatic syringomyelia. Testing before surgery included the following: clinical examination; evaluation of anatomy by using T1-weighted magnetic resonance (MR) imaging; evaluation of the syrinx and cerebrospinal fluid (CSF) velocity and flow by using phase-contrast cine MR imaging; and evaluation of lumbar and cervical subarachnoid pressure at rest, during the Valsalva maneuver, during jugular compression, and following removal of CSF (CSF compliance measurement). During surgery, cardiac-gated ultrasonography and pressure measurements were obtained from the intracranial, ce...

Elucidating the pathophysiology of syringomyelia

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Elucidating the pathophysiology of syringomyelia

Elucidating the pathophysiology of syringomyelia