The review, led by neonatologist Yunus E. Dogan of the University of Florida together with colleagues spanning neonatology, cardiac surgery, and radiology, integrated eleven prospective and retrospective cohort studies published between 2016 and 2025. Its central numbers are sobering. Preoperative brain injury, detected on magnetic resonance imaging performed before any surgical intervention, is found in between 12 and 54 percent of neonates with congenital heart disease. That enormous range reflects differences in lesion definitions, imaging protocols, and cardiac diagnoses across studies, but even the most conservative estimates mean that at least one in eight babies arrives at the cardiac operating table with a brain that has already been injured. After surgery, the burden persists, with new lesions appearing on postoperative scans in a substantial fraction of survivors.

The patterns of injury are distinctive and diagnostically revealing. Before surgery, the most common findings are white matter injury, arterial ischemic stroke, and cerebral hemorrhage. White matter injury, sometimes described as periventricular leukomalacia-like damage, strikes the fatty sheathed fibers that connect distant brain regions and are still being actively myelinated in the third trimester. After surgery, the imaging signature shifts: white matter injury remains dominant, but clinicians also see focal infarctions that are often thromboembolic in origin, tiny microhemorrhages scattered through the parenchyma, and cerebral venous thrombosis. This temporal fingerprint, captured by serial MRI, allows researchers to distinguish lesions that were present at birth from those acquired in the operating room or intensive care unit, and it has fundamentally changed the framing of the problem from a surgical complication to a continuum of vulnerability that begins in utero.

Why is the fetal brain so fragile when the heart is malformed? The answer lies in the peculiar plumbing of fetal circulation and the metabolic demands of the rapidly growing brain. In a normal fetus, the placenta delivers oxygenated blood, and the brain enjoys a privileged, high-flow supply. In fetuses with critical heart defects, however, the anatomy reroutes this flow. In conditions such as hypoplastic left heart syndrome or transposition of the great arteries, oxygen-rich and oxygen-poor blood mix abnormally, and the cerebral circulation may be perfused at lower pressure, lower oxygen content, or both. Advanced fetal MRI studies have measured this directly, showing reduced fetal cerebral oxygen consumption associated with smaller brain size, delayed cortical development correlated with reduced oxygen delivery, and altered hemodynamic responses when mothers are given supplemental oxygen. The result is a brain that reaches birth with globally reduced volumes, microstructural abnormalities in structures like the corpus callosum, and in some cases aberrant functional connectivity detectable before any operation.

The maternal-fetal environment adds another layer of risk. The review highlights evidence linking placental dysfunction and preeclampsia to preoperative focal white matter injury in neonates with complex heart disease, an emerging field some researchers call neuroplacentology. Three-dimensional volumetric MRI of the placenta in fetuses with complex congenital heart disease has revealed measurable differences compared with controls, and placental pathology correlates with neuroimaging abnormalities after birth. In other words, the same compromised maternal-fetal conditions that stress the heart may simultaneously starve the developing brain of oxygen and nutrients. Perinatal and neonatal characteristics compound this vulnerability: male sex, prematurity, and low birth weight all emerge as risk factors, echoing patterns seen in preterm brain injury more broadly. Notably, the immature oligodendrocytes that build myelin in the third trimester are exquisitely sensitive to hypoxia-ischemia and inflammation, which helps explain why white matter bears the brunt of the damage in this population.

Cerebral autoregulation, the brain’s ability to maintain steady blood flow despite swings in blood pressure, appears to be impaired in many of these newborns even before surgery. Studies of preoperative infants with congenital heart disease have documented blunted autoregulatory capacity, and novel noninvasive measures of cerebrovascular stability are being tested against invasive monitoring to bring this physiology to the bedside. The clinical implication is profound: a blood pressure that is perfectly adequate for one baby’s brain may be dangerously low for another’s, and the transition from fetal to neonatal circulation, with its shifting shunts and falling pulmonary resistance, is a period of particular hazard. Preoperative procedures such as balloon atrial septostomy have been scrutinized as potential stroke triggers, though large studies suggest that oxygenation and time to surgery are more important determinants of injury than the procedure itself.

Then comes the operation, and with it a new set of insults. Cardiopulmonary bypass, the heart-lung machine that sustains circulation during repair, exposes the brain to nonphysiological flow, embolic debris, inflammatory activation, and ischemia-reperfusion injury when the heart is restarted. Neonatal blood is uniquely challenging in this setting: standard heparin doses achieve less consistent thrombin inhibition in newborns than in older patients, and the coagulation system swings between thrombosis and bleeding with little margin for error. Anticoagulation strategy, surgical timing, hemodynamic instability, and the use of extracorporeal membrane oxygenation all emerge in the review as procedural risk factors for postoperative brain injury. Focal infarctions after surgery are frequently thromboembolic, and cerebral sinovenous thrombosis has been documented in infants undergoing cardiac surgery, sometimes producing thalamic hemorrhage and requiring difficult anticoagulation decisions in a fragile patient.

There is, however, genuine cause for optimism embedded in the data. The review notes that advances in blood pressure management, tailored perfusion strategies, and optimized surgical timing have already reduced postoperative injury rates, and recent multicenter work has documented a declining incidence of postoperative neonatal brain injury over time. Studies comparing cohorts with different practice approaches show that institutional choices matter, and European collaborative data have begun to map which perioperative factors predict long-term neurodevelopmental outcomes better than conventional imaging alone. The stakes of these improvements are high: perioperative brain injury on neonatal MRI is associated with worse school-age neurodevelopment, reduced white matter volume predicts language difficulties, and hippocampal volume reductions in adolescents with congenital heart disease track with intellectual function. Survivors face elevated rates of motor delay, cognitive and executive function deficits, and abnormalities in brain regions regulating anxiety and mood.

The path forward, as the authors frame it, is precision neuroprotection across the entire continuum of care. Antenatal interventions, including maternal hyperoxia strategies being tested with blood oxygenation level dependent fetal MRI, could potentially bolster the fetal brain before birth. Individualized hemodynamic management targets, guided by continuous cerebral autoregulation monitoring rather than population-wide blood pressure thresholds, could protect the brain during bypass and in the intensive care unit. Multimodal neuromonitoring, incorporating continuous electroencephalography and amplitude-integrated EEG, which has been shown to predict preoperative MRI findings, could catch injury in real time. Risk-stratified anticoagulation could balance clot and bleeding risks, and neuroprotective drugs such as allopurinol are already in phase III randomized trials for babies requiring bypass surgery. Finally, long-term neurodevelopmental surveillance programs would ensure that early injuries, however subtle, are met with early intervention.

For the roughly one percent of newborns whose hearts form differently, the message of this synthesis is both a warning and a promise. The brain injury that shadows congenital heart disease is not an inevitable consequence of a defective heart, nor simply the price of a heroic operation. It is a mechanistically traceable process, visible on MRI from fetal life onward, driven by hypoxemia, impaired autoregulation, inflammation, and thrombosis, and shaped by the placenta, the delivery room, the bypass circuit, and the intensive care unit. Each of those checkpoints is now a target. If the trajectory of declining postoperative injury continues, and if antenatal and precision perioperative strategies mature from promising trials into standard care, the generation of children born with heart defects may one day keep their hearts repaired without paying a hidden neurological price.

Subject of Research: Brain injury mechanisms, MRI patterns, and perioperative risk factors in neonates with congenital heart disease

Article Title: Brain injury in congenital heart disease: pathophysiology, MRI patterns, and perioperative risk factors

Article References: Dogan, Y. E., Vargas-Boggiano, D. A., Bleiweis, M., Philip, J., Narasimhulu, S. S., Tuna, I., & Weiss, M. D. (2026). Brain injury in congenital heart disease: pathophysiology, MRI patterns, and perioperative risk factors. Pediatric Research. https://doi.org/10.1038/s41390-026-05454-x

Image Credits: AI Generated

DOI: 10.1038/s41390-026-05454-x

Keywords: congenital heart disease, brain injury, white matter injury, neonatal stroke, MRI, cardiopulmonary bypass, cerebral autoregulation, placental dysfunction, neuroprotection, neurodevelopmental outcomes, fetal circulation, thromboembolism

The scale of the physiological transformation is striking. The most common technique, decompressive hemicraniectomy, involves removing a bone flap averaging 14 by 14 centimeters and opening the dura widely, which enlarges the cranial cavity by an estimated 120 to 200 milliliters. A meta-analysis cited in the viewpoint quantified the immediate effect: intracranial pressure drops by an average of 17.59 millimeters of mercury, a reduction sustained at 24 and 48 hours, while cerebral perfusion pressure rises by 7.37 millimeters of mercury. Cerebral blood flow and brain tissue oxygenation typically improve as well. But the surgery also produces a cascade of adverse changes: rapid outward brain expansion, impaired cerebrovascular autoregulation, disrupted cerebrospinal fluid dynamics that predispose patients to hydrocephalus, altered intracranial pressure waveform morphology, and even cardiovascular effects mediated through autonomic mechanisms.

The central paradox the authors highlight is that decompressive craniectomy is a temporizing hemodynamic intervention. It relieves the mechanical consequences of high intracranial pressure but does nothing to reverse the underlying structural brain injury. This means the rationale for continued invasive neuromonitoring remains as strong as ever, despite lingering skepticism in some centers that clinical assessment and neuroimaging suffice once the skull is open. Two major consensus statements support continued monitoring: the Milan Consensus Conference recommended intracranial pressure monitoring after secondary decompressive craniectomy to assess the effectiveness of the surgery and guide further therapy, and an international neurosurgical consensus stated that monitoring and treatment should continue until pressure values remain controlled and stable.

The empirical data make a compelling case. Observational studies show that intracranial hypertension persists or recurs in 36 to 76.5 percent of traumatic brain injury patients after decompressive craniectomy, with similar rates reported after surgery for malignant middle cerebral artery infarction. The rationale for continued monitoring includes persistence of the underlying pathophysiology, the risk of recurrent intracranial hypertension or de novo hematomas, and the need to rationalize therapies such as osmotherapy, sedation, and cerebrospinal fluid drainage. The authors also draw a critical distinction between primary decompressive craniectomy, performed as the first intervention, and secondary surgery after conventional pressure management fails. The greatest lesion evolution occurs in the first 8 to 12 hours after the initial insult, a window that coincides with the early postoperative period in primary cases where no prior monitoring was in place. Contralateral epidural hematoma, a well-recognized complication, occurs predominantly after primary surgery, providing an additional argument for sustained surveillance.

Where exactly to place the pressure sensor turns out to be a question with no evidence-based answer. Neither current consensus statements nor major decompressive craniectomy trials report data on sensor implantation site. The limited published series favor ipsilateral placement, on the reasoning that intracranial pressure is compartmentalized, interhemispheric pressure gradients may develop, and regional hypertension can persist or emerge despite decompression. The authors stress that this recommendation rests on pathophysiological reasoning rather than high-quality prospective evidence. Contralateral placement risks underestimating true pressure and brain tissue oxygenation, leaving focal hypoxia or hypertension undetected, though specific scenarios may warrant it: extensive hemispheric parenchymal destruction, large hemorrhages with marked midline shift, diffuse bilateral injury, a nonviable ipsilateral surgical trajectory, infection of pre-existing sensors, or post-primary surgery where no prior monitoring exists.

The choice of monitoring modality adds another layer of complexity. External ventricular drains offer both pressure measurement and therapeutic cerebrospinal fluid diversion but can be technically challenging after surgery because of ventricular distortion. Intraparenchymal probes are easier to deploy but provide only regional measurements without drainage capability. The authors suggest a staged approach, beginning with an ipsilateral parenchymal probe and adding a contralateral ventricular drain in selected patients. Meanwhile, the evidence base for noninvasive monitoring in the decompressed brain remains sparse and contradictory. Optic nerve sheath diameter ultrasonography has shown that postoperative reductions correlate with outcome in malignant stroke and traumatic brain injury, yet other studies report poor performance of both this technique and transcranial Doppler for estimating pressure and perfusion after surgery. The discrepancies likely reflect heterogeneous reference standards, variable timing of measurements, and the fact that optic nerve sheath measurements reflect global rather than regional pressure dynamics.

Even electroencephalography becomes harder to interpret in these patients. The skull defect produces the so-called breach rhythm, high-voltage physiological waveforms that can mimic epileptiform discharges, while magnetoencephalography is less affected by the missing bone. Near-infrared spectroscopy demonstrated significant bilateral improvement in cerebral oxygen saturation after surgery for malignant infarction, though only contralateral changes correlated with 30-day outcome. Novel noninvasive devices that detect cranial vault micro-expansions to reconstruct pressure waveforms are particularly controversial in the absence of a bone flap, and an artificial intelligence-based pulse shape index for classifying intracranial compliance requires especially cautious interpretation in this population. A systematic review and meta-analysis concluded that invasive and noninvasive methods show similar effectiveness after decompressive craniectomy, and a prospective study by Alhamdan and colleagues demonstrated that invasive monitoring provides significant prognostic information after malignant infarction, with autonomic indices such as heart rate variability, baroreflex sensitivity, and signal complexity potentially complementing standard pressure data.

Perhaps the most provocative section of the viewpoint concerns treatment thresholds. Current Brain Trauma Foundation and Seattle International consensus guidelines recommend initiating treatment for intracranial hypertension at pressures above 22 millimeters of mercury, recommendations based on low-level evidence and extrapolated to decompressed patients despite fundamental physiological differences. Multiple observational studies now challenge this. A large prospective analysis identified 19 millimeters of mercury as the value most strongly associated with outcome, a finding maintained in patients undergoing decompressive craniectomy. After surgery for malignant infarction, Hernández-Durán and colleagues found 10 millimeters of mercury as the threshold most strongly associated with mortality, and in a comparable population pressures above 15 millimeters of mercury correlated with unfavorable outcomes, as did a pressure reactivity index near zero or perfusion pressure below 80 millimeters of mercury. A retrospective traumatic brain injury analysis using a 15-millimeter treatment threshold found Glasgow Outcome Scale Extended scores of 1 versus 5 depending on whether pressures exceeded 25 millimeters, and identified 40 millimeters of mercury as the functional lower limit of cerebral perfusion pressure.

A German retrospective cohort that monitored pressures for seven days after surgery adds further weight. Favorable outcomes corresponded to pressures that never exceeded 14 millimeters of mercury, with a mean of 11.5, while unfavorable outcomes corresponded to a mean of 17.5 millimeters, with statistical significance for both traumatic brain injury and malignant infarction independently. Kaplan-Meier analysis showed 75 percent versus 40 percent survival probability respectively. The authors are careful to note that all these data are exclusively retrospective, small-sample, and heterogeneous, and must be considered hypothesis-generating rather than practice-defining. Still, the pattern is consistent: clinically relevant deterioration appears to occur at substantially lower pressures in the decompressed brain than conventional guidelines assume.

The viewpoint distills the problem into six key physiological differences that undermine extrapolation from intact-skull physiology: abolition of the closed-box condition negates the Monro-Kellie doctrine and profoundly alters the pressure-volume relationship; cerebrospinal fluid dynamics are disrupted with predisposition to hydrocephalus; pressure waveform morphology and pulse amplitude characteristics are fundamentally changed; interhemispheric pressure gradients may render single-site measurements unrepresentative; autoregulatory indices require reinterpretation in the altered compliance environment; and noninvasive tools relying on acoustic or mechanical coupling through an intact skull lose reliability without a bone flap. The authors call for prospective, standardized research to fill these gaps and suggest that, in the interim, a structured consensus-based approach could harmonize clinical practice and identify research priorities. For a procedure performed thousands of times each year worldwide, the message is sobering: the brain without its skull is, in monitoring terms, an almost entirely uncharted organ.

Subject of Research: Neuromonitoring physiology and intracranial pressure thresholds after decompressive craniectomy

Article Title: Neuromonitoring in the Decompressed Brain: Rethinking Physiology, Monitoring, and Thresholds After Decompressive Craniectomy

Article References: Godoy, D. A., Paiva, W. S., de Amorim, R. L. O., Rovegno, M., & Rubiano, A. M. (2026). Neuromonitoring in the Decompressed Brain: Rethinking Physiology, Monitoring, and Thresholds After Decompressive Craniectomy. Neurocritical Care. https://doi.org/10.1007/s12028-026-02622-z

Image Credits: AI Generated

DOI: 10.1007/s12028-026-02622-z

Keywords: decompressive craniectomy, intracranial pressure, neuromonitoring, cerebral perfusion pressure, traumatic brain injury, malignant cerebral infarction, neurocritical care, ICP thresholds, sensor placement, noninvasive monitoring, cerebral autoregulation, Monro-Kellie doctrine

The protocol was developed through the CLINICCA initiative, a global effort focused on the clinical use of continuous cerebral autoregulation information. A 2023 survey of 44 experts found that approximately half were already using an autoregulation index to influence clinical decisions, but only 39% of those clinicians had incorporated the information into a written local protocol. PRx was the most frequently used index among respondents. The new workgroup therefore invited clinicians who used PRx or PRx-derived cerebral perfusion pressure targets in adult or paediatric traumatic brain injury to edit a common template, share examples of local practice and, where available, submit written protocols. Eight invited experts responded from centres with established protocols or structured practice, while two additional clinicians contributed paediatric applications. After excluding practices unrelated to traumatic brain injury, the authors synthesised the feedback into a five-part framework.

PRx is designed to provide a continuous estimate of how well cerebral blood vessels react to changes in perfusion pressure. Under normal conditions, small arteries and arterioles in the brain constrict or dilate to help maintain relatively stable blood flow despite fluctuations in arterial blood pressure. This buffering process is known as cerebral autoregulation. When autoregulation is impaired after traumatic brain injury, changes in arterial pressure may be transmitted more directly to the cerebral circulation, increasing the risk of inadequate perfusion or pressure-driven swelling. PRx is calculated from slow waves in arterial blood pressure and intracranial pressure, using a moving Pearson correlation over roughly five minutes. A positive correlation generally suggests impaired pressure reactivity, whereas a lower or negative value is more consistent with preserved vascular responsiveness. Because the calculation is global and depends on high-quality, continuously streamed physiological signals, PRx should not be interpreted as a direct measurement of regional blood flow or tissue oxygenation.

The first component of the harmonised protocol uses an elevated or persistently abnormal PRx value as a trigger for clinical review. In the participating centres, a threshold near 0.3 was commonly used, although published studies have examined values ranging from approximately 0.2 to 0.5. When PRx indicates impaired reactivity, clinicians may check the patient’s head and neck position, verify arterial and intracranial pressure transducers, inspect signal quality and review intracranial pressure, cerebral perfusion pressure, carbon dioxide and brain-tissue oxygenation. Other possible contributors include fever, sedation changes, ventilator alterations, seizures, systemic hypotension and evolving intracranial pathology. The workgroup stresses that an abnormal PRx is a warning signal rather than an automatic instruction to intervene. If conventional physiological variables remain acceptable and no corroborating evidence of cerebral hypoperfusion or dangerous intracranial hypertension is present, some centres would continue observation rather than launch a treatment escalation.

The second component concerns intracranial hypertension management and reflects a counterintuitive feature of autoregulation-guided care. When PRx is impaired, raising arterial pressure may not produce the expected reduction in intracranial pressure and can potentially increase cerebral blood volume or worsen pressure transmission. Several contributors therefore consider reducing arterial pressure, cautiously and under defined safety conditions, when impaired reactivity accompanies intracranial hypertension. By contrast, preserved PRx may support a carefully monitored increase in arterial pressure or cerebral perfusion pressure as part of a “MAP or CPP challenge.” If the cerebrovascular bed can constrict appropriately, increasing perfusion pressure may improve vascular tone and help lower intracranial pressure. The protocol does not present either strategy as universal. Each decision must be considered alongside the patient’s neurological examination, imaging, systemic circulation, oxygen delivery and other neuromonitoring data.

The third and fourth components address cerebral perfusion pressure targets derived from PRx. Cerebral perfusion pressure is commonly approximated as mean arterial pressure minus intracranial pressure, and it is a key determinant of the pressure gradient driving blood through the brain. A fixed target may be useful, but it cannot account for the changing autoregulatory state that often follows severe brain injury. One derived target is CPPopt, or optimal cerebral perfusion pressure, the pressure associated with the lowest PRx over a range of observed perfusion pressures. Other approaches estimate the lower limit of reactivity, where autoregulatory capacity begins to fail, or the upper limit of reactivity, where pressure may become excessive. More than half of the contributing centres reported using one or more derived targets to optimise cerebrovascular physiology, although the specific algorithms, thresholds, timing and degree of clinical reliance varied substantially.

The protocol also recognises that perfusion targets may be used to reduce treatment burden rather than simply maximise physiological measurements. If a patient maintains stable cerebral autoregulation and other monitoring signals at a lower pressure, clinicians may be able to avoid unnecessary fluid loading, high doses of vasopressors or prolonged exposure to interventions that can damage the heart, lungs or kidneys. This approach seeks a balance between supporting the injured brain and limiting harm elsewhere in the body. However, the authors caution that PRx is a global summary measure and may behave differently in diffuse injury compared with focal contusions, haematomas or areas of infarction. A pressure that appears favourable globally may not guarantee adequate perfusion in every vulnerable region. For that reason, derived targets should be treated as dynamic decision-support information, not as rigid numbers that override the clinical picture.

The fifth component places PRx within multimodality monitoring, combining it with measurements such as brain-tissue oxygen tension, transcranial Doppler, near-infrared spectroscopy, electroencephalography, arterial carbon dioxide and end-tidal carbon dioxide. In one possible decision pathway, a low brain-tissue oxygen signal accompanied by impaired PRx could prompt assessment of perfusion pressure, oxygen delivery and intracranial pressure together rather than isolated treatment of any single value. Preserved PRx may support a cautious perfusion-pressure challenge when oxygen delivery appears pressure-dependent. Paediatric centres described particularly intensive use of multimodal information, including PRx, transcranial Doppler, near-infrared spectroscopy and brain-tissue oxygenation, to balance sufficient cerebral perfusion against control of intracranial volume. Yet multimodal strategies were among the least consistently adopted elements of the survey, reflecting differences in equipment, staffing, expertise and confidence in how the signals should be combined.

A major message from the workgroup is that technical reliability is inseparable from clinical interpretation. PRx requires continuous acquisition of arterial blood pressure and intracranial pressure at adequate sampling rates, correct signal calibration, reliable time synchronisation and effective removal or recognition of artefacts. Disconnections, damping, flushing, waveform distortion, patient movement and abrupt therapeutic changes can create misleading correlations. The calculation also depends on slow spontaneous fluctuations; a flat or highly unstable signal may generate a number without providing meaningful physiological information. Derived CPP targets can be similarly unreliable when the data contain insufficient variation, when autoregulation is changing rapidly or when the algorithm is applied without quality-control indicators. The supplementary technical addendum accompanying the article provides practical advice for data acquisition, preprocessing and bedside interpretation, but the authors note that standardisation across devices and software remains incomplete.

The workgroup’s findings are likely to attract attention because they capture a field already moving into clinical practice before definitive outcome evidence has arrived. Observational studies have linked cerebrovascular reactivity with prognosis after traumatic brain injury, and a phase-two randomised feasibility trial found that targeting CPPopt was safe and feasible in selected adults. Nevertheless, no strong evidence yet demonstrates that treating patients according to PRx improves long-term neurological outcomes compared with conventional management. The new protocol therefore serves two purposes: it offers clinicians a transparent starting point for local implementation, and it exposes the areas where practice is most uncertain. Agreement was strongest around using PRx to prompt reassessment and to inform intracranial-hypertension management. The greatest variation involved CPP-derived targets and multimodal algorithms. By making these differences visible, the CLINICCA workgroup hopes to encourage collaboration, improve reproducibility and support future prospective trials capable of testing whether autoregulation-guided care can change the course of traumatic brain injury.

Subject of Research: Use of continuous cerebral autoregulation monitoring and the pressure reactivity index (PRx) to guide management of adult and paediatric traumatic brain injury patients with intracranial pressure monitoring.

Article Title: A Harmonised Protocol for the Use of PRx in Adult and Paediatric TBI Patients with ICP Monitoring: CLINICCA Workgroup Output

Article References: Beqiri E, Lavinio A, Dias C, et al. “A Harmonised Protocol for the Use of PRx in Adult and Paediatric TBI Patients with ICP Monitoring: CLINICCA Workgroup Output.” Neurocritical Care (2026). Related references include Czosnyka et al., “Continuous assessment of the cerebral vasomotor reactivity in head injury,” Neurosurgery (1997); Tas et al., the COGiTATE feasibility randomized controlled trial, Journal of Neurotrauma (2021); and Beqiri et al., studies of CPPopt and the lower limit of reactivity.

Image Credits: AI Generated

DOI: 10.1007/s12028-026-02595-z

Keywords: PRx, CPPopt, cerebral perfusion pressure, cerebral autoregulation, traumatic brain injury, intracranial pressure, paediatric neurocritical care, multimodal monitoring, lower limit of reactivity, upper limit of reactivity.