Wave reflections in the umbilical artery measured by Doppler ultrasound as a novel predictor of placental pathology.

BACKGROUND: The umbilical artery (UA) Doppler pulsatility index is used clinically to detect elevated feto-placental vascular resistance. However, this metric is confounded by variation in fetal cardiac function and is only moderately predictive of placental pathology. Our group developed a novel ultrasound methodology that measures wave reflections in the UA, thereby isolating a component of the Doppler signal that is specific to the placenta. The present study examined whether wave reflections in the UA are predictive of placental vascular pathology. METHODS: Standard clinical Doppler ultrasound of the UAs was performed in 241 pregnant women. Of these, 40 women met narrowly defined preset criteria for the control group, 36 had maternal vascular malperfusion (MVM) and 16 had fetal vascular malperfusion (FVM). Using a computational procedure, the Doppler waveforms were decomposed into a pair of forward and backward propagating waves. FINDINGS: Compared to controls, wave reflections were significantly elevated in women with either MVM (p<0.0001) or FVM pathology (p = 0.02). In contrast, the umbilical and uterine artery pulsatility indices were only elevated in the MVM group (p<0.0001) and there were no differences between women with FVM and the controls. INTERPRETATION: The measurement of wave reflections in the UA, combined with standard clinical ultrasound parameters, has the potential to improve the diagnostic performance of UA Doppler to detect placental vascular pathology. Identifying women with FVM pathology is particularly challenging prenatally and future investigations will determine if women at risk of this specific placental disease could benefit from this novel diagnostic technique.

Interpretation of Wave Reflections in the Umbilical Arterial Segment of the Feto-Placental Circulation: Computational Modeling of the Feto-Placental Arterial Tree.

Placental vascular abnormalities are associated with a host of pregnancy complications including placenta mediated fetal growth restriction (FGR). Umbilical arterial (UA) Doppler ultrasound velocity waveforms are widely used in the diagnosis of underlying placental vascular abnormalities in pregnancies with suspected FGR, which greatly helps to prevent stillbirth via ongoing fetal monitoring and timely delivery. However, the sensitivity of UA Doppler diagnosis diminishes late in gestation. Our goal was to present a generalized wave decomposition method to compute forward and reflected components from UA waveforms. A detailed anatomical based model was also developed to explain observed UA flow waveform and to explore how vascular properties affect the shape of flow wave components. Using data from a previous study of pregnant mice using high frequency ultrasound microscopy, we examined in utero Doppler and M-mode ultrasound measurements in 15 fetuses' UA. Following ultrasound, the placentas had been collected and perfused with contrast agent to obtain high-resolution 3D images of the feto-placental arteries. Model of these specimens indicates the significant role of terminal load impedance (capillary and/or veins) in creating positive or negative reflected flow waveforms. A negative flow reflected waveform is obtained when terminal impedance is elevated. This is consistent with the elongated and non-branching terminal villi that are proposed to cause the highly abnormal UA waveforms found in early-onset FGR. The significance of these findings for the diagnostic utility of UA Doppler in human pregnancy is that the identification and measurement of wave reflections may aid in discriminating between healthy and abnormal placental vasculature in pregnancies with suspected late-onset FGR.

Sex differences in modulation of fetoplacental vascular resistance in growth-restricted mouse fetuses following betamethasone administration: comparisons with human fetuses.

BACKGROUND: Maternally administered corticosteroids are routinely used to accelerate fetal lung maturation in pregnancies at risk of early preterm delivery. Although, among the subgroup with growth restriction, a majority show a temporary improvement in umbilical artery Doppler waveforms that may be sustained up to 7 days, a minority will acutely decompensate in response to corticosteroids in association with deteriorating umbilical and fetal Doppler waveforms. The basis for such acute Doppler changes is presently unknown. Our group has developed a noninvasive ultrasound methodology to measure wave reflections in the umbilical artery and have established that wave reflection metrics are sensitive to structural changes in the placental vasculature and to acute changes in vascular tone. Using this approach, we demonstrated in healthy pregnant mice that fetoplacental vascular resistance decreased in betamethasone-treated mice compared with saline-treated controls. OBJECTIVE: This study aimed to investigate the effects of betamethasone administration on the wave reflection metrics in a mouse model of fetal growth restriction and to compare these findings with equivalent measurements in human fetuses. STUDY DESIGN: Pregnant CD-1 mice were housed from embryonic day 14.5 to embryonic day 17.5 in either a normoxic (21% O2, n=24) or hypoxic environment (11% O2, n=22), the latter being an established mouse model of fetal growth restriction. To investigate the effect of maternally administered betamethasone on the fetoplacental vasculature, ultrasound imaging was performed at baseline and 4 hours after treatment (either betamethasone or sterile saline). Umbilical artery wave reflection metrics were compared between the groups and for the effect of fetal sex. In addition, a cohort of 10 pregnant women with elevated umbilical artery pulsatility index and evidence of fetal growth restriction and 6 controls were imaged before and after corticosteroid administration. RESULTS: In the mouse model, after betamethasone administration, the female fetuses from the hypoxia group showed a 15% increase in umbilical artery diameter, a 98% increase in umbilical artery blood flow, and a 27% decrease in umbilical artery reflection coefficient, whereas the males from the hypoxia group showed no substantial changes. In agreement with our mouse findings, umbilical artery reflections were found to be larger in human growth-restricted fetuses than controls in women at risk of preterm birth. CONCLUSION: Our studies provide insight into the mechanism whereby the human growth-restricted fetus may exhibit a temporary favorable fetoplacental vascular response to maternally administered corticosteroids. Further investigations are needed to understand why the male growth-restricted fetus seems unable to mount this favorable vascular response.

Asymmetric Regional Work Contributes to Right Ventricular Fibrosis, Inefficiency, and Dysfunction in Pulmonary Hypertension versus Regurgitation.

BACKGROUND: Right ventricular (RV) pressure loading from pulmonary hypertension (PH) and volume loading from pulmonary regurgitation (PR) lead to RV dysfunction, a critical determinant of clinical outcomes, but their impact on regional RV mechanics and fibrosis is poorly characterized. The aim of this study was to test the hypothesis that regional myocardial mechanics and efficiency in RV pressure and volume loading are associated with RV fibrosis and dysfunction. METHODS: Eight PH, six PR, and five sham-control rats were studied. The PH rat model was induced using Sugen5416, a vascular endothelial growth factor receptor 2 inhibitor, combined with chronic hypoxia. PR rats were established by surgical laceration of the pulmonary valve leaflets. Six (n = 4) or 9 (n = 4) weeks after Sugen5416 and hypoxia and 12 weeks after PR surgery, myocardial strain and RV pressure were measured and RV pressure-strain loops generated. We further studied RV regional mechanics in 11 patients with PH. Regional myocardial work was calculated as the pressure-strain loop area (mm Hg ∙ %). Regional myocardial work efficiency was quantified through wasted work (ratio of systolic lengthening to shortening work). The relation of regional myocardial work to RV fibrosis and dysfunction was analyzed. RESULTS: In rats, PH and PR induced similar RV dilatation, but fractional area change (%) was lower in PH than in PR. RV lateral wall work was asymmetrically higher in PH compared with sham, while septal work was similar to sham. In PR, lateral and septal work were symmetrically higher versus sham. Myocardial wasted work ratio was asymmetrically increased in the PH septum versus sham. Fibrosis in the RV lateral wall, but not septum, was higher in PH than PR. RV fibrosis burden was linearly related to regional work and to measures of RV systolic and diastolic function but not to wasted myocardial work ratio. Patients with PH demonstrated similar asymmetric and inefficient regional myocardial mechanics. CONCLUSIONS: Asymmetric RV work and increased wasted septal work in experimental PH are associated with RV fibrosis and dysfunction. Future investigation should examine whether assessment of asymmetric regional RV work and efficiency can predict clinical RV failure and influence patient management.

Quantification of Wave Reflection in the Human Umbilical Artery From Asynchronous Doppler Ultrasound Measurements.

Elevated umbilical artery pulsatility is a widely used biomarker for placental pathology leading to intra-uterine growth restriction and, in severe cases, still-birth. It has been hypothesized that placental pathology modifies umbilical artery pulsatility by altering the degree to which the pulse pressure wave, which originates from the fetal heart, is reflected from the placental vasculature to interfere with the incident wave. Here we present a method for estimating the reflected pulse wave in the umbilical artery of human fetuses using asynchronously acquired Doppler ultrasound measurements from the two ends of the umbilical cord. This approach assumes non-dispersive and loss-less propagation of the waves along the artery and models the reflection process as a linear system with a parameterized impulse response. Model parameters are determined from the measured Doppler waveforms by constrained optimization. Velocity waveforms were obtained from 142 pregnant volunteers where 123 met data quality criteria in at least one umbilical artery. The reflection model was consistent with the measured waveforms in 183 of 212 arteries that were analyzed. The analysis method was validated by applying it to simulated datasets and comparing solutions to ground-truth. With measurement noise levels typical of clinical ultrasound, parameters describing the reflected wave were accurately determined.

Non-Invasive Ultrasound Detection of Cerebrovascular Changes in a Mouse Model of Traumatic Brain Injury.

Traumatic brain injury (TBI) can induce changes in vascular architecture. Although ultrasound metrics such as pulsatility index (PI) are sensitive to changes in hemodynamic resistance downstream from major arteries, these metrics depend on features unrelated to vessel architecture, such as blood pressure and heart rate. In contrast, input impedance and reflection coefficient that are derived from wave reflection theory seek to minimize the effects of altered cardiac output or heart rate. In this article, we investigate the use of ultrasound to assess changes in vascular impedance and wave reflection in the common carotid arteries of mice exposed to a controlled cortical impact. Focusing on the first harmonics of the reflected waves, the impedance phase was increased ipsilaterally in impacted mice compared with shams, whereas the magnitude of the impedance was unchanged. In contrast, PI was reduced bilaterally. Interestingly, PI and the first harmonic magnitude of input impedance in the carotid artery were correlated on the contralateral but not ipsilateral side. We investigated the use of these metrics to classify mice as sham or TBI, finding an area under the receiver operating characteristic curve ipsilaterally of 0.792 (confidence interval [CI]: 0.648-0.936) for correct classification with first harmonic impedance magnitude and phase as predictors and 0.716 (CI: 0.553-0.879) using carotid artery PI and diameter as predictors. Overall, the findings support the use of wave reflection analysis as a more specific measure of vascular changes following TBI and motivate the translation of this approach for monitoring vascular changes in humans affected by TBI.

Effect of maternal betamethasone administration on feto-placental vascular resistance in the mouse†.

Antenatal corticosteroids are often administered to women at risk of preterm birth to accelerate fetal lung development; however, there is evidence that this treatment may adversely affect placental function in some fetuses. Our group has recently demonstrated that wave reflections in the umbilical artery (UA), measured using high-frequency ultrasound, are sensitive to placental vascular abnormalities. In the present study, we used this approach to investigate the effect of maternal administration of betamethasone, a clinically relevant corticosteroid, on the feto-placental vasculature of the mouse. Fetuses were assessed at embryonic day (E)15.5 and E17.5 in C57BL6/J mice. At both gestational ages, the UA diameter, UA blood flow, and the wave reflection coefficient were significantly elevated in the betamethasone-treated mice compared to vehicle-treated controls. These observations support the interpretation that placental vascular resistance dropped with betamethasone treatment to an extent that could not be explained by vasodilation of the UA alone. Consistent with clinical studies, the effect of betamethasone on UA end-diastolic velocity was heterogeneous. Our results suggest that UA wave reflections are more sensitive to acute changes in placental vascular resistance compared with the UA pulsatility index, and this technique may have clinical application to identify a favorable placental vascular response to fetal therapies such as antenatal corticosteroids, where the fetal heart rate is likely to vary.

Regional hypometabolism in the 3xTg mouse model of Alzheimer's disease.

Alzheimer's disease (AD) is a progressive age-related neurodegenerative disease. Although neurofibrillary tangles and amyloid beta are classic hallmarks of AD, the earliest deficits in AD progression may be caused by unknown factors. One suspected factor has to do with brain energy metabolism. To investigate this factor, brain metabolic activity in 3xTg-AD mice and age-matched controls were measured with FDG-PET. Significant hypometabolic changes (p < .01) in brain metabolism were detected in the cortical piriform and insular regions of AD brains relative to controls. These regions are associated with olfaction, which is a potential clinical marker for AD progression as well as neurogenesis. The activity of the terminal component of the mitochondrial respiratory chain (complex IV) and the expression of complex I-V were significantly decreased (p < .05), suggesting that impaired metabolic activity coupled with impaired oxidative phosphorylation leads to decreased mitochondrial bioenergetics and subsequent Neurodegeneration. Although there is an association between neuroinflammatory pathological markers (microglial) and hypometabolism in AD, there was no association found between neuropathological (Aß, tau, and astrocytes) and functional changes in AD sensitive brain regions, also suggesting that brain hypometabolism occurs prior to AD pathology. Therefore, targeting metabolic mechanisms in cortical piriform and insular regions at early stages may be a promising approach for preventing, slowing, and/or blocking the onset of AD and preserving neurogenesis.

Reflected hemodynamic waves influence the pattern of Doppler ultrasound waveforms along the umbilical arteries.

The pulsatile pattern of blood motion measured by Doppler ultrasound within the umbilical artery is known to contain useful diagnostic information and is widely used to monitor pregnancies at risk of fetal growth restriction or stillbirth. Animal studies have identified reflected pressure waves traveling counter to the direction of blood flow as an important factor in the shape of these waveforms. In the present study, we establish a method to measure reflected waves in the human umbilical artery and assess their influence on blood velocity pulsation. Ninety-five pregnant women were recruited from a general obstetrics clinic between 26 and 37 wk of gestation and examined by Doppler ultrasound. Blood velocity waveforms were recorded for each umbilical artery at three locations along the umbilical cord. With the use of a computational procedure, a pair of forward and reverse propagating waves was identified to explain the variation in observed Doppler ultrasound waveforms along the cord. Among the data sets that met data quality requirements, waveforms in 93 of the 130 arteries examined agreed with the wave reflection model to within 1.5% and showed reflections ranging in magnitude from 3 to 52% of the forward wave amplitude. Strong reflections were associated with large differences in pulsatility between the fetal and placental ends of the cord. As reflections arise from transitions in the biomechanical properties of blood vessels, these observations provide a plausible mechanism for the link between abnormal waveforms and clinically significant placental pathology and could lead to more precise screening methods for detecting pregnancies complicated by placental disease. NEW & NOTEWORTHY The pulsatile pattern of blood motion measured by Doppler ultrasound within the umbilical artery is known to contain useful diagnostic information and is widely used to monitor pregnancies at risk of fetal growth restriction. We demonstrate based on a study of 95 pregnant women that the shape of these umbilical artery waveforms is explained by the presence of a reflected pressure wave traveling counter to the direction of blood flow.

Placental vascular abnormalities in the mouse alter umbilical artery wave reflections.

Current methods to detect placental vascular pathologies that monitor Doppler ultrasound changes in umbilical artery (UA) pulsatility have only moderate diagnostic utility, particularly in late gestation. In fetal mice, we recently demonstrated that reflected pressure waves propagate counter to the direction of flow in the UA and proposed the measurement of these reflections as a means to detect abnormalities in the placental circulation. In the present study, we used this approach in combination with microcomputed tomography to investigate the relationship between altered placental vascular architecture and changes in UA wave reflection metrics. Fetuses were assessed at embryonic day (E) 15.5 and E17.5 in control C57BL6/J mice and dams treated with combination antiretroviral therapy (cART), a known model of fetal growth restriction. Whereas the reflection coefficient was not different between groups at E15.5, it was 27% higher at E17.5 in cART-treated mice compared with control mice. This increase in reflection coefficient corresponded to a 36% increase in the total number of vessel segments, a measure of overall architectural complexity. Interestingly, there was no difference in UA pulsatility index between groups, suggesting that the wave reflections convey information about vascular architecture that is not captured by conventional ultrasound metrics. The wave reflection parameters were found to be associated with the morphology of the fetoplacental arterial tree, with the area ratio between the UA and first branch points correlating with the reflection coefficient. This study highlights the potential for wave reflection to aid in the noninvasive clinical assessment of placental vascular pathology. NEW & NOTEWORTHY We used a novel ultrasound methodology based on detecting pulse pressure waves that propagate along the umbilical artery to investigate the relationship between changes in wave reflection metrics and altered placental vascular architecture visualized by microcomputed tomography. Using pregnant mice treated with combination antiretroviral therapy, a model of fetal growth restriction, we demonstrated that reflections in the umbilical artery are sensitive to placental vascular abnormalities and associated with the geometry of the fetoplacental tree.

Fetal hemodynamics and cardiac streaming assessed by 4D flow cardiovascular magnetic resonance in fetal sheep.

BACKGROUND: To date it has not been possible to obtain a comprehensive 3D assessment of fetal hemodynamics because of the technical challenges inherent in imaging small cardiac structures, movement of the fetus during data acquisition, and the difficulty of fusing data from multiple cardiac cycles when a cardiac gating signal is absent. Here we propose the combination of volumetric velocity-sensitive cardiovascular magnetic resonance imaging ("4D flow" CMR) and a specialized animal preparation (catheters to monitor fetal heart rate, anesthesia to immobilize mother and fetus) to examine fetal sheep cardiac hemodynamics in utero. METHODS: Ten pregnant Merino sheep underwent surgery to implant arterial catheters in the target fetuses. Anesthetized ewes underwent 4D flow CMR with acquisition at 3 T for fetal whole-heart coverage with 1.2-1.5 mm spatial resolution and 45-62 ms temporal resolution. Flow was measured in the heart and major vessels, and particle traces were used to visualize circulatory patterns in fetal cardiovascular shunts. Conservation of mass was used to test internal 4D flow consistency, and comparison to standard 2D phase contrast (PC) CMR was performed for validation. RESULTS: Streaming of blood from the ductus venosus through the foramen ovale was visualized. Flow waveforms in the major thoracic vessels and shunts displayed normal arterial and venous patterns. Combined ventricular output (CVO) was 546 mL/min per kg, and the distribution of flows (%CVO) were comparable to values obtained using other methods. Internal 4D flow consistency across 23 measurement locations was established with differences of 14.2 ± 12.1%. Compared with 2D PC CMR, 4D flow showed a strong correlation (R2 = 0.85) but underestimated flow (bias = - 21.88 mL/min per kg, p < 0.05). CONCLUSIONS: The combination of fetal surgical preparation and 4D flow CMR enables characterization and quantification of complex flow patterns in utero. Visualized streaming of blood through normal physiological shunts confirms the complex mechanism of substrate delivery to the fetal heart and brain. Besides offering insight into normal physiology, this technology has the potential to qualitatively characterize complex flow patterns in congenital heart disease phenotypes in a large animal model, which can support the development of new interventions to improve outcomes in this population.

Performance of a PET Insert for High-Resolution Small-Animal PET/MRI at 7 Tesla.

We characterize a compact MR-compatible PET insert for simultaneous preclinical PET/MRI. Although specifically designed with the strict size constraint to fit inside the 114-mm inner diameter of the BGA-12S gradient coil used in the BioSpec 70/20 and 94/20 series of small-animal MRI systems, the insert can easily be installed in any appropriate MRI scanner or used as a stand-alone PET system. Methods: The insert consists of a ring of 16 detector-blocks each made from depth-of-interaction-capable dual-layer-offset arrays of cerium-doped lutetium-yttrium oxyorthosilicate crystals read out by silicon photomultiplier arrays. Scintillator crystal arrays are made from 22 × 10 and 21 × 9 crystals in the bottom and top layers, respectively, with respective layer thicknesses of 6 and 4 mm, arranged with a 1.27-mm pitch, resulting in a useable field of view 28 mm long and about 55 mm wide. Results: Spatial resolution ranged from 1.17 to 1.86 mm full width at half maximum in the radial direction from a radial offset of 0-15 mm. With a 300- to 800-keV energy window, peak sensitivity was 2.2% and noise-equivalent count rate from a mouse-sized phantom at 3.7 MBq was 11.1 kcps and peaked at 20.8 kcps at 14.5 MBq. Phantom imaging showed that features as small as 0.7 mm could be resolved. 18F-FDG PET/MR images of mouse and rat brains showed no signs of intermodality interference and could excellently resolve substructures within the brain. Conclusion: Because of excellent spatial resolvability and lack of intermodality interference, this PET insert will serve as a useful tool for preclinical PET/MR.

An algorithm for automatic crystal identification in pixelated scintillation detectors using thin plate splines and Gaussian mixture models.

A typical positron emission tomography detector is comprised of a scintillator crystal array coupled to a photodetector array or other position sensitive detector. Such detectors using light sharing to read out crystal elements require the creation of a crystal lookup table (CLUT) that maps the detector response to the crystal of interaction based on the x-y position of the event calculated through Anger-type logic. It is vital for system performance that these CLUTs be accurate so that the location of events can be accurately identified and so that crystal-specific corrections, such as energy windowing or time alignment, can be applied. While using manual segmentation of the flood image to create the CLUT is a simple and reliable approach, it is both tedious and time consuming for systems with large numbers of crystal elements. In this work we describe the development of an automated algorithm for CLUT generation that uses a Gaussian mixture model paired with thin plate splines (TPS) to iteratively fit a crystal layout template that includes the crystal numbering pattern. Starting from a region of stability, Gaussians are individually fit to data corresponding to crystal locations while simultaneously updating a TPS for predicting future Gaussian locations at the edge of a region of interest that grows as individual Gaussians converge to crystal locations. The algorithm was tested with flood image data collected from 16 detector modules, each consisting of a 409 crystal dual-layer offset LYSO crystal array readout by a 32 pixel SiPM array. For these detector flood images, depending on user defined input parameters, the algorithm runtime ranged between 17.5-82.5 s per detector on a single core of an Intel i7 processor. The method maintained an accuracy above 99.8% across all tests, with the majority of errors being localized to error prone corner regions. This method can be easily extended for use with other detector types through adjustment of the initial template model used.

Development of a PET scanner for simultaneously imaging small animals with MRI and PET.

Recently, positron emission tomography (PET) is playing an increasingly important role in the diagnosis and staging of cancer. Combined PET and X-ray computed tomography (PET-CT) scanners are now the modality of choice in cancer treatment planning. More recently, the combination of PET and magnetic resonance imaging (MRI) is being explored in many sites. Combining PET and MRI has presented many challenges since the photo-multiplier tubes (PMT) in PET do not function in high magnetic fields, and conventional PET detectors distort MRI images. Solid state light sensors like avalanche photo-diodes (APDs) and more recently silicon photo-multipliers (SiPMs) are much less sensitive to magnetic fields thus easing the compatibility issues. This paper presents the results of a group of Canadian scientists who are developing a PET detector ring which fits inside a high field small animal MRI scanner with the goal of providing simultaneous PET and MRI images of small rodents used in pre-clinical medical research. We discuss the evolution of both the crystal blocks (which detect annihilation photons from positron decay) and the SiPM array performance in the last four years which together combine to deliver significant system performance in terms of speed, energy and timing resolution.

Development and evaluation of a LOR-based image reconstruction with 3D system response modeling for a PET insert with dual-layer offset crystal design.

In this study we present a method of 3D system response calculation for analytical computer simulation and statistical image reconstruction for a magnetic resonance imaging (MRI) compatible positron emission tomography (PET) insert system that uses a dual-layer offset (DLO) crystal design. The general analytical system response functions (SRFs) for detector geometric and inter-crystal penetration of coincident crystal pairs are derived first. We implemented a 3D ray-tracing algorithm with 4π sampling for calculating the SRFs of coincident pairs of individual DLO crystals. The determination of which detector blocks are intersected by a gamma ray is made by calculating the intersection of the ray with virtual cylinders with radii just inside the inner surface and just outside the outer-edge of each crystal layer of the detector ring. For efficient ray-tracing computation, the detector block and ray to be traced are then rotated so that the crystals are aligned along the X-axis, facilitating calculation of ray/crystal boundary intersection points. This algorithm can be applied to any system geometry using either single-layer (SL) or multi-layer array design with or without offset crystals. For effective data organization, a direct lines of response (LOR)-based indexed histogram-mode method is also presented in this work. SRF calculation is performed on-the-fly in both forward and back projection procedures during each iteration of image reconstruction, with acceleration through use of eight-fold geometric symmetry and multi-threaded parallel computation. To validate the proposed methods, we performed a series of analytical and Monte Carlo computer simulations for different system geometry and detector designs. The full-width-at-half-maximum of the numerical SRFs in both radial and tangential directions are calculated and compared for various system designs. By inspecting the sinograms obtained for different detector geometries, it can be seen that the DLO crystal design can provide better sampling density than SL or dual-layer no-offset system designs with the same total crystal length. The results of the image reconstruction with SRFs modeling for phantom studies exhibit promising image recovery capability for crystal widths of 1.27-1.43 mm and top/bottom layer lengths of 4/6 mm. In conclusion, we have developed efficient algorithms for system response modeling of our proposed PET insert with DLO crystal arrays. This provides an effective method for both 3D computer simulation and quantitative image reconstruction, and will aid in the optimization of our PET insert system with various crystal designs.