Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics.

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we develop efficient strategies to nonuniformly sample observational data. We also investigate different approaches to enforce Dirichlet-type boundary conditions (BCs) as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.

Frequency-dependent changes in cerebral blood flow and evoked potentials during somatosensory stimulation in the rat.

Contrary to the concept of neuronal-vascular coupling, cortical evoked potentials do not always correlate with blood flow responses during somatosensory stimulation at changing stimulus rates. The goal of this study is to clarify the effects of stimulus frequency on the relationship between somatosensory evoked potentials (SEPs) and cerebral blood flow. In rats anesthetized with alpha-chloralose, we measured SEPs by signal-averaging field potentials recorded with an electrode placed on dura overlying the hindlimb somatosensory cortex. Regional blood flow was simultaneously assessed in the same region with a laser-Doppler flow (LDF) probe. The contralateral sciatic nerve was stimulated with 0.1 A pulses at the frequencies of 1, 2, 5, 10 and 20 Hz. SEPs (both P1 and N1 components) declined with increasing frequency regardless whether stimulus duration (20 s) or number (100) were kept constant, suggesting that frequency is an important determinant of neuronal activity. In contrast, LDF responses increased to a maximum at 5 Hz, and do not correlate with SEPs. Because CBF should reflect integrated neuronal activity, we computed the sum of SEPS (summation operatorSEP = SEP x stimulus frequency) as an index of total neuronal activity at each frequency. Summation operatorSEP indeed correlates positively (P<0.001) with LDF responses. Thus, during somatosensory stimulation at various frequencies, cerebral blood flow is coupled to integrated neuronal activity but not to averaged evoked potentials.

Suppression of somatosensory evoked potentials by nitric oxide synthase inhibition in rats: methodological differences.

We have previously shown that topically applied N(G)-nitro-L-arginine (L-NNA), a nitric oxide synthase (NOS) inhibitor, suppressed both somatosensory evoked potentials (SEPs) and vascular responses during sciatic nerve stimulation in rats. Due to the normal tight coupling between cerebral blood flow and neuronal activity, we surmise that the vascular response attenuation may be secondary to the SEP decrease. However, a recent study, in which SEPs were recorded with a 'non-contact' electrode placed longitudinally across the cranial window without touching the cortex, did not find a SEP decrease following NOS inhibition. In the present study, we compared SEPs recorded with 'contact' and 'non-contact' electrodes. Regardless of stimulation methods (sciatic nerve or hindpaw), an electrode in contact with the pial surface overlying the hindlimb somatosensory cortex recorded a steady SEP decline during I-NNA application. In contrast, a 'non-contact' electrode did not detect a significant SEP change in the presence of I-NNA. The present results thus confirm the attenuation of SEPs by NOS inhibition.