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NASA NTRS2004

Progress in Low-Power Digital Microwave Radiometer Technologies

Three component technologies were combined into a digital correlation microwave radiometer. The radiometer comprises a dual-channel X-band superheterodyne receiver, low-power high-speed cross-correlator (HSCC), three-level ADCs, and a correlated noise source (CNS). The HSCC dissipates 10 mW and operates at 500 MHz clock speed. The ADCs are implemented using ECL components and dissipate more power than desired. Thus, a low-power ADC development is underway. The new ADCs arc predicted to dissipated less than 200 mW and operate at 1 GSps with 1.5 GHz of input bandwidth. The CNS provides different input correlation values for calibration of the radiometer. The correlation channel had a null offset of 0.0008. Test results indicate that the correlation channel can be calibrated with 0.09% error in gain.

Piepmeier, Jeffrey R.↗

NASA NTRS2003

Coordinated turn-and-reach movements. I. Anticipatory compensation for self-generated coriolis and interaction torques

When reaching movements involve simultaneous trunk rotation, additional interaction torques are generated on the arm that are absent when the trunk is stable. To explore whether the CNS compensates for such self-generated interaction torques, we recorded hand trajectories in reaching tasks involving various amplitudes and velocities of arm extension and trunk rotation. Subjects pointed to three targets on a surface slightly above waist level. Two of the target locations were chosen so that a similar arm configuration relative to the trunk would be required for reaching to them, one of these targets requiring substantial trunk rotation, the other very little. Significant trunk rotation was necessary to reach the third target, but the arm's radial distance to the body remained virtually unchanged. Subjects reached at two speeds-a natural pace (slow) and rapidly (fast)-under normal lighting and in total darkness. Trunk angular velocity and finger velocity relative to the trunk were higher in the fast conditions but were not affected by the presence or absence of vision. Peak trunk velocity increased with increasing trunk rotation up to a maximum of 200 degrees /s. In slow movements, peak finger velocity relative to the trunk was smaller when trunk rotation was necessary to reach the targets. In fast movements, peak finger velocity was approximately 1.7 m/s for all targets. Finger trajectories were more curved when reaching movements involved substantial trunk rotation; however, the terminal errors and the maximal deviation of the trajectory from a straight line were comparable in slow and fast movements. This pattern indicates that the larger Coriolis, centripetal, and inertial interaction torques generated during rapid reaches were compensated by additional joint torques. Trajectory characteristics did not vary with the presence or absence of vision, indicating that visual feedback was unnecessary for anticipatory compensations. In all reaches involving trunk rotation, the finger movement generally occurred entirely during the trunk movement, indicating that the CNS did not minimize Coriolis forces incumbent on trunk rotation by sequencing the arm and trunk motions into a turn followed by a reach. A simplified model of the arm/trunk system revealed that additional interaction torques generated on the arm during voluntary turning and reaching were equivalent to < or =1.8 g (1 g = 9.81 m/s(2)) of external force at the elbow but did not degrade performance. In slow-rotation room studies involving reaching movements during passive rotation, Coriolis forces as small as 0.2 g greatly deflect movement trajectories and endpoints. We conclude that compensatory motor innervations are engaged in a predictive fashion to counteract impending self-generated interaction torques during voluntary reaching movements.

NASA Discipline Neuroscience↗

NASA NTRS2002

Drosophila atonal fully rescues the phenotype of Math1 null mice: new functions evolve in new cellular contexts

Many genes share sequence similarity between species, but their properties often change significantly during evolution. For example, the Drosophila genes engrailed and orthodenticle and the onychophoran gene Ultrabithorax only partially substitute for their mouse or Drosophila homologs. We have been analyzing the relationship between atonal (ato) in the fruit fly and its mouse homolog, Math1. In flies, ato acts as a proneural gene that governs the development of chordotonal organs (CHOs), which serve as stretch receptors in the body wall and joints and as auditory organs in the antennae. In the fly CNS, ato is important not for specification but for axonal arborization. Math1, in contrast, is required for the specification of cells in both the CNS and the PNS. Furthermore, Math1 serves a role in the development of secretory lineage cells in the gut, a function that does not parallel any known to be served by ato. We wondered whether ato and Math1 might be more functionally homologous than they appear, so we expressed Math1 in ato mutant flies and ato in Math1 null mice. To our surprise, the two proteins are functionally interchangeable.

Non-NASA Center↗

NASA NTRS2001

Monoclonal L-citrulline immunostaining reveals nitric oxide-producing vestibular neurons

Nitric oxide is an unstable free radical that serves as a novel messenger molecule in the central nervous system (CNS). In order to understand the interplay between classic and novel chemical communication systems in vestibular pathways, the staining obtained using a monoclonal antibody directed against L-citrulline was compared with the labeling observed using more traditional markers for the presence of nitric oxide. Brainstem tissue from adult rats was processed for immunocytochemistry employing a monoclonal antibody directed against L-citrulline, a polyclonal antiserum against neuronal nitric oxide synthase, and/or NADPH-diaphorase histochemistry. Our findings demonstrate that L-citrulline can be fixed in situ by vascular perfusion, and can be visualized in fixed CNS tissue sections by immunocytochemistry. Further, the same vestibular regions and cell types are labeled by NADPH-diaphorase histochemistry, by the neuronal nitric oxide synthase antiserum, and by our anti-L-citrulline antibody. Clusters of L-citrulline-immunoreactive neurons are present in subregions of the vestibular nuclei, including the caudal portion of the inferior vestibular nucleus, the magnocellular portion of the medial vestibular nucleus, and the large cells in the ventral tier of the lateral vestibular nucleus. NADPH-diaphorase histochemical staining of these neurons clearly demonstrated their multipolar, fusiform and globular somata and long varicose dendritic processes. These results provide support for the suggestion that nitric oxide serves key roles in both vestibulo-autonomic and vestibulo-spinal pathways.

NASA Discipline Neuroscience↗

NASA NTRS2004

Fourth Integrated Communications, Navigation, and Surveillance (ICNS) Conference and Workshop 2004: Conclusions and Recommendations

The NASA Glenn Research Center organized and hosted the Fourth Integrated Communications, Navigation, and Surveillance (ICNS) Technologies Conference and Workshop, which took place April 26-30, 2004 at the Hyatt Fair Lakes Hotel in Fairfax, Virginia. This fourth conference of the annual series followed the very successful first ICNS Conference (May 1-3, 2001 in Cleveland, Ohio), second ICNS conference (April 29-May 2, 2002 in Vienna, Virginia), and third ICNS conference (May 19-22, 2003 in Annapolis, Maryland). The purpose of the Fourth ICNS Conference was to assemble government, industry and academic communities performing research and development for advanced digital communications, surveillance and navigation systems and associated applications supporting the national and global air transportation systems to: 1) Understand current efforts and recent results in near- and far-term R&D and technology demonstration; 2) Identify integrated digital communications, navigation and surveillance R&D requirements necessary for a safe, secure and reliable, high-capacity, advanced air transportation system; 3) Provide a forum for fostering collaboration and coordination; and 4) Discuss critical issues and develop recommendations to achieve the future integrated CNS vision for national and global air transportation. The workshop attracted 316 attendees from government, industry and academia to address these purposes through technical presentations, breakout sessions, and individual and group discussions during the workshop and after-hours events, and included 16 international attendees. An Executive Committee consisting of representatives of several key segments of the aviation community concerned with CNS issues met on the day following the workshop to consider the primary outcomes and recommendations of the workshop. This report presents an overview of the conference, workshop breakout session results, and the findings of the Executive Committee.

Phillips, Brent↗

NASA NTRS2004

Frequency Spectrum for New Aviation Data Links: Initial Study Results

We describe results from an initial study to assess the suitability of various spectral bands for supporting the deployment of new aviation data links (ADL). The study focused on systems and spectral bands that can deliver VHF data link (VDL)-or-higher data rates in a two-way communication setting, including air-ground, ground-air, and air-air modes of operation. In the first part of our paper, we briefly discuss the current situation regarding communications, navigation, and surveillance (CNS) links and existing spectrum, and the well-known need for new aviation data links. We next provide an overview of related systems, and discuss key factors involved in the use of spectrum in various bands for any future integrated CNS data link, addressing primarily the lower few layers of the communications protocol stack. Desired attributes of a new ADL system are discussed, and the beneficial aspects of a particular transmission technique spread spectrum are summarized. We also provide a short list of several example potential spectral regions, and note that while none of the existing systems will likely meet the full range of desired features of a new ADL, several systems and spectral regions offer promise in terms of one or more characteristics. A detailed discussion and evaluation of these spectral regions is proposed as future work. We include a few brief examples to illustrate initial technical results regarding spread spectrum overlay, also a subject for future work.

Matolak, David W.↗

NASA NTRS1998

Role of heat shock protein Hsp25 in the response of the orofacial nuclei motor system to physiological stress

Although expression of the small heat shock protein family member Hsp25 has been previously observed in the central nervous system (CNS), both constitutively and upon induction, its function in the CNS remains far from clear. In the present study we have characterized the spatial pattern of expression of Hsp25 in the normal adult mouse brain as well as the changes in expression patterns induced by subjecting mice to experimental hyperthermia or hypoxia. Immunohistochemical analysis revealed a surprisingly restricted pattern of constitutive expression of Hsp25 in the brain, limited to the facial, trigeminal, ambiguus, hypoglossal and vagal motor nuclei of the brainstem. After hyperthermia or hypoxia treatment, significant increases in the levels of Hsp25 were observed in these same areas and also in fibers of the facial and trigeminal nerve tracts. Immunoblot analysis of protein lysates from brainstem also showed the same pattern of induction of Hsp25. Surprisingly, no other area in the brain showed expression of Hsp25, in either control or stressed animals. The highly restricted expression of Hsp25 implies that this protein may have a specific physiological role in the orofacial motor nuclei, which govern precise coordination between muscles of mastication and the pharynx, larynx, and face. Its rapid induction after stress further suggests that Hsp25 may serve as a specific molecular chaperone in the lower cholinergic motor neurons and along their fibers under conditions of stress or injury. Copyright 1998 Elsevier Science B.V.

Non-NASA Center↗

NASA NTRS1996

Transneuronal pathways to the vestibulocerebellum

The alpha-herpes virus (pseudorabies, PRV) was used to observe central nervous system (CNS) pathways associated with the vestibulocerebellar system. Retrograde transneuronal migration of alpha-herpes virions from specific lobules of the gerbil and rat vestibulo-cerebellar cortex was detected immunohistochemically. Using a time series analysis, progression of infection along polyneuronal cerebellar afferent pathways was examined. Pressure injections of > 20 nanoliters of a 10(8) plaque forming units (pfu) per ml solution of virus were sufficient to initiate an infectious locus which resulted in labeled neurons in the inferior olivary subnuclei, vestibular nuclei, and their afferent cell groups in a progressive temporal fashion and in growing complexity with increasing incubation time. We show that climbing fibers and some other cerebellar afferent fibers transported the virus retrogradely from the cerebellum within 24 hours. One to three days after cerebellar infection discrete cell groups were labeled and appropriate laterality within crossed projections was preserved. Subsequent nuclei labeled with PRV after infection of the flocculus/paraflocculus, or nodulus/uvula, included the following: vestibular (e.g., z) and inferior olivary nuclei (e.g., dorsal cap), accessory oculomotor (e.g., Darkschewitsch n.) and accessory optic related nuclei, (e.g., the nucleus of the optic tract, and the medial terminal nucleus); noradrenergic, raphe, and reticular cell groups (e.g., locus coeruleus, dorsal raphe, raphe pontis, and the lateral reticular tract); other vestibulocerebellum sites, the periaqueductal gray, substantia nigra, hippocampus, thalamus and hypothalamus, amygdala, septal nuclei, and the frontal, cingulate, entorhinal, perirhinal, and insular cortices. However, there were differences in the resulting labeling between infection in either region. Double-labeling experiments revealed that vestibular efferent neurons are located adjacent to, but are not included among, flocculus-projecting supragenual neurons. PRV transport from the vestibular labyrinth and cervical muscles also resulted in CNS infections. Virus propagation in situ provides specific connectivity information based on the functional transport across synapses. The findings support and extend anatomical data regarding vestibulo-olivo-cerebellar pathways.

NASA Discipline Neuroscience↗

NASA NTRS1992

Recovery of postural equilibrium control following spaceflight

Decreased postural stability is observed in most astronauts immediately following spaceflight. Because ataxia may present postflight operational hazards, it is important to determine the incidence of postural instability immediately following landing and the dynamics of recovery of normal postural equilibrium control. It is postulated that postflight postural instability results from in-flight adaptive changes in central nervous system (CNS) processing of sensory information from the visual, vestibular, and proprioceptive systems. The purpose of the present investigation was to determine the magnitude and time course of postflight recovery of postural equilibrium control and, hence, readaptation of CNS processing of sensory information. Thirteen crew members from six spaceflight missions were studied pre- and postflight using a modified commercial posturography system. Postural equilibrium control was found to be seriously disrupted immediately following spaceflight in all subjects. Readaptation to the terrestrial environment began immediately upon landing, proceeded rapidly for the first 10-12 hours, and then proceeded much more slowly for the subsequent 2-4 days until preflight stability levels were reachieved. It is concluded that the overall postflight recovery of postural stability follows a predictable time course.

NASA Discipline Neuroscience↗

NASA NTRS2005

Development and Function of the Mouse Vestibular System in the Absence of Gravity Perception

The hypothesis that was tested in this research was that the absence of gravity perception, such as would occur in space, would affect the development and function of the vestibular and central nervous systems. Further, we postulated that these effects would be more significant at specific stages of post-natal development of the animal. We also proposed the use of molecular genetic approaches that would provide important information as to the hierarchy of gene function during the development and subsequent function of the vestibular system. The tilted (tlt) mutant mouse has been characterized as lacking the ability to provide sensory input to the gravity receptors. The tlt/tlt mutant mice were a particularly attractive model for the study of vestibular function since the primary defect was limited to the receptor part of the vestibular system, and there were no detectable abnormal phenotypes in other organ systems. The goal of the proposed studies was to assess immediate and delayed effects of the lack of gravity perception on the vestibular system. Particular attention was paid to characterizing primarily affected periods of vestibular morphogenesis, and to identifying downstream genetic pathways that are altered in the CNS of the tlt/tlt mutant mouse. The specific aims were: (1) to characterize the postnatal morphogenesis of the CNS in the tlt mutant mouse, using detailed morphometric analysis of isolated vestibular ganglia and brain tissue at different stages of postnatal development and assessment of apoptotic cell death; (2) to examine the expression of selected genes implicated by mutational analysis to be important in vestibular development or function by in situ hybridization or immunohistochemistry in the mutant mice; and (3) to identify other genes involved in vestibular development and function, using differential cloning strategies to isolate genes whose expression is changed in the mutant versus normal vestibular system.

Wolgemuth, Debra J.↗

NASA NTRS2005

NASA's Proposed Requirements for the Global Aeronautical Network and a Summary of Responses

In October 2003, NASA embarked on the ACAST project (Advanced CNS Architectures and System Technologies) to perform research and development on selected communications, navigation, and surveillance (CNS) technologies to enhance the performance of the National Airspace System (NAS). The Networking Research Group of NASA's ACAST project, in order to ensure global interoperability and deployment, formulated their own salient list of requirements. Many of these are not necessarily of concern to the FAA, but are a concern to those who have to deploy, operate, and pay for these systems. These requirements were submitted to the world s industries, governments, and academic institutions for comments. The results of that request for comments are summarized in this paper.

Ivancic, William D.↗

NASA NTRS2004

Sensory-Motor Adaptation to Space Flight: Human Balance Control and Artificial Gravity

Gravity, which is sensed directly by the otolith organs and indirectly by proprioceptors and exteroceptors, provides the CNS a fundamental reference for estimating spatial orientation and coordinating movements in the terrestrial environment. The sustained absence of gravity during orbital space flight creates a unique environment that cannot be reproduced on Earth. Loss of this fundamental CNS reference upon insertion into orbit triggers neuro-adaptive processes that optimize performance for the microgravity environment, while its reintroduction upon return to Earth triggers neuro-adaptive processes that return performance to terrestrial norms. Five pioneering symposia on The Role of the Vestibular Organs in the Exploration of Space were convened between 1965 and 1970. These innovative meetings brought together the top physicians, physiologists, and engineers in the vestibular field to discuss and debate the challenges associated with human vestibular system adaptation to the then novel environment of space flight. These highly successful symposia addressed the perplexing problem of how to understand and ameliorate the adverse physiological effects on humans resulting from the reduction of gravitational stimulation of the vestibular receptors in space. The series resumed in 2002 with the Sixth Symposium, which focused on the microgravity environment as an essential tool for the study of fundamental vestibular functions. The three day meeting included presentations on historical perspectives, vestibular neurobiology, neurophysiology, neuroanatomy, neurotransmitter systems, theoretical considerations, spatial orientation, psychophysics, motor integration, adaptation, autonomic function, space motion sickness, clinical issues, countermeasures, and rehabilitation. Scientists and clinicians entered into lively exchanges on how to design and perform mutually productive research and countermeasure development projects in the future. The problems posed by long duration missions dominated these discussions and were driven by the paucity of data available. These issues along with more specific recommendations arising from the above discussions will be addressed an upcoming issue of the Journal of Vestibular Research.

Paloski, William H.↗

NASA NTRS2005

Proceedings of the Fifth Integrated Communications, Navigation, and Surveillance (ICNS) Conference and Workshop

Contents includes papers on the following: JPDO: Inter-Agency Cooperation for the Next Generation ATS; R&T Programs; Integrated CNS Systems and Architectures; Datalink Communication Systems; Navigation, System Demonstrations and Operations; Safety and Security Initiatives Impacting CNS; Global Communications Initiatives; Airborne Internet; Avionics for System-Level Enhancements; SWIM (System Wide Information Management); Weather Products and Data Dissemination Technologies; Airsapce Communication Networks; Surveillance Systems; Workshop Breakouts Sessions and ; ICNS Conference Information.

Fujikawa, Gene↗

NASA NTRS2006

Space Radiation

Astronauts receive the highest occupational radiation exposure. Effective protections are needed to ensure the safety of astronauts on long duration space missions. Increased cancer morbidity or mortality risk in astronauts may be caused by occupational radiation exposure. Acute and late radiation damage to the central nervous system (CNS) may lead to changes in motor function and behavior, or neurological disorders. Radiation exposure may result in degenerative tissue diseases (non-cancer or non-CNS) such as cardiac, circulatory, or digestive diseases, as well as cataracts. Acute radiation syndromes may occur due to occupational radiation exposure.

Wu, Honglu↗

NASA NTRS2006

Development of a Countermeasure to Mitigate Postflight Locomotor Dysfunction

Astronauts returning from space flight experience locomotor dysfunction following their return to Earth. Our laboratory is currently developing a gait adaptability training program that is designed to facilitate recovery of locomotor function following a return to a gravitational environment. The training program exploits the ability of the sensorimotor system to generalize from exposure to multiple adaptive challenges during training so that the gait control system essentially learns to learn and therefore can reorganize more rapidly when faced with a novel adaptive challenge. Evidence for the potential efficacy of an adaptive generalization gait training program can be obtained from numerous studies in the motor learning literature which have demonstrated that systematically varying the conditions of training enhances the ability of the performer to learn and retain a novel motor task. These variable practice training approaches have been used in applied contexts to improve motor skills required in a number of different sports. The central nervous system (CNS) can produce voluntary movement in an almost infinite number of ways. For example, locomotion can be achieved with many different combinations of joint angles, muscle activation patterns and forces. The CNS can exploit these degrees of freedom to enhance motor response adaptability during periods of adaptive flux like that encountered during a change in gravitational environment. Ultimately, the functional goal of an adaptive generalization countermeasure is not necessarily to immediately return movement patterns back to normal. Rather the training regimen should facilitate the reorganization of available sensory and motor subsystems to achieve safe and effective locomotion as soon as possible after long duration space flight. Indeed, this approach has been proposed as a basic feature underlying effective neurological rehabilitation. We have previously confirmed that subjects participating in an adaptive generalization training program using a variety of visuomotor distortions and throwing as the dependent measure can learn to enhance their ability to adapt to a novel sensorimotor environment (Roller et al., 2001). Importantly, this increased adaptability was retained even one month after completion of the training period. Adaptive generalization has been observed in a variety of other tasks requiring sensorimotor transformations including manual control tasks and reaching (Bock et al., 2001, Seidler, 2003) and obstacle avoidance during walking (Lam and Dietz, 2004). Taken together, the evidence suggests that a training regimen exposing crewmembers to variation in locomotor conditions, with repeated transitions among states, may enhance their ability to learn how to reassemble appropriate locomotor patterns upon return from microgravity. We believe exposure to this type of training will extend crewmembers locomotor behavioral repertoires, facilitating the return of functional mobility after long duration space flight. In other words, our proposed training protocol will compel subjects to develop new behavioral solutions under varying sensorimotor demands. Over time subjects will learn to create appropriate locomotor solution more rapidly enabling acquisition of mobility sooner after long-duration space flight. A gait adaptability training program can be superimposed on nominal treadmill exercise activities thus ensuring that no additional crew time is required to perform this type of training regimen and that it can be implemented with current in-flight exercise systems available on the International Space Station.

Bloomberg, J. J.↗

NASA NTRS2009

Space Flight and Manual Control: Implications for Sensorimotor Function on Future Missions

Control of vehicles, and other complex mechanical motion systems, is a high-level integrative function of the central nervous system (CNS) that requires good visual acuity, eye-hand coordination, spatial (and, in some cases, geographic) orientation perception, and cognitive function. Existing evidence from space flight research (Paloski et.al., 2008, Clement and Reschke 2008, Reschke et al., 2007) demonstrates that the function of each of these systems is altered by removing (and subsequently by reintroducing) a gravitational field that can be sensed by vestibular, proprioceptive, and haptic receptors and used by the CNS for spatial orientation, navigation, and coordination of movements. Furthermore, much of the operational performance data collected as a function of space flight has not been available for independent analysis, and those data that have been reviewed are equivocal owing to uncontrolled environmental and/or engineering factors. Thus, our current understanding, when it comes to manual control, is limited primarily to a review of those situations where manual control has been a factor. One of the simplest approaches to the manual control problem is to review shuttle landing data. See the Figure below for those landing for which we have Shuttle velocities over the runway threshold.

Reschke, Millard F.↗

NASA NTRS2009

Development of a GCR Event-based Risk Model

A goal at NASA is to develop event-based systems biology models of space radiation risks that will replace the current dose-based empirical models. Complex and varied biochemical signaling processes transmit the initial DNA and oxidative damage from space radiation into cellular and tissue responses. Mis-repaired damage or aberrant signals can lead to genomic instability, persistent oxidative stress or inflammation, which are causative of cancer and CNS risks. Protective signaling through adaptive responses or cell repopulation is also possible. We are developing a computational simulation approach to galactic cosmic ray (GCR) effects that is based on biological events rather than average quantities such as dose, fluence, or dose equivalent. The goal of the GCR Event-based Risk Model (GERMcode) is to provide a simulation tool to describe and integrate physical and biological events into stochastic models of space radiation risks. We used the quantum multiple scattering model of heavy ion fragmentation (QMSFRG) and well known energy loss processes to develop a stochastic Monte-Carlo based model of GCR transport in spacecraft shielding and tissue. We validated the accuracy of the model by comparing to physical data from the NASA Space Radiation Laboratory (NSRL). Our simulation approach allows us to time-tag each GCR proton or heavy ion interaction in tissue including correlated secondary ions often of high multiplicity. Conventional space radiation risk assessment employs average quantities, and assumes linearity and additivity of responses over the complete range of GCR charge and energies. To investigate possible deviations from these assumptions, we studied several biological response pathway models of varying induction and relaxation times including the ATM, TGF -Smad, and WNT signaling pathways. We then considered small volumes of interacting cells and the time-dependent biophysical events that the GCR would produce within these tissue volumes to estimate how GCR event rates mapped to biological signaling induction and relaxation times. We considered several hypotheses related to signaling and cancer risk, and then performed simulations for conditions where aberrant or adaptive signaling would occur on long-duration space mission. Our results do not support the conventional assumptions of dose, linearity and additivity. A discussion on how event-based systems biology models, which focus on biological signaling as the mechanism to propagate damage or adaptation, can be further developed for cancer and CNS space radiation risk projections is given.

Cucinotta, Francis A.↗

NASA NTRS2009

Detection of presence of chemical precursors

Methods and systems for determining if one or more target molecules are present in a gas, by exposing a functionalized carbon nanostructure (CNS) to the gas and measuring an electrical parameter value EPV(n) associated with each of N CNS sub-arrays. In a first embodiment, a most-probable concentration value C(opt) is estimated, and an error value, depending upon differences between the measured values EPV(n) and corresponding values EPV(n;C(opt)) is computed. If the error value is less than a first error threshold value, the system interprets this as indicating that the target molecule is present in a concentration C.apprxeq.C(opt). A second embodiment uses extensive statistical and vector space analysis to estimate target molecule concentration.

Li, Jing↗