Multi-parametric cell profiling with a CMOS quad-modality cellular interfacing array for label-free fully automated drug screening

A Multi-Functional CMOS Biosensor Array With On-Chip DEP-Assisted Sensing for Rapid Low-Concentration Analyte Detection and Close-Loop Particle Manipulation With No External Electrodes

This article presents a fully-integrated dielectrophoresis (DEP)-assisted multi-functional CMOS biosensor array chip with 4096 working electrodes (WEs), 12288 photodiodes (PDs), reference electrodes (REs), and counter electrodes (CEs), while each WE and photodiode can be reconfigured to support on-chip DEP actuation, electrochemical potentiostat, optical shadow imaging, and complex impedance sensing. The proposed CMOS biosensor is an example of an actuation-assisted label-free biosensor for the rapid sensing of low-concentration analytes. The DEP actuator of the proposed CMOS biosensor does not require any external electrode. Instead, on-chip WE pairs can be re-used for DEP actuation to simplify the sensor array design. The CMOS biosensor is implemented in a standard 130-nm BiCMOS process. Theoretical analyses and finite element method (FEM) simulations of the on-chip DEP operations are conducted as proof of concept. Biological assay measurements (DEP actuation/electrochemical potentiostat/impedance sensing) with E.coli bacteria and microbeads (optical shadow imaging) demonstrate rapid detection of low-concentration analytes and simultaneous manipulation and detection of large particles. The on-chip DEP operations draw the analytes closer to the sensor electrode surface, which overcomes the diffusion limit and accelerates low-concentration analyte sensing. Moreover, the DEP-based movement of large particles can be readily detected by on-chip photodiode arrays to achieve close-loop manipulation and sensing of particles and droplets. These show the unique advantages of the DEP-assisted multi-functional biosensor.

A semiconductor 96-microplate platform for electrical-imaging based high-throughput phenotypic screening

High-content imaging for compound and genetic profiling is popular for drug discovery but limited to endpoint images of fixed cells. Conversely, electronic-based devices offer label-free, live cell functional information but suffer from limited spatial resolution or throughput. Here, we introduce a semiconductor 96-microplate platform for high-resolution, real-time impedance imaging. Each well features 4096 electrodes at 25 µm spatial resolution and a miniaturized data interface allows 8× parallel plate operation (768 total wells) for increased throughput. Electric field impedance measurements capture >20 parameter images including cell barrier, attachment, flatness, and motility every 15 min during experiments. We apply this technology to characterize 16 cell types, from primary epithelial to suspension cells, and quantify heterogeneity in mixed co-cultures. Screening 904 compounds across 13 semiconductor microplates reveals 25 distinct responses, demonstrating the platform's potential for mechanism of action profiling. The scalability and translatability of this semiconductor platform expands high-throughput mechanism of action profiling and phenotypic drug discovery applications.

A semiconductor 96-microplate platform for electrical-imaging based high-throughput phenotypic screening

Profiling compounds and genetic perturbations via high-content imaging has become increasingly popular for drug discovery, but the technique is limited to endpoint images of fixed cells. In contrast, electronic-based devices offer label-free, functional information of live cells, yet current approaches suffer from low-spatial resolution or single-well throughput. Here, we report a semiconductor 96-microplate platform designed for high-resolution real-time impedance "imaging" at scale. Each well features 4,096 electrodes at 25 µm spatial resolution while a miniaturized data interface allows 8× parallel plate operation (768 total wells) within each incubator for enhanced throughputs. New electric field-based, multi-frequency measurement techniques capture >20 parameter images including tissue barrier, cell-surface attachment, cell flatness, and motility every 15 min throughout experiments. Using these real-time readouts, we characterized 16 cell types, ranging from primary epithelial to suspension, and quantified heterogeneity in mixed epithelial and mesenchymal co-cultures. A proof-of-concept screen of 904 diverse compounds using 13 semiconductor microplates demonstrates the platform's capability for mechanism of action (MOA) profiling with 25 distinct responses identified. The scalability of the semiconductor platform combined with the translatability of the high dimensional live-cell functional parameters expands high-throughput MOA profiling and phenotypic drug discovery applications.

The next generation of hybrid microfluidic/integrated circuit chips: recent and upcoming advances in high-speed, high-throughput, and multifunctional lab-on-IC systems

Since the field's inception, pioneers in microfluidics have made significant progress towards realizing complete lab-on-chip systems capable of sophisticated sample analysis and processing. One avenue towards this goal has been to join forces with the related field of microelectronics, using integrated circuits (ICs) to perform on-chip actuation and sensing. While early demonstrations focused on using microfluidic-IC hybrid chips to miniaturize benchtop instruments, steady advancements in the field have enabled a new generation of devices that expand past miniaturization into high-performance applications that would not be possible without IC hybrid integration. In this review, we identify recent examples of labs-on-chip that use high-resolution, high-speed, and multifunctional electronic and photonic chips to expand the capabilities of conventional sample analysis. We focus on three particularly active areas: a) high-throughput integrated flow cytometers; b) large-scale microelectrode arrays for stimulation and multimodal sensing of cells over a wide field of view; c) high-speed biosensors for studying molecules with high temporal resolution. We also discuss recent advancements in IC technology, including on-chip data processing techniques and lens-free optics based on integrated photonics, that are poised to further advance microfluidic-IC hybrid chips.

A Multimodal and Multifunctional CMOS Cellular Interfacing Array for Digital Physiology and Pathology Featuring an Ultra Dense Pixel Array and Reconfigurable Sampling Rate

The article presents a fully integrated multimodal and multifunctional CMOS biosensing/actuating array chip and system for multi-dimensional cellular/tissue characterization. The CMOS chip supports up to 1,568 simultaneous parallel readout channels across 21,952 individually addressable multimodal pixels with 13 μm × 13 μm 2-D pixel pitch along with 1,568 Pt reference electrodes. These features allow the CMOS array chip to perform multimodal physiological measurements on living cell/tissue samples with both high throughput and single-cell resolution. Each pixel supports three sensing and one actuating modalities, each reconfigurable for different functionalities, in the form of full array (FA) or fast scan (FS) voltage recording schemes, bright/dim optical detection, 2-/4-point impedance sensing (ZS), and biphasic current stimulation (BCS) with adjustable stimulation area for single-cell or tissue-level stimulation. Each multi-modal pixel contains an 8.84 μm × 11 μm Pt electrode, 4.16 μm × 7.2 μm photodiode (PD), and in-pixel circuits for PD measurements and pixel selection. The chip is fabricated in a standard 130nm BiCMOS process as a proof of concept. The on-chip electrodes are constructed by unique design and in-house post-CMOS fabrication processes, including a critical Al shorting of all pixels during fabrication and Al etching after fabrication that ensures a high-yield planar electrode array on CMOS with high biocompatibility and long-term measurement reliability. For demonstration, extensive biological testing is performed with human and mouse progenitor cells, in which multidimensional biophysiological data are acquired for comprehensive cellular characterization.

Advances in non-invasive biosensing measures to monitor wound healing progression

Impaired wound healing is a significant financial and medical burden. The synthesis and deposition of extracellular matrix (ECM) in a new wound is a dynamic process that is constantly changing and adapting to the biochemical and biomechanical signaling from the extracellular microenvironments of the wound. This drives either a regenerative or fibrotic and scar-forming healing outcome. Disruptions in ECM deposition, structure, and composition lead to impaired healing in diseased states, such as in diabetes. Valid measures of the principal determinants of successful ECM deposition and wound healing include lack of bacterial contamination, good tissue perfusion, and reduced mechanical injury and strain. These measures are used by wound-care providers to intervene upon the healing wound to steer healing toward a more functional phenotype with improved structural integrity and healing outcomes and to prevent adverse wound developments. In this review, we discuss bioengineering advances in 1) non-invasive detection of biologic and physiologic factors of the healing wound, 2) visualizing and modeling the ECM, and 3) computational tools that efficiently evaluate the complex data acquired from the wounds based on basic science, preclinical, translational and clinical studies, that would allow us to prognosticate healing outcomes and intervene effectively. We focus on bioelectronics and biologic interfaces of the sensors and actuators for real time biosensing and actuation of the tissues. We also discuss high-resolution, advanced imaging techniques, which go beyond traditional confocal and fluorescence microscopy to visualize microscopic details of the composition of the wound matrix, linearity of collagen, and live tracking of components within the wound microenvironment. Computational modeling of the wound matrix, including partial differential equation datasets as well as machine learning models that can serve as powerful tools for physicians to guide their decision-making process are discussed.

Impedance Imaging of Cells and Tissues: Design and Applications

Due to their label-free and noninvasive nature, impedance measurements have attracted increasing interest in biological research. Advances in microfabrication and integrated-circuit technology have opened a route to using large-scale microelectrode arrays for real-time, high-spatiotemporal-resolution impedance measurements of biological samples. In this review, we discuss different methods and applications of measuring impedance for cell and tissue analysis with a focus on impedance imaging with microelectrode arrays in in vitro applications. We first introduce how electrode configurations and the frequency range of the impedance analysis determine the information that can be extracted. We then delve into relevant circuit topologies that can be used to implement impedance measurements and their characteristic features, such as resolution and data-acquisition time. Afterwards, we detail design considerations for the implementation of new impedance-imaging devices. We conclude by discussing future fields of application of impedance imaging in biomedical research, in particular applications where optical imaging is not possible, such as monitoring of ex vivo tissue slices or microelectrode-based brain implants.

Multi-parametric functional imaging of cell cultures and tissues with a CMOS microelectrode array

Electrode-based impedance and electrochemical measurements can provide cell-biology information that is difficult to obtain using optical-microscopy techniques. Such electrical methods are non-invasive, label-free, and continuous, eliminating the need for fluorescence reporters and overcoming optical imaging's throughput/temporal resolution limitations. Nonetheless, electrode-based techniques have not been heavily employed because devices typically contain few electrodes per well, resulting in noisy aggregate readouts. Complementary metal-oxide-semiconductor (CMOS) microelectrode arrays (MEAs) have sometimes been used for electrophysiological measurements with thousands of electrodes per well at sub-cellular pitches, but only basic impedance mappings of cell attachment have been performed outside of electrophysiology. Here, we report on new field-based impedance mapping and electrochemical mapping/patterning techniques to expand CMOS-MEA cell-biology applications. The methods enable accurate measurement of cell attachment, growth/wound healing, cell-cell adhesion, metabolic state, and redox properties with single-cell spatial resolution (20 μm electrode pitch). These measurements allow the quantification of adhesion and metabolic differences of cells expressing oncogenes versus wild-type controls. The multi-parametric, cell-population statistics captured by the chip-scale integrated device opens up new avenues for fully electronic high-throughput live-cell assays for phenotypic screening and drug discovery applications.

Review of wearable technologies and machine learning methodologies for systematic detection of mild traumatic brain injuries

Mild traumatic brain injuries (mTBIs) are the most common type of brain injury. Timely diagnosis of mTBI is crucial in making 'go/no-go' decision in order to prevent repeated injury, avoid strenuous activities which may prolong recovery, and assure capabilities of high-level performance of the subject. If undiagnosed, mTBI may lead to various short- and long-term abnormalities, which include, but are not limited to impaired cognitive function, fatigue, depression, irritability, and headaches. Existing screening and diagnostic tools to detect acute andearly-stagemTBIs have insufficient sensitivity and specificity. This results in uncertainty in clinical decision-making regarding diagnosis and returning to activity or requiring further medical treatment. Therefore, it is important to identify relevant physiological biomarkers that can be integrated into a mutually complementary set and provide a combination of data modalities for improved on-site diagnostic sensitivity of mTBI. In recent years, the processing power, signal fidelity, and the number of recording channels and modalities of wearable healthcare devices have improved tremendously and generated an enormous amount of data. During the same period, there have been incredible advances in machine learning tools and data processing methodologies. These achievements are enabling clinicians and engineers to develop and implement multiparametric high-precision diagnostic tools for mTBI. In this review, we first assess clinical challenges in the diagnosis of acute mTBI, and then consider recording modalities and hardware implementation of various sensing technologies used to assess physiological biomarkers that may be related to mTBI. Finally, we discuss the state of the art in machine learning-based detection of mTBI and consider how a more diverse list of quantitative physiological biomarker features may improve current data-driven approaches in providing mTBI patients timely diagnosis and treatment.

Charge Effects Provide Ångström-Level Control of Lipid Bilayer Morphology on Titanium Dioxide Surfaces

Interfaces between molecular organic architectures and oxidic substrates are a central feature of biosensors and applications of biomimetics in science and technology. For phospholipid bilayers, the large range of pH- and ionic strength-dependent surface charge densities adopted by titanium dioxide and other oxidic surfaces leads to a rich landscape of phenomena that provides exquisite control of membrane interactions with such substrates. Using neutron reflectometry measurements, we report sharp, reversible transitions that occur between closely surface-associated and weakly coupled states. We show that these states arise from a complex interplay of the tunable length scale of electrostatic interactions with the length scale arising from other forces that are independent of solution conditions. A generalized free energy potential, with its inputs only derived from established measurements of surface and bilayer properties, quantitatively describes these and previously reported observations concerning the unbinding of bilayers from supporting substrates.

A CMOS Multi-Modal Electrochemical and Impedance Cellular Sensing Array for Massively Paralleled Exoelectrogen Screening

The paper presents a 256-pixel CMOS sensor array with in-pixel dual electrochemical and impedance detection modalities for rapid, multi-dimensional characterization of exoelectrogens. The CMOS IC has 16 parallel readout channels, allowing it to perform multiple measurements with a high throughput and enable the chip to handle different samples simultaneously. The chip contains a total of 2 × 256 working electrodes of size 44 μm × 52 μm, along with 16 reference electrodes of dimensions 56 μm × 399 μm and 32 counter electrodes of dimensions 399 μm × 106 μm, which together facilitate the high resolution screening of the test samples. The chip was fabricated in a standard 130nm BiCMOS process. The on-chip electrodes are subjected to additional fabrication processes, including a critical Al-etch step that ensures the excellent biocompatibility and long-term reliability of the CMOS sensor array in bio-environment. The electrochemical sensing modality is verified by detecting the electroactive analyte NaFeEDTA and the exoelectrogenic Shewanella oneidensis MR-1 bacteria, illustrating the chip's ability to quantify the generated electrochemical current and distinguish between different analyte concentrations. The impedance measurements with the HEK-293 cancer cells cultured on-chip successfully capture the cell-to-surface adhesion information between the electrodes and the cancer cells. The reported CMOS sensor array outperforms the conventional discrete setups for exoelectrogen characterization in terms of spatial resolution and speed, which demonstrates the chip's potential to radically accelerate synthetic biology engineering.

Contact photolithography-free integration of patterned and semi-transparent indium tin oxide stimulation electrodes into polydimethylsiloxane-based heart-on-a-chip devices for streamlining physiological recordings

Controlled electrical stimulation is essential for evaluating the physiology of cardiac tissues engineered in heart-on-a-chip devices. However, existing stimulation techniques, such as external platinum electrodes or opaque microelectrode arrays patterned on glass substrates, have limited throughput, reproducibility, or compatibility with other desirable features of heart-on-a-chip systems, such as the use of tunable culture substrates, imaging accessibility, or enclosure in a microfluidic device. In this study, indium tin oxide (ITO), a conductive, semi-transparent, and biocompatible material, was deposited onto glass and polydimethylsiloxane (PDMS)-coated coverslips as parallel or point stimulation electrodes using laser-cut tape masks. ITO caused substrate discoloration but did not prevent brightfield imaging. ITO-patterned substrates were microcontact printed with arrayed lines of fibronectin and seeded with neonatal rat ventricular myocytes, which assembled into aligned cardiac tissues. ITO deposited as parallel or point electrodes was connected to an external stimulator and used to successfully stimulate micropatterned cardiac tissues to generate calcium transients or propagating calcium waves, respectively. ITO electrodes were also integrated into the cantilever-based muscular thin film (MTF) assay to stimulate and quantify the contraction of micropatterned cardiac tissues. To demonstrate the potential for multiple ITO electrodes to be integrated into larger, multiplexed systems, two sets of ITO electrodes were deposited onto a single substrate and used to stimulate the contraction of distinct micropatterned cardiac tissues independently. Collectively, these approaches for integrating ITO electrodes into heart-on-a-chip devices are relatively facile, modular, and scalable and could have diverse applications in microphysiological systems of excitable tissues.

High-Aspect-Ratio Nanostructured Surfaces as Biological Metamaterials

Materials patterned with high-aspect-ratio nanostructures have features on similar length scales to cellular components. These surfaces are an extreme topography on the cellular level and have become useful tools for perturbing and sensing the cellular environment. Motivation comes from the ability of high-aspect-ratio nanostructures to deliver cargoes into cells and tissues, access the intracellular environment, and control cell behavior. These structures directly perturb cells' ability to sense and respond to external forces, influencing cell fate, and enabling new mechanistic studies. Through careful design of their nanoscale structure, these systems act as biological metamaterials, eliciting unusual biological responses. While predominantly used to interface eukaryotic cells, there is growing interest in nonanimal and prokaryotic cell interfacing. Both experimental and theoretical studies have attempted to develop a mechanistic understanding for the observed behaviors, predominantly focusing on the cell-nanostructure interface. This review considers how high-aspect-ratio nanostructured surfaces are used to both stimulate and sense biological systems.

Multimodal Integrated Sensor Platform for Rapid Biomarker Detection

Precision metabolomics and quantification for cost-effective rapid diagnosis of disease are the key goals in personalized medicine and point-of-care testing. At present, patients are subjected to multiple test procedures requiring large laboratory equipment. Microelectronics has already made modern computing and communications possible by integration of complex functions within a single chip. As More than Moore technology increases in importance, integrated circuits for densely patterned sensor chips have grown in significance. Here, we present a versatile single complementary metal-oxide-semiconductor chip forming a platform to address personalized needs through on-chip multimodal optical and electrochemical detection that will reduce the number of tests that patients must take. The chip integrates interleaved sensing subsystems for quadruple-mode colorimetric, chemiluminescent, surface plasmon resonance, and hydrogen ion measurements. These subsystems include a photodiode array and a single photon avalanche diode array with some elements functionalized to introduce a surface plasmon resonance mode. The chip also includes an array of ion sensitive field-effect transistors. The sensor arrays are distributed uniformly over an active area on the chip surface in a scalable and modular design. Bio-functionalization of the physical sensors yields a highly selective simultaneous multiple-assay platform in a disposable format. We demonstrate its versatile capabilities through quantified bio-assays performed on-chip for glucose, cholesterol, urea, and urate, each within their naturally occurring physiological range.

Correlation of Capacitance and Microscopy Measurements Using Image Processing for a Lab-on-CMOS Microsystem

We present a capacitance sensor chip developed in a 0.35-μm complementary metal-oxide-semiconductor process for monitoring biological cell viability and proliferation. The chip measures the cell-to-substrate binding through capacitance-to-frequency conversion with a sensitivity of 590 kHz/fF. In vitro experiments with two human ovarian cancer cell lines (CP70 and A2780) were performed and showed the ability to track cell viability in realtime over three days. An imaging platform was developed to provide time-lapse images of the sensor surface, which allowed for concurrent visual and capacitance observation of the cells. The results showed the ability to detect single-cell binding events and changes in cell morphology. Image processing was performed to estimate the cell coverage of sensor electrodes, showing good linear correlation and providing a sensor gain of 1.28 ± 0.29 aF/μm², which agrees with values reported in the literature. The device is designed for unsupervised operation with minimal packaging requirements. Only a microcontroller is required for readout, making it suitable for applications outside the traditional laboratory setting.

Optical Imaging Approaches to Monitor Static and Dynamic Cell-on-Chip Platforms: A Tutorial Review

Miniaturized laboratories on chip platforms play an important role in handling life sciences studies. The platforms may contain static or dynamic biological cells. Examples are a fixed medium of an organ-on-a-chip and individual cells moving in a microfluidic channel, respectively. Due to feasibility of control or investigation and ethical implications of live targets, both static and dynamic cell-on-chip platforms promise various applications in biology. To extract necessary information from the experiments, the demand for direct monitoring is rapidly increasing. Among different microscopy methods, optical imaging is a straightforward choice. Considering light interaction with biological agents, imaging signals may be generated as a result of scattering or emission effects from a sample. Thus, optical imaging techniques could be categorized into scattering-based and emission-based techniques. In this review, various optical imaging approaches used in monitoring static and dynamic platforms are introduced along with their optical systems, advantages, challenges, and applications. This review may help biologists to find a suitable imaging technique for different cell-on-chip studies and might also be useful for the people who are going to develop optical imaging systems in life sciences studies.

High-Density Electrical Recording and Impedance Imaging With a Multi-Modal CMOS Multi-Electrode Array Chip

Multi-electrode arrays, both active or passive, emerged as ideal technologies to unveil intricated electrophysiological dynamics of cells and tissues. Active MEAs, designed using complementary metal oxide semiconductor technology (CMOS), stand over passive devices thanks to the possibility of achieving single-cell resolution, the reduced electrode size, the reduced crosstalk and the higher functionality and portability. Nevertheless, most of the reported CMOS MEA systems mainly rely on a single operational modality, which strongly hampers the applicability range of a single device. This can be a limiting factor considering that most biological and electrophysiological dynamics are often based on the synergy of multiple and complex mechanisms acting from different angles on the same phenomena. Here, we designed a CMOS MEA chip with 16,384 titanium nitride electrodes, 6 independent operational modalities and 1,024 parallel recording channels for neuro-electrophysiological studies. Sixteen independent active areas are patterned on the chip surface forming a 4 × 4 matrix, each one including 1,024 electrodes. Electrodes of four different sizes are present on the chip surface, ranging from 2.5 × 3.5 μm² up to 11 × 11.0 μm², with 15 μm pitch. In this paper, we exploited the impedance monitoring and voltage recording modalities not only to monitor the growth and development of primary rat hippocampal neurons, but also to assess their electrophysiological activity over time showing a mean spike amplitude of 144.8 ± 84.6 μV. Fixed frequency (1 kHz) and high sampling rate (30 kHz) impedance measurements were used to evaluate the cellular adhesion and growth on the chip surface. Thanks to the high-density configuration of the electrodes, as well as their dimension and pitch, the chip can appreciate the evolutions of the cell culture morphology starting from the moment of the seeding up to mature culture conditions. The measurements were confirmed by fluorescent staining. The effect of the different electrode sizes on the spike amplitudes and noise were also discussed. The multi-modality of the presented CMOS MEA allows for the simultaneous assessment of different physiological properties of the cultured neurons. Therefore, it can pave the way both to answer complex fundamental neuroscience questions as well as to aid the current drug-development paradigm.

Electrode-Electrolyte Interface Impedance Characterization of Ultra-Miniaturized Microelectrode Arrays Over Materials and Geometries for Sub-Cellular and Cellular Sensing and Stimulation

Electrochemical interfaces with low-impedance, high biocompatibility, and long-term stability are of paramount importance for microelectrode arrays (MEAs), that are widely used in numerous cellular sensing/stimulation applications, e.g., brain interface, electroceuticals, neuroprosthetics, drug discovery, chemical screening, and fundamental biological research. It is becoming increasingly critical since sensing/actuations at sub-cellular resolution necessitate ultra-miniaturized electrodes, which exhibit exacerbated electrochemical interfaces, especially on interfacial impedance. This paper reports the first comprehensive characterization and interfacial electrochemical impedance spectroscopy (EIS) of the ultra-miniaturized electrodes for different electrode sizes ( 8×8 μm² , 16×16 μm² , and 32×32 μm² ) and a wide material collection (Au, Pt, TiN, and ITO). Equivalent electrochemical interfacial circuit models with interface capacitance, charge transfer resistance, and solution resistance are obtained for all the electrode designs based on their EIS measurements. The results can potentially guide the designs of ultra-miniaturized MEAs for future bioelectronics systems.

LTCC Packaged Ring Oscillator Based Sensor for Evaluation of Cell Proliferation

A complementary metal-oxide-semiconductor (CMOS) chip biosensor was developed for cell viability monitoring based on an array of capacitance sensors utilizing a ring oscillator. The chip was packaged in a low temperature co-fired ceramic (LTCC) module with a flip chip bonding technique. A microcontroller operates the chip, while the whole measurement system was controlled by PC. The developed biosensor was applied for measurement of the proliferation stage of adherent cells where the sensor response depends on the ratio between healthy, viable and multiplying cells, which adhere onto the chip surface, and necrotic or apoptotic cells, which detach from the chip surface. This change in cellular adhesion caused a change in the effective permittivity in the vicinity of the sensor element, which was sensed as a change in oscillation frequency of the ring oscillator. The sensor was tested with human lung epithelial cells (BEAS-2B) during cell addition, proliferation and migration, and finally detachment induced by trypsin protease treatment. The difference in sensor response with and without cells was measured as a frequency shift in the scale of 1.1 MHz from the base frequency of 57.2 MHz. Moreover, the number of cells in the sensor vicinity was directly proportional to the frequency shift.