try ai
Popular Science
Edit
Share
Feedback
  • Pediatric Trauma

Pediatric Trauma

SciencePediaSciencePedia
Key Takeaways
  • A child's compliant anatomy causes unique injury patterns, such as severe internal organ damage without accompanying bone fractures.
  • Children in shock can maintain normal blood pressure until sudden collapse, making tachycardia and poor perfusion more reliable indicators than blood pressure itself.
  • Statistical models like the PECARN rule and Bayes' theorem guide clinical decisions, optimizing care by minimizing unnecessary risks and quantifying evidence.
  • Trauma can cause lasting psychological and biological harm through epigenetic changes, highlighting the need for trauma-informed care focused on creating safety.

Introduction

The management of an injured child is one of the most challenging and critical responsibilities in medicine. The fundamental principle that a child is not merely a small adult is central to effective pediatric trauma care, yet its deep implications are often underappreciated. This seemingly simple statement conceals a complex world of unique anatomical, physiological, and psychological responses to injury that differ profoundly from those of adults. This article addresses this knowledge gap by deconstructing the science of pediatric trauma from first principles. The journey will begin by exploring the "Principles and Mechanisms," where we will uncover the biomechanics of injury, the deceptive resilience of the pediatric cardiovascular system, and the unseen psychological and biological scars of trauma. Following this, the chapter on "Applications and Interdisciplinary Connections" will demonstrate how these foundational principles translate into life-saving clinical judgments, powerful statistical tools, and comprehensive public health strategies.

Principles and Mechanisms

To truly understand pediatric trauma, we must begin with a simple, yet profound, declaration: ​​a child is not a small adult​​. This is not a mere platitude; it is the central theorem from which all other principles of pediatric trauma care are derived. The differences are not just of scale, but of substance, woven into the very fabric of a child's anatomy, physiology, and even their response to the world around them. Let us embark on a journey, starting from first principles, to explore why this is so.

The Physics of Impact: A Tale of Energy and Anatomy

Everything in trauma begins with energy. When a body in motion is suddenly stopped, as in a fall or a car crash, its kinetic energy, Ek=12mv2E_k = \frac{1}{2} m v^2Ek​=21​mv2, must go somewhere. That "somewhere" is the body's tissues, and it is this transfer of energy that causes injury. How that energy is absorbed and distributed is the critical difference between a minor bump and a life-threatening event.

An adult's thoracic cage is like a rigid fortress. The ribs are calcified and strong. When struck, they tend to break, absorbing a great deal of energy in the process, much like the crumple zone of a modern car. This sacrificial act shields the delicate organs within. A child's thoracic cage, however, is a different beast entirely. It is wonderfully compliant, with ribs that are more cartilaginous and elastic. Imagine striking a sheet of plywood versus a trampoline. The plywood might crack, but it stops the blow. The trampoline deforms, absorbs very little of the impact itself, and transmits the force directly to whatever is behind it.

A child’s chest wall is the trampoline. During a blunt impact, it can bend dramatically inward, transmitting the full brunt of the kinetic energy directly to the lung parenchyma. This can cause a sudden, catastrophic spike in alveolar pressure, PAlvP_{\mathrm{Alv}}PAlv​, leading to alveolar rupture. The result is an air leak, which can manifest as a pneumothorax (collapsed lung) or subcutaneous emphysema (air trapped under the skin). This principle explains a common and initially bewildering finding in pediatric emergency rooms: a child can suffer a severe lung injury without a single broken rib. The absence of fractures is not a sign of a minor impact; rather, it is a hallmark of the unique pediatric mechanism of injury.

This same principle of increased energy transmission applies to the abdomen. The combination of a compliant chest, a thinner abdominal wall, and proportionally larger and more anteriorly placed organs like the spleen and liver, means that even seemingly low-energy impacts can cause devastating internal injuries.

Nowhere is this interplay of physics and anatomy more tragically elegant than in the ​​seat-belt syndrome​​. In a properly restrained adult, the lap belt is anchored by the strong, bony iliac crests of the pelvis. In a child, these bones are underdeveloped. During a high-speed collision, the lap belt can slide upward, off the pelvis and onto the soft abdomen. The belt ceases to be an anchor and instead becomes a fulcrum. As the upper body hurtles forward, the child's torso snaps over the belt in acute flexion. This action concentrates immense force on the structures directly beneath the belt—the hollow loops of the bowel and their mesenteric blood supply—crushing them against the spine. Simultaneously, it yanks the posterior elements of the lumbar spine apart. This creates a specific and devastating triad of injuries: abdominal wall bruising, hollow viscus or mesenteric injury, and a flexion-distraction fracture of the spine known as a ​​Chance fracture​​. A device designed for safety is transformed by developmental anatomy and simple lever mechanics into a source of severe harm.

The Resilient but Deceptive Engine: Cardiovascular Response

If a child’s anatomy makes them uniquely vulnerable to energy transfer, their cardiovascular system gives them a seemingly miraculous, yet deceptive, resilience. When an adult begins to lose blood, their blood pressure often falls in a somewhat predictable way. A child’s response is different. Possessing a young, healthy heart and exquisitely reactive blood vessels, a child can compensate for significant volume loss with incredible tenacity.

In response to hemorrhage, a child mounts a powerful catecholamine surge, leading to intense peripheral vasoconstriction and a rapid heart rate (tachycardia). This clamps down on blood flow to the skin and extremities, shunting the remaining blood to the vital core—the brain, heart, and kidneys. This state is known as ​​compensated shock​​. The child might have a racing heart, cool skin, and a prolonged capillary refill time, but their systolic blood pressure may remain stubbornly, reassuringly normal.

This compensation is a double-edged sword. It keeps the child alive, but it masks the true extent of the blood loss. An unwary observer might look at the "normal" blood pressure and be falsely reassured, not realizing the child is standing at the edge of a cliff. A child can maintain their blood pressure until they have lost up to 30−45%30-45\%30−45% of their circulating blood volume, at which point they fall off that cliff in a sudden, catastrophic decompensation. In pediatric trauma, ​​blood pressure is a liar​​; tachycardia and poor perfusion are the truth-tellers.

This unique physiology also helps explain why non-operative management of solid organ injuries, like a splenic laceration, is so successful in children. Success rates often exceed 90%90\%90%. It is not, as is sometimes thought, because children have a "greater tolerance for hemorrhage." In fact, because their total blood volume is smaller, a given absolute blood loss is proportionally more significant for a child than for an adult. The true advantage lies in physics. The spontaneous stoppage of bleeding (hemostasis) is a battle between the body's clotting ability and the physical forces driving the blood out. These forces are governed by simple laws:

  • ​​Poiseuille's Law​​ tells us that flow rate (QQQ) is proportional to the fourth power of the vessel's radius (rrr), so Q∝r4Q \propto r^4Q∝r4.
  • The ​​Law of Laplace​​ tells us that the stress on the vessel wall (σ\sigmaσ) is proportional to the pressure (PPP) and the radius (rrr), so σ∝P⋅r\sigma \propto P \cdot rσ∝P⋅r.

A child has both a lower mean arterial pressure and smaller vessel radii than an adult. These two factors combine with enormous effect. The lower pressure and smaller radius drastically reduce the wall stress on an injured vessel, making a clot more likely to hold. Even more dramatically, the smaller radius leads to an exponentially lower rate of bleeding. This favorable physical environment, not some magical tolerance, is the secret to the high rates of splenic salvage in children.

But what happens when compensation fails? When the oxygen debt becomes too great? Unlike adults, whose hearts are often prone to primary electrical problems like ventricular fibrillation, a child's heart is usually the last organ to fail. Cardiac arrest in children is typically the final consequence of progressive respiratory failure and shock—an asphyxial arrest. The heart, starved of oxygen, can no longer sustain its function. Its electrical activity slows, and it eventually grinds to a halt, resulting in ​​Pulseless Electrical Activity (PEA)​​ or asystole. The treatment, therefore, is not primarily to shock the heart, but to address the root cause: to restore the airway, provide oxygen, and ventilate the lungs, giving the heart the fuel it has been desperately denied.

When the System Spirals: The Body's Response to Overwhelming Injury

Sometimes, a traumatic injury is so massive and widespread that the body's local responses are overwhelmed, triggering a systemic, self-destructive cascade. One of the most feared of these is ​​Disseminated Intravascular Coagulation (DIC)​​.

Imagine the body's coagulation system as a disciplined army of first responders, rushing to patch up leaks as they appear. Now imagine a thousand fires breaking out all at once. In the face of massive tissue injury and shock, enormous quantities of ​​Tissue Factor (TF)​​—the body's universal "on" switch for clotting—are released into the bloodstream. The army panics. It tries to form clots everywhere at once, deploying all of its soldiers (platelets) and supplies (clotting factors) throughout the body's microscopic blood vessels.

This has two disastrous consequences. First, the widespread micro-clots begin to block blood flow, causing organ damage and ischemic injury. Red blood cells are physically sheared apart as they try to squeeze through the fibrin-choked vessels, creating fragmented cells called ​​schistocytes​​. Second, the frenzied response consumes all the available platelets and clotting factors. The body has exhausted its ability to form new clots. The paradoxical and terrifying result is a patient who is simultaneously forming life-threatening clots in their microvasculature while bleeding uncontrollably from every IV site and wound. This is DIC: a state of clotting and bleeding to death at the same time. It is a powerful reminder that trauma is not just a local event, but an assault that can unravel the body's most fundamental systems.

The Unseen Wounds: Trauma Beyond the Physical

Our journey through the mechanics of injury would be incomplete if we only considered the visible, physical wounds. The most profound insights in pediatric trauma often come from understanding the unseen context and the invisible scars.

Consider a 4-month-old infant brought to the hospital with a bruise on their ear and a small tear inside their upper lip. Medically, these are trivial injuries. But in the world of pediatric forensics, they can be ​​sentinel injuries​​—heralds of a terrible secret. A 4-month-old cannot crawl, let alone walk. An explanation that the baby "fell while walking" is not just unlikely; it is a developmental impossibility. The significance lies not in the injury itself, but in the glaring contradiction between the physical finding and the history provided. That discrepancy is the signal. It demands that we look deeper for occult injuries and, most importantly, act to ensure the child's safety, because these minor injuries are often the precursors to more severe, or even fatal, abuse. It is a stark example of how medicine, at its best, is a science of observation and logical deduction.

Finally, we must recognize that trauma's impact extends into the mind and spirit, reprogramming the very systems that allow a child to feel safe in the world. For a child with a history of neglect or violence, the world is a different place. The brain's stress-response system, the hypothalamic-pituitary-adrenal (HPA) axis, becomes sensitized. A sudden transition, a loud noise, or a stern look can be perceived not as an annoyance, but as an existential threat, triggering a full-blown fight-flight-freeze response. In this state of high arousal, the brain's capacity for reason, language, and learning shuts down.

This is the foundation of ​​trauma-informed care​​. It recognizes that "misbehavior" in these children is often a manifestation of terror, not defiance. It understands that punitive or isolating discipline can be re-traumatizing, reinforcing the child's belief that they are unsafe and alone. The "mechanism" of healing, therefore, is not punishment, but the active creation of safety through predictability, the offering of choice to restore a sense of control, and the process of ​​co-regulation​​, where a calm adult lends their regulated nervous system to a dysregulated child.

The scars of early life trauma can run deeper still, embedding themselves into our very biology through ​​epigenetic​​ changes. Research has shown that severe stress can alter the methylation of genes like ​​FKBP5​​. In essence, trauma can remove a "silencer" from a gene that helps turn off the cortisol stress response. The result is a system that is not only hyper-reactive to stress but also inefficient at returning to baseline. It is a biological memory of the trauma, a vicious cycle written into the code of how our genes are expressed.

From the gross mechanics of a car crash to the subtle chemical tags on our DNA, pediatric trauma is a subject of staggering complexity and profound unity. Understanding its principles requires us to be physicists, physiologists, detectives, and humanists all at once. It reminds us that each child is a unique universe, governed by laws that are both beautifully resilient and terrifyingly fragile.

Applications and Interdisciplinary Connections

Having explored the fundamental principles of pediatric trauma, we now arrive at a thrilling part of our journey. We will see how these principles are not merely abstract concepts confined to textbooks, but are in fact powerful, practical tools that clinicians, scientists, and even policymakers use every day. To understand pediatric trauma is to see a beautiful convergence of physics, physiology, statistics, ethics, and public health. It is a field where a simple formula can save a life, where the laws of fluid dynamics guide a surgeon’s hand, and where the logic of probability can shape the destiny of an entire community. In this chapter, we will witness these principles in action, moving from the immediacy of the bedside to the broad landscape of societal well-being.

The Art of Clinical Judgment: Physics and Physiology at the Bedside

Imagine the controlled chaos of a pediatric emergency department. An injured child has just arrived. The clinician does not have time for leisurely contemplation; they must act. In these critical moments, the clinician becomes an applied physicist and a hands-on engineer, reading the body’s physical signals and applying fundamental principles to stabilize a failing system.

This process begins with the most basic observations—the vital signs. But these are not just numbers; they are physical clues. A child's blood pressure, for instance, is a direct measure of the force exerted by circulating blood on vessel walls. In pediatrics, what constitutes a "low" pressure changes dramatically with age. To navigate this, clinicians don't rely on guesswork; they use simple, powerful rules derived from population physiology. A well-established rule of thumb states that the minimum acceptable systolic blood pressure for a child between one and ten years old can be estimated with the formula SBPmin=70+(2×Ageyears)SBP_{\text{min}} = 70 + (2 \times \text{Age}_{\text{years}})SBPmin​=70+(2×Ageyears​). For a six-year-old, this threshold is 828282 mmHg. A child presenting with a blood pressure of 848484 mmHg might seem stable, but this simple calculation reveals they are teetering on the very edge of hypotensive shock, prompting a higher level of vigilance and faster intervention. This is a perfect example of physiology distilled into a life-saving algorithm.

The clinician’s role as an engineer becomes even more apparent when an intervention is required. Consider a child with a collapsed lung—a pneumothorax. The solution is to insert a chest tube to allow the trapped air to escape. But what size tube? This is not a trivial question. The choice involves a direct application of the principles of fluid dynamics. As Poiseuille’s law tells us, the flow rate through a tube is exquisitely sensitive to its radius, proportional to the radius to the fourth power (Q∝r4Q \propto r^4Q∝r4). A tube that is too small will have a very high resistance, insufficient to evacuate a rapid air leak, potentially leading to a life-threatening tension pneumothorax. On the other hand, a tube that is too large can cause unnecessary pain and damage to the delicate tissues of a child’s chest wall.

The decision must therefore balance the physics of flow with the anatomy of the patient. A neonate with a small, low-flow air leak can be managed with a small-bore tube, minimizing trauma. However, an infant on a ventilator with a high-flow, continuous air leak from a torn airway (a bronchopleural fistula) needs a much larger tube to overcome the immense flow resistance and keep the lung from collapsing again. And if the problem is not just air, but thick, viscous blood from a traumatic hemothorax, an even larger tube is required to prevent clotting and obstruction. The surgeon, in selecting the right tube, is making a calculation worthy of any fluid engineer—a beautiful synthesis of physics, physiology, and anatomy.

This quantitative approach is the bedrock of resuscitation. When a child is suffering from severe blood loss (hemorrhagic shock), the goal is to restore what was lost. Modern trauma care treats this as a problem of "balanced resuscitation." It's not enough to just give back red blood cells to carry oxygen; one must also replace the plasma containing critical clotting factors and the platelets that form the initial plug. Based on the child’s weight, clinicians calculate precise volumes of packed red blood cells, plasma, and platelets, often in a 1:1:1 or similar ratio to mimic whole blood. For a 20-kilogram child, this might mean an initial order of 400400400 mL of red cells, 400400400 mL of plasma, and 200200200 mL of platelets, alongside medications like tranexamic acid to prevent clots from breaking down too quickly. This isn't just medicine; it's a form of quantitative physiological reconstruction.

Perhaps the pinnacle of this clinical art is the decision of when not to intervene. Consider an 8-year-old with a severe spleen injury. A CT scan shows an AAST grade IV laceration with a small "blush" of contrast, indicating a small, active arterial bleed. Decades ago, this would have meant automatic surgery. Today, the decision is far more nuanced. The clinician must weigh the risk of the spleen continuing to bleed against the risks of the intervention itself, which in this case would be angioembolization—a procedure where a catheter is threaded through the arteries to plug the bleeding vessel.

This decision rests on a beautiful integration of multiple scientific domains. From hemodynamics, we know the child's body is compensating for blood loss by increasing its systemic vascular resistance (SVRSVRSVR) to maintain blood pressure (MAP=CO×SVRMAP = CO \times SVRMAP=CO×SVR). The deep sedation required for the procedure would cause vasodilation, dropping the SVRSVRSVR and potentially leading to a sudden cardiovascular collapse. From fluid dynamics, we know that threading the required catheter through the child's small femoral artery could obstruct a huge portion of its diameter, risking a blood clot and threatening the limb. And from clinical epidemiology, we know that nonoperative management is successful in over 95%95\%95% of such cases in children, even with high-grade injuries. Balancing these factors, the wise decision is often to watch and wait in a high-acuity setting, reserving the high-risk intervention for clear signs of deterioration. This is the art of medicine at its finest: a judgment call informed by a deep, multi-disciplinary scientific understanding.

Beyond the Individual: Statistics as a Guiding Hand

The "art" of medicine, as we have seen, is deeply scientific. But a single clinician’s experience is finite. To make the best decisions, we must learn from the collective experience of thousands. This is the role of statistics and epidemiology—to provide a guiding hand that helps us see beyond our own biases and assumptions.

A classic example is the management of minor head trauma. Millions of children fall and hit their heads each year. A tiny fraction of them will have a life-threatening brain injury, while the vast majority will be perfectly fine. How do we find the needle in the haystack without subjecting every child to a CT scan, which carries a small but real lifetime risk of radiation-induced cancer? The answer comes from large-scale, meticulous studies like the Pediatric Emergency Care Applied Research Network (PECARN). By analyzing data from tens of thousands of children, researchers developed a clinical decision rule. This rule identifies a handful of specific high-risk predictors (like altered mental status or signs of a skull fracture) that warrant a CT scan. It also identifies intermediate-risk factors (like vomiting or a brief loss of consciousness). For a child with only an isolated intermediate-risk factor, such as vomiting after a simple fall, the PECARN rule guides the clinician to a path of observation and shared decision-making with the parents, rather than an automatic CT scan. This is evidence-based medicine in action—a statistical tool that protects thousands of children from unnecessary radiation while maintaining an exceptionally high sensitivity for catching the injuries that matter.

This same statistical logic underpins the entire field of public health screening. Imagine a clinic wants to screen its population for trauma-related psychological symptoms. They have a tool, but how good is it? And what are the consequences of its imperfections? Here, we turn to the elegant logic of Bayes' theorem. Let's say a screening tool has a sensitivity of 0.900.900.90 (it correctly identifies 90%90\%90% of children who truly have symptoms) and a specificity of 0.800.800.80 (it correctly identifies 80%80\%80% of children who do not). In a community where the prevalence of these symptoms is 0.250.250.25, we can calculate the tool's real-world performance.

The Positive Predictive Value (PPV)—the probability that a child with a positive screen actually has symptoms—turns out to be only 0.600.600.60. This means that for every 10 children who screen positive and are referred for follow-up, 4 of them are false positives. This is the cost of "over-referral." Conversely, the Negative Predictive Value (NPV)—the probability that a child with a negative screen is truly symptom-free—is a very high 0.960.960.96. The clinic can be quite confident that a negative screen means the child is okay. This analysis reveals the inherent trade-off in any screening program: the clinic accepts a significant burden of false positives on its mental health services in order to achieve high sensitivity and miss very few true cases. This is not a matter of opinion, but a mathematical reality that must guide policy.

The power of Bayesian reasoning extends into one of the most difficult areas of pediatrics: forensic medicine, specifically the diagnosis of child abuse. When a young infant presents with injuries like multiple posterior rib fractures and the caregivers provide no credible history of trauma, a terrible suspicion arises. But how can a clinician move from suspicion to a more objective assessment? Bayes' theorem provides a formal framework. The clinician starts with a "prior probability"—the background rate of abuse in similar cases, which might be low, say 0.030.030.03. Then comes the evidence: the specific finding of posterior rib fractures. Medical literature provides a "likelihood ratio" for this finding, which tells us how much more likely this finding is in a case of abuse versus an accidental injury. For these specific fractures, the likelihood ratio is extremely high, perhaps around 757575.

Bayes' theorem in its odds form allows us to combine these numbers: Posterior Odds=Prior Odds×Likelihood Ratio\text{Posterior Odds} = \text{Prior Odds} \times \text{Likelihood Ratio}Posterior Odds=Prior Odds×Likelihood Ratio. The initially low probability is dramatically magnified by the powerful evidence. A prior probability of 0.030.030.03 (or 1-in-33) is transformed into a posterior probability of nearly 0.700.700.70 (or more than 2-in-3). This doesn't "prove" abuse, but it quantifies the weight of the evidence, providing an objective foundation for the physician's duty to protect the child. It is a profound application of probability theory to a question of immense human consequence.

A Wider Lens: Trauma in the Fabric of Society

An injured child does not exist in a vacuum. They are part of a family, a school, and a community. A truly comprehensive approach to pediatric trauma must therefore zoom out from the individual to see the wider systems and societal structures that influence a child's risk and recovery. This is the domain of trauma-informed care and public health.

The first step is to recognize that "trauma" is not a single event. A health system must be prepared to address both acute, large-scale disasters like a hurricane and chronic, pervasive stressors like community violence. The response must be tailored to the nature of the threat and phased over time, following the public health framework of preparedness, response, and recovery.

In the preparedness phase, before a disaster strikes, the system builds its capacity. This means training all staff in the principles of trauma-informed care—safety, trustworthiness, collaboration, empowerment. It means building partnerships with schools and community organizations. It also means developing workflows for screening, but doing so wisely. A crucial distinction must be made between screening for trauma exposure (e.g., using tools like the Adverse Childhood Experiences, or ACEs, questionnaire) and screening for trauma symptoms (e.g., using a PTSD checklist like the CATS). The goal of exposure screening is not to diagnose, but to identify risk and provide anticipatory guidance and support.

In the immediate response phase after an event, the focus shifts to ensuring safety and providing what is known as Psychological First Aid (PFA). PFA is not therapy; it is a humane, supportive response that helps people meet their basic needs, normalizes stress reactions, and connects them with resources, all while avoiding intrusive practices like mandatory debriefing, which can actually be harmful.

Finally, in the long-term recovery phase, the system provides ongoing support. This includes continued screening for persistent symptoms and offering evidence-based treatments like Trauma-Focused Cognitive Behavioral Therapy (TF-CBT) for those who need it. Crucially, for chronic stressors like community violence, this phase also involves sustained partnership with community programs to address the root causes and reduce ongoing exposure. This is a public health model that sees healing not just as an individual process, but as a collective, systemic one.

This journey from the individual to the societal brings us to the most profound questions of all—the ethical dilemmas that arise when needs outstrip resources. Consider a military surgical team in a forward-operating area, faced with two critically injured casualties—a 4-year-old child and a 28-year-old adult—but with the capacity to operate on only one. This is the crucible of triage. The guiding principles of International Humanitarian Law (IHL) demand medical impartiality, non-discrimination, and proportionality (maximizing the number of lives saved).

The decision process must be an algorithm of ethics and evidence. The team has a survival prediction model, but they know it was developed for adults and underestimates survival in children. The first ethical imperative is to use the best available evidence. Using data from a validation study, they must apply a correction factor to the child's predicted survival, raising it from, say, 0.400.400.40 to an evidence-based estimate of 0.600.600.60. The adult's prediction remains 0.550.550.55. The principle of proportionality now clearly points toward treating the child, who has the higher probability of survival. This act of statistical calibration is, in itself, an ethical act.

What about fairness? The doctrine may allow for a small "life-cycle" tie-breaker, giving a slight preference to the younger patient, but only when the clinical benefit is near-equal. This prevents age from overriding a clear medical advantage. The framework must also respect safety constraints, treating a procedure's time not as a penalty to be subtracted from a patient's "score," but as a hard eligibility cutoff to protect the medical team. A scheme that ignores evidence, uses arbitrary bonuses, or discriminates based on combatant status would be a violation of this sacred trust. Here, in the most difficult of circumstances, we see that a just decision is not born of emotion, but of a rigorous, evidence-based application of ethical principles.

The Unity of Understanding

Our exploration of pediatric trauma has taken us from a simple formula for blood pressure to the complex ethics of battlefield triage. Along the way, we have seen how the principles of physiology are inseparable from the laws of physics, how the art of clinical judgment is guided by the logic of statistics, and how the care of a single child is connected to the health of an entire society. To understand this field is to appreciate a magnificent tapestry woven from many different threads of human knowledge. It is the recognition that in the quest to protect and heal our most vulnerable, science and humanity are, and must always be, one and the same.